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1. Population 1 This Section to subsequent populations Copy Input Valves Vortex 9 21 Enter a non empty scenario name a CAPS NUM INS Date Time 10 24 03 10 30AM 4 Figure 38 Multiple means for moving among alternative Scenarios The first task you should complete after creating new Scenarios is to change their names to something more descriptive You do this in the top input box Scenario Name of the Scenario Settings screen After Chapter 3 67 The Data Input Process VORTEX Version 9 User s Manual changing the Scenario name to something more descriptive go to the Input sections where you want to vary the parameters in the new Scenarios and make the desired changes Once you have many Scenarios in your Project it is easy to accidentally change the labels and input values for the wrong Scenario because the screens for the various Scenarios look so similar Before you start editing input values make sure that you are working on the intended Scenario After you create a new set of Scenarios it is always wise to save the Project so that you won t lose your Scenarios if something later goes wrong However VORTEX always prompts you to save each open Project when you exit the program so you do have a chance later to save everything if nothing does go wrong Deleting Scenarios from Your Project If you have created Scenarios that you no longer want you can delete them by hitting the Delete Scenario
2. A lt 10 C A 5 10 C A gt 9 oa re 50 0 45 0 40 0 35 0 f 30 0 25 0 f 20 0 15 0 10 0 F 5 0 0 0 O 10 20 30 40 50 60 70 80 90 100 Age Years 90 0 F 80 0 F 70 0 f 60 0 50 0 40 0 30 0 f 20 0 f 10 0 0 0 O 10 20 30 40 50 60 70 80 90 100 Inbreeding Coefficient 10 CY gt 10 10 CCY gt 20 10 C CY gt 30 10 90 0 F 80 0 F 70 0 60 0 50 0 40 0 30 0 20 0 10 0 0 0 10 20 30 40 50 60 70 80 90 100 Year of Simulation Chapter 5 93 Using Functions in VORTEX VORTEX Version 9 User s Manual 11 Different rates at different intervals RATE 10 A lt 3 25 A 3 30 A 4 OR A 5 35 CCA gt 5 AND A lt 10 20 A gt 10 AND A lt 15 The rate increases stepwise with age then 50 0 F drops to a lower level for years 10 through 45 0 14 and then drops to zero for animals 15 years and older Note that although it can be tedious any rate function can be modeled by specifying the rate for each interval of the dependent variable 40 0 35 0 30 0 25 0 f 20 0 15 0 10 0 5 0 0 0 Demographic Rate 30 40 50 60 70 80 90 100 Age Years 12 Cyclical response RATE 50 10 SINC PI Y 5 Here the rate fluctuates between 40 and 60 according to a sine wave with a 10 year periodicity g S 30 0 d e E 20 0
3. Chapter2 9 Getting Started with VORTEX VORTEX Version 9 User s Manual xl ct Open Project Recent Projects Blank Project r Description V Show this dialog when the program starts Ok Cancel Figure 2 The dialog box for starting a Project Figure 3 shows the dialog box for opening an existing Project This screen may look a little different on your computer depending on where you installed the VORTEX program Navigate to the ZPG directory and then select the ZPG Project by double clicking on the ZPG vpj file or single clicking on it and then selecting OK Note that windows in VORTEX can usually be resized or moved with the cursor xl New Project Open Project Recent Projects ZPO YD E Quick Info Project Name Users EJ Vortex9 Project Notes 4 sample analysis of a population that has 4 deterministically projected zero population growth IV Show this dialog when the program starts Ok Cancel Figure 3 The dialog box for opening an existing Project The ZPG Project does not represent any particular species It has a set of input values that define a population that would have an expected long term zero population growth r 0 0 based on the mean birth and death rates as modified by occasional catastrophes This projection of zero population growth is dependent upon an assumption that stochastic processes such as demographic stochasticity temporary
4. Maternal allele identifier VV i and ZZ i the paternal and maternal alleles at the ith modeled locus IS1 IS2 IS3 IS9 Individual State Variables previously defined 86 Chapter 5 Using Functions in VORTEX VORTEX Version 9 User s Manual Table 2 Valid Operators Note that there are alternative names for several operators Function Description Unary Operators ABS NEG CEIL FLOOR ROUND SQRT SQR LN LOG LOG10 EXP Absolute value Negative Ceiling Truncate Round Square root Natural logarithm Base 10 logarithm e raised to specified power Binary Operators Addition Subtraction Multiplication Division Exponentiation Maximum Minimum Modulus Division remainder Pow A MAX MIN MOD Topical Boolean Operators Ta Is equal to NOT Negation l Not equal to AND amp amp And OR l l Or gt Greater than lt Less than gt Greater than or equal to lt Less than or equal to Trigonometric Operators SIN Sine cos Cosine TAN Tangent ASIN Arcsine ACOS Arccosine ATAN Arctangent Defined Constants PI 3 1415927 E 2 7182818 TRUE 1 FALSE 0 Random Number Generators RAND Uniform random 0 1 NRAND Normal random deviate SRAND SNRAND Example ABS 10 10 NEG 10 aA CEIL 3 12 FLOOR 3 12 e ROUND 3 12 3 SQR 1 44 Ap 2 LNC1 60 47 cio so 0 EXP 0 47 1 6 ROUND 5 5 20412 0 0 2 0 0 1 0 3 0 6 0 2
5. N a AO ean A AA ao va NA ASN oe Ww 20 a i 10 0 f 0 10 20 30 40 50 60 70 80 90 100 Year Project ZPG Scenario ZPG2 Iteration Figure 36 VORTEX Simulation population size graph Chapter 3 65 The Data Input Process VORTEX Version 9 User s Manual Adding and Deleting Scenarios Congratulations You have created and run your first scenario However it is highly unlikely that you are now done with your analysis of the particular species population and issue at hand Almost certainly you were uncertain about some of the input parameters you entered Possibly the estimate was based on few or no data It may be that the data came from field studies conducted in a different part of the species range And it may be that the data are accurate descriptions of the past or even present status of the population but are not likely to be good descriptors of the future performance of the population in light of expected or planned changes to the habitat or populations In any case a major part of almost all population viability analyses is sensitivity testing the examination of the impacts of varied input parameters on the projected population performance You should refer to the background material in Appendix I and in the references for a more thorough discussion of the topic of sensitivity testing To conduct sensitivity testing or any investigation of alternative scenarios that may be used to describe the population
6. oe 3 S Copy input values from Population 1 This Section to subsequent populations Copy Input Values Age 1 Harvested Adults Harvested Vortex 9 21 Check this if individuals are removed at regular intervals NUM INS Date Time 10 24 03 10 23AM 4 CAPS Figure 33 Harvest input section Harvest can mimic hunting culling research related removals removal of young individuals for translocation programs etc Check the Population Harvested box to request a regular harvest of individuals The harvest can begin and end at any time during the stipulated length of the simulation Enter the First Year of Harvest and the Last Year of Harvest For example if you wish to begin harvesting in year 10 and end in year 25 enter 10 and 25 for these two questions respectively No harvest will be allowed before or after the time frame that you have specified If you wish to harvest every year within the specified time frame enter 1 for the Interval Between Harvests If you wish to harvest animals every other year enter 2 As another example if the first year of harvest is 10 the final year is 50 and the interval is 10 years then harvesting will take place in years 10 20 30 40 and 50 Chapter 3 61 The Data Input Process VORTEX Version 9 User s Manual Optional Threshold for Harvest You can specify here some criteria that will restrict harvesting to occur only if the population
7. 10 Chapter 2 Getting Started with VORTEX VORTEX Version 9 User s Manual mate limitation inbreeding and annual fluctuations environmental variation do not reduce mean population performance The population size in this case however is low enough that these stochastic processes are important impacts on the population causing it to be unstable often decline and be highly vulnerable to extinction as we will see The ZPG Project has the same input values as the default values in the earlier DOS versions of VORTEX When you open a Project VORTEX opens a screen that shows the Project Settings interface and the tabs for the other screens Simulation Input Text Output Graphs and Tables and Project Report Figure 4 On the Project Settings screen you can specify a different Project name enter the names of any collaborators and add any Project Notes text that you wish to describe your Project It is wise to take the time to document your work by typing Project Notes and on a screen you will see later on Input Notes At the time you are working it may be seem obvious what decisions you were making when you created your Project However months later it may be very difficult for you or others to recall what led you to design the Project as you did If you want ever to go back to a Project take the time now to document your work within the VORTEX Project see Chapter 3 for more information on entering Input Notes
8. Age Range Youngest and Oldest In these boxes enter the youngest and oldest ages of those individuals that move between populations If both sexes are capable of moving between populations and the ages at which males and females disperse are different you must decide which age s you use for these fields This decision will be based largely upon how conservative you want to be about your estimation of potential risk For example if males begin moving among populations at 3 years of age and females at 5 years of age entering 3 as the youngest age to disperse may underestimate the risk of population decline and or extinction since females are allowed to move at an earlier age in the model Dispersing Sex es Check the appropriate box es to specify whether males females or both can disperse from the natal population Percent Survival of Dispersers Often dispersal among populations occupying discrete areas of suitable habitat is dangerous Traversing the matrix of unsuitable habitat between populations may expose an individual to additional risks of predation or lack of food and entry into a new population may require competition with the established residents Enter here the survival rate as a percent of individuals that are dispersing between populations The dispersal mortality is imposed separately from other mortality detailed elsewhere in the program More specifically this dispersal mortality is imposed after annual mortality See
9. Many conservation biologists assume that slow in breeding will not reduce fitness because selection can re move deleterious alleles during generations of inbreeding Charlesworth and Charlesworth 1987 Yet experimental evidence shows that such purging of the genetic load of deleterious alleles from a population often does not work many populations continue to decline in fitness as they become increasingly inbred Ballou 1997 Lacy and Ballou 1998 and may go extinct as a consequence Frankham 1995b Theoretical work indicates why selection is often ineffective in reducing inbreeding depression At the small population sizes at which inbreeding occurs random ge netic drift is a much larger force in determining which alle les increase or decrease in frequency than is all but the strongest selection random loss of adaptive alleles is al most as likely as loss of the deleterious alleles Except when inbreeding depression is due primarily to a few highly del eterious recessive alleles inbreeding is more likely to lead ECOLOGICAL BULLETINS 48 2000 to population extinction than to significant reduction of the genetic load Hedrick 1994 Some populations may be fortunate enough not to carry a genetic load of deleteri ous alleles which would be expressed under inbreeding but the evidence suggests that sensitivity to inbreeding may be determined by chance events such as founder ef fects as much as by any predictable factors Ral
10. N K lt 0 25 then supplements will be added only if the ratio of the population size to the varying capacity is at less then 0 25 and if it is a supplementation year as defined above Leave the grid cell entry as 1 if you do not want to provide any criterion for supplementing Female Male Ages being Supplemented Enter the number of females and or males that you will add at each time interval defined for each age class through adults Enter 0 for no individuals to be supplemented in a given age class These parameters differ slightly from the partameters defining harvesting in that the last age class listed on the screen corresponds to the first year of adulthood instead of the aggregate adult stage This difference results from the fact that while harvesting selects any adult individual regardless of age VORTEX must assign a specific age class to each adult that is being added to 62 Chapter 3 The Data Input Process VORTEX Version 9 User s Manual the recipient population The age of adults added to the population is always equal to the age at which breeding commences 4 Vortex Stochastic Simulation of the Extinction Process File Edt Vortex Window Help D n se SB los ZPG D WVORTEXS ZPG ZPG Ypi Project Settings Simulation Input Text Output Graphs and Tables Project Report Add Scenario Delete Scenario lt zpa2 gt Reorder ZPG1 I ZPG2 cenario Settings pecies Description Supplementation abels
11. Next click on the box below Rows in order to specify which populations you want to list as rows of your data table and as separate lines on the graph that will be created The way you select populations is the same as selecting years except that in this Scenario there is only one population so selecting it is fairly trivial Select Population 1 and hit OK You will see now that a table has been created displaying one of the result statistics for the years and population s that you specified With the dropdown lists in the left side of the screen you can change the table to display other output statistics Change the Variable to N all and then hit the Data Graphs tab to show a graph of the values in the table Figure 13 The labels legend and line thickness can all be changed By right clicking on the graph itself you can also access a broader set of graph properties By clicking on labels at the lower left the graph can be sent to the Project Report do this now or printed or saved as a bitmap bmp file on your disk 18 Chapter 2 Getting Started with VORTEX VORTEX Version 9 User s Manual EJ Vortex Stochastic Simulation of the Extinction Process File Edt Wortes Window Help Ose s Bel SB lls o Page D WWORTEXS 2ZPG 2ZPG Ypi Project Settings Simulation Input Text Output Graphs and Tables l Project Report Data Specification Data Graphs Graph Options Legend Text Position M ean N al
12. Population 1 to all subsequent populations Copy Input Values I Note that you can and should put notes about input values de f 75 75 50 N 2K 2N 2 1 N m Vortex 9 04 Click here to see a plot of the density dependence function Figure 25 Specifying and graphing density dependence Chapter 3 47 The Data Input Process VORTEX Version 9 User s Manual Case Study VII Modeling density dependence in reproductive success Peary caribou Rangifer tarandus are distributed in fragmented populations across the Canadian Arctic These animals are continually stressed by food resource limitation in the harsh winter climate with this stress becoming magnified as population density increases Consequently a risk analysis conducted on this taxon Gunn et al 1998 included density dependent reproductive success at high population densities Allee effects were not considered to be a factor Field data show 80 of adult females are able to breed under optimal density conditions while only 10 are expected to be successful when the population reaches carrying capacity In other words P 0 80 and P K 10 To approximate the expected shape of the density dependence curve modeled in Vortex the exponential steepness parameter B was set to 4 The functional form of this relationship is shown in the top panel of Figure V 1 In contrast the winged mapleleaf mussel Quadrula fragosa inhabits isolated stretches of the
13. 893 9 10 Lee H D Garshelis U S Seal and J Shillcox eds 2001 Asiatic Black Bears PHVA Final Report Apple Valley MN Conservation Breeding Specialist Group SSC TUCN Leighton M U S Seal K Soemarna Adjisasmito M Wijaya T Mitra Setia G Shapiro L Perkins K Traylor Holzer and R Tilson 1995 Orangutan life history and vortex analysis Pages 97 107 in Nadler R D B F M Galdikas L K Sheeran and N Rosen eds The Neglected Ape New York Plenum Press de Leon J N Lawas R Escalada P Ong R Callo S Hedges J Ballou D Armstrong and U S Seal eds 1996 Tamaraw Bubalus mindorensis Population and Habitat Viability Assessment Report Apple Valley MN Conservation Breeding Specialist Group SSCAUCN Li X H D M Li Y G Yong and J Zhang 1997 A preliminary analysis on population viability analysis for giant panda in Foping Acta Zoologica Sinica 43 3 285 293 Li X and D Li 1998 Current state and the future of the crested ibis Nipponia nippon A case study by population viability analysis Ecological Research 13 3 323 333 Lindenmayer D B M A Burgman H R Ak akaya R C Lacy and H P Possingham 1995 A review of the generic computer programs ALEX RAMAS Space and VORTEX for modelling the viability of wildlife populations Ecological Modelling 82 161 174 Lindenmayer D B T W Clark R C Lacy and V C Thomas 1993 Population viability analysis as a tool in wildlife c
14. B W et al 1997 Does population viability analysis soft ware predict the behaviour of real populations A retrospec tive study on the Lord Howe Island woodhen Tricholimnas sylvestris Sclater Biol Conserv 82 119 128 49 Brook B W et al 1999 Comparison of the population viability analysis packages GAPPS INMAT RAMAS and VORTEX for the whooping crane Grus americana Anim Conserv 2 2331 ok ence ae ph ke Brook B W et al 2000 Predictive accuracy of population via bility analysis in conservation biology Nature 404 385 387 Brown J H and Kodric Brown A 1977 Turnover rates in insu lar biogeography effect of immigration on extinction Ecology 58 445 449 Caro T M and Laurenson M K 1994 Ecological and genetic factors in conservation a cautionary tale Science 263 485 486 Caughley G 1994 Directions in conservation biology J Anim Ecol 63 215 244 Charlesworth D and Charlesworth B 1987 Inbreeding de pression and its evolutionary consequences Annu Rev Ecol Syst 18 237 268 Clark T W 1989 Conservation biology of the black footed fer ret Wildlife Preservation Trust International Philadelphia Courchamp F Clutton Brock T and Grenfell B 1999 Inverse density dependence and the Allee effect Trends Ecol Evol 14 405 410 Dietz J M Baker A J and Ballou J D 2000 Demographic evidence of inbreeding depression in golden lion ta
15. E ZPG D WORTEX9 ZPG ZPG vpi Project Settings Simulation Input Text Output Graphs and Tables Project Report Add Scenario Delete Scenario lt zPpa2 gt Reorder ZPG1 I ZPG2 cenario Settin z eim Labels and State Variables abeis and State Vars Population Labels and State Yariables ispersal Label UserDefVarB UserDef Yar C Population Population 1 Population Population 2 ortality Rates atastrophes Meta model linkages to other programs ate Monopolization T Link to Outbreak with specification ois Browse nitial Population Size A PEA anying Capacity ow many other models to be linked fo Initialization Call Timestep Call Closing Call T ra sic aia GIG 3 3 e EW 2 S S upplementation Copy input values from Population 1 Individual State Parameters How many state parameters would you like fi aU Var Name Label Init fn Bitthfn Transition fn populations mtDNA CEIL RAND 10 151 51 Gopy Input Values After entering a note don t forget to hit the button to save it Vortex 9 21 Enter a name for the Individual State Variable Z NUM INS Date Time 10 24 03 3 42AM CAPS Figure 21 Labels and State Variables Input section Meta model linkages to other programs VORTEX provides the capacity to run the population simulation simultaneously functionally in parallel with one or more other models that might describe the dynamic
16. File Edt Vortex Window Help D u trela i Page D WORTEXS 2ZPG ZPG Ypi Of x Project Settings Simulation Input Text Output Graphs and Tables Project Report Add Scenario Delete Scenario lt zp gt Reorder ZPE ZPG2 cenario Settings pecies Description abels and State Vars Species Description Reproductive Rates Lethal Equivalents fai 4 ortality Rates Percent Due to Recessive Lethals 50 tas al IV EV Concordance of Reproduction amp Survival ate Monopolization nitial Population Size EV Correlation Among Populations fi 5 arrying Capacity Number of Types of Catastrophes 2 Reproductive System Harvest upplementation Copy input values from Population 1 z This Section Vortex 9 21 Check this if you want to model inbreeding depression as an increase in 1st year mortality caps NUM INS Date Time 10 24 03 915AM Figure 6 Species Description input section Chapter 2 13 Getting Started with VORTEX VORTEX Version 9 User s Manual Step through each of the input sections looking at the input values that are requested by VORTEX and the values that were entered for this ZPG Scenario In some sections you may need to use vertical or horizontal scroll bars to see all of the data entered You can also make the input screens larger by clicking and dragging the corner of the window Go now to the Catastrophes section Figure 7 fea Vortex Stochastic Si
17. IF NumberFemales p x lt NumberFemalesToBeHarvested p x All females age x die ELSE WHILE number harvested lt NumberFemales ToBeHarvested p x from age class Choose at random a living female in age class x Female dies END WHILE ECOLOGICAL BULLETINS 48 2000 END IF ELSE END LOOP Adjust tallies of population size END FUNCTION HARVEST BEGIN FUNCTION SUPPLEMENT for population p FOR each age x up to MaleBreedingAge WHILE number males created lt NumberMales ToBeSupplemented p x Create a male assigning ID age sex alleles population Set kinships to all other animals 0 Set Inbreeding 0 END WHILE END LOOP FOR each age x up to FemaleBreedingAge WHILE number females created lt NumberFemales ToBeSupplemented p x Create a female assigning ID age sex alleles population Set kinships to all other animals 0 Set Inbreeding 0 END WHILE END LOOP END FUNCTION SUPPLEMENT BEGIN FUNCTION CALC_GENETIC_METRICS for population p FOR each living animal in the population Increment NumberAlleleCopies a for each of the two alleles a at a neutral locus IF allele 1 is same as allele 2 Increment NumberHomozygotes END IF END LOOP FOR each allele a of the neutral locus IF NumberAlleleCopies a gt 0 Increment NumberExtantAlleles Add 0 25 NumberAlleleCopies a PopulationSize p NumberAlleleCopies a PopulationSize p to ExpectedHomozygosity p E
18. Lacy 1991 The population viability assessment workshop A tool for threatened species management Endangered Species Update 8 1 5 Clark T W and Seebeck J H eds 1990 Management and Conservation of Small Populations Brookfield Illinois Chicago Zoological Society Clarke G M 1995 Relationships between developmental stability and fitness Application for conservation biology Conservation Biology 9 18 24 Crow J F and Kimura M 1970 Introduction to Population Genetics Theory New York Harper and Row Doughty R W 1989 Return of the Whooping Crane Austin University of Texas Press Edroma E L N Rosen and P S Miller eds 1997 Conserving the Chimpanzees of Uganda Population and Habitat Viability Assessment for Pan troglodytes schweinfurthii Apple Valley MN Conservation Breeding Specialist Group SSC IUCN Ellis S K Hughes C Kuehler R C Lacy and U S Seal eds 1992a Alala Akohekohe and Palila Population and Habitat Viability Assessment Reports Apple Valley MN Captive Breeding Specialist Group SSC IUCN Ellis S C Kuehler R C Lacy K Hughes and U S Seal eds 1992b Hawai ian Forest Birds Conservation Assessment and Management Plan Apple Valley MN Captive Breeding Specialist Group SSC IUCN Falconer D S 1981 Introduction to Quantitative Genetics 2 ed New York Longman Fisher R A 1958 The Genetical Theory of Natural Selection 2 ed New York Dover Fowler C W
19. N gt K IF Tally PopulationSize p IF population is extinct Decrement NumberExtantPopulations p IF population was not extinct in prior year Set YearExtinct p Current Year IF population has not been recolonized First extinction Set Time ToExtinction p Current Year Increment NumberOfExtinctions p ELSE Re extinction of population Set Time ToReextinction p Current Year YearOfRecolonization p END recolonized IF ELSE END was not extinct IF ELSE I Not extinct ECOLOGICAL BULLETINS 48 2000 IF population was extinct in prior year Recolonization Set YearRecolonized p CurrentYear Set Time ToRecolonization p Current Year YearExtinct p Increment NumberOfRecolonizations p END was extinct IF Set YearExtinct p 0 Flag for not extinct END extinct IF ELSE Display PopulationSize p on screen graph END population LOOP FOR each population p CALC_GENETIC_METRICS p END population LOOP END year LOOP END iteration LOOP At this point the simulation is complete and summary statistics can be calculated FOR each population p Calculate and report means SDs and SEs across iterations for Population growth rate r p N Current Year N Previous Year TimeToExtinction p Time ToRecolonization p Time ToReextinction p FOR each year Calculate and output means SDs and SEs across iterations for Probability of extinction PE p SE SQRT
20. R C and T W Clark 1990 Population viability assessment of the eastern barred bandicoot in Victoria Pages 131 146 in Clark T W and J H Seebeck eds Management and Conservation of Small Populations Brookfield IL Chicago Zoological Society Lacy R C N R Flesness and U S Seal eds 1989 Puerto Rican Parrot Population Viability Analysis Report to the U S Fish and Wildlife Service Apple Valley MN Captive Breeding Specialist Group SSC TUCN Lacy R C and D B Lindenmayer 1995 A simulation study of the impacts of population sub division on the mountain brushtail possum Trichosurus caninus Ogilby Phalangeridae Marsupialia in south eastern Appendix IT 125 Literature Cited VORTEX Version 9 User s Manual Australia II Loss of genetic variation within and between sub populations Biological Conservation 73 131 142 Lacy R C and P S Miller 2002 Incorporating human populations and activities into population viability analysis Pages 490 510 in S R Beissinger and D R McCullough eds Population Viability Analysis Chicago University of Chicago Press Lacy R C Petric A M and Wameke M 1993 Inbreeding and outbreeding depression in captive populations of wild species Pages 352 374 in Thornhill N W ed The Natural History of Inbreeding and Outbreeding Chicago University of Chicago Press Lande R and G F Barrowclough 1987 Effective population size genetic variation and their use in popu
21. Somers M J 1997 The sustainability of harvesting a warthog population Assessment of management opinions using simulation modelling South African Journal of Wildlife Research 27 2 37 43 Sommer S A T Volahy and U S Seal 2002 A population and habitat viability assessment for the highly endangered giant jumping rat Hypogeomys antimena the largest extant endemic rodent of Madagascar Animal Conservation 5 4 263 273 Song Y L 1996 Population viability analysis for two isolated populations of Haianan Eld s deer Conservation Biology 10 1467 1472 South A B S P Rushton and D W Macdonald 2000 Simulating the proposed reintroduction of the European beaver Castor fiber to Scotland Biological Conservation 93 103 116 Strier K B 2000 Population viabilities and conservation implications for muriquis Brachyteles arachnoides in Brazil s Atlantic Forest Biotropica 32 4B 903 913 Supriatna J R Tilson K Gurmaya J Manansang W Wardojo A Sriyanto A Teare K Castle and U S Seal eds 1994 Javan Gibbon and Javan Langur Population and Habitat Viability Analysis Report Apple Valley MN Conservation Breeding Specialist Group SSC IUCN Taylor B L P R Wade U Ramakrishnan M Gilpin and H R Ak akaya 2002 Incorporating uncertainty in population viability analyses for the purpose of classifying species by risk Pages 239 252 in Beissinger S R and D R McCullough eds Population Viability Analysis
22. VORTEX is still undergoing considerable improvements as are many other sections 80 Chapter 4 Viewing Model Results VORTEX Version 9 User s Manual Project Report The Project Report tab takes you to a simple word processor utility that you can and should use to document your work and begin to develop a report for sharing with others Figure 49 4 Vortex Stochastic Simulation of the Extinction Process O x File Edit Yortex Window Help D u taal Ss Fare f42PG C Yortex9 ZPG 2ZPG vpj Project Settings Simulation Input Text Output Graphs and Tables Project Report Times New Roman fe JE ow amp B Z U ase E AE a 1 temales years old 1 female adults 2 lt age lt 10 1 males 1 years old 1 male adults 2 lt age lt 10 Animals added to Population 1 year 10 through year 50 at 4 year intervals 1 females 1 years old 1 females 2 years old 1 males 1 years old 1 males 2 years old Mean N all 2761 Popatation 1 f 2PG2 Popatstion 1 ZPG2 Pon ttine 7 Vortex 9 04 CAPS NUM INS Date Time 5 15 2003 3 46AM Figure 49 The Project Report In the earlier sections for Project Settings Text Output and Graphs and Tables you had the option to send text tables and graphs to your Project Report This is where you were sending them It is always a good idea to liberally send information to your Project Report whenever you think that it may be information that you will wa
23. cies The species for which historic population trajectories were modeled in the above studies had been reduced to single populations rather than existing within metapopu lations and most had relatively simple breeding systems rather than complex social structures Also PVA models may be more reliable when habitat is not limiting popula tion growth than when dynamics near carrying capacity are modeled Mills et al 1996 Brook et al 1997 How small is small The processes and cases described in this paper suggest that when it comes to assessing whether wildlife populations have declined to dangerously small sizes small may be bigger than we usually think it is Isolated populations with fewer than ca 50 breeding adults may suffer from inbreeding depression within a few genera tions Larger populations that are fragmented into partially isolated subunits of fewer than ca 50 breeding animals in each may lose variability much faster than would be esti mated from the total metapopulation size Lacy and Lindenmayer 1995 Genetic decay in populations with fewer than ca 500 breeding adults or even 5000 adults Lande 1995 may eventually reduce adaptability and po tential for recovery Lacy 1997 Monogamous species and species with complex social systems may have reduced breeding if numbers fall below several hundred adults Each of these factors tends to be a greater threat in those species such as many mammals and birds that have
24. clicking on the same icon on the program toolbar or directly typing into the long text box below the input window After you type a note into the text box showing on the Simulation Input screen hit the button to add that Note to your Project or just hit Enter Your Note is then associated with the input parameter or question that last had cursor control Be careful not to enter a Note and then immediately click on another data entry box If you didn t hit or Enter your Note will be discarded When you open Input Notes by clicking on its icon you then select the Input section input parameter for which you wish to enter a note Figure 19 You then enter the text of your note in the box at the right Projecti Scenario 1 Notes Section Note Note For Section Simulation Settings Scenario Name Number of Iterations Number of ears Extinction Definition Number of Populations This is my note about why decided to define extinction as N lt 100 Paste Into Report Print Note Paste All Notes Into Report Print All Notes Close Figure 19 Input Notes pop up utility As you move among input screens and boxes the Note for the input box that is selected is displayed in the text box below the input window The Input Notes screen provides commands for pasting the displayed Note or All Notes into your Project Report and for printing the displayed Note or All Notes Thus it is easy to quick
25. or indirectly in the form of the propor tion of males that breed or as the average number of litters per breeding male If the proportion in the breeding pool is given indirectly VORTEX will assume that the distribu tion of male reproductive success follows a Poisson distri bution The proportion of males in the breeding pool is 202 then calculated by solving the following equations for the unknowns LittersPerMale ProportionFemalesProducingLitters NumberAdultFemales NumberAdultMales Note Adult sex ratio is deter mined from stable age distribution LittersPerMale ProportionMalesInBreedingPool Lit tersPerMaleInBreedingPool ProportionMalesBreeding ProportionMalesInBreeding Pool 1 exp LittersPerMaleInBreedingPool This last equation adjusts for the fact that in any given year some males in the breeding pool will not happen to be successful breeders the zero class of the Poisson distribu tion Note 5 The occurrence of probabilistic events is deter mined by a random number generator The event is deemed to occur if a random number between 0 and 1 is less than the probability of occurrence for that event Note 6 Environmental variation EV in breeding and in each mortality rate is modeled as a binomial distribution or as a normal distribution depending on whether the magnitude of EV is large The user specifies a mean and standard deviation for each rate The binomial distribution that has a sta
26. so that SRAND 65636 SRAND 100 J Notes Regarding Function Syntax and Use e Variables of trigonometric functions are assumed to be in radians e The operator NEG is the same as using a minus sign before a number By the context VORTEX will interpret whether a minus sign signifies subtraction a binary operation or the negative a unary operation 88 Chapter 5 Using Functions in VORTEX VORTEX Version 9 User s Manual CEIL FLOOR and ROUND convert real numbers to integer values but all expressions are evaluated as real numbers For example FLOOR 3 7 FLOOR 4 1 CEIL 2 1 CEIL 3 7 ROUND 3 1 ROUND 3 6 0 75 Numbers may be written with or without leading and trailing zeroes Decimal points for integral values are optional For example all of the following are valid expressions 3 3 00 0 03 03 0 30 5 Functions containing invalid mathematical expressions are prohibited such as SQR 10 Square root of a negative number LN 10 Natural log of a negative number or zero 5 0 Division by zero TAN 1 5707963 Tangent of PI 2 ASINC1 1 Arcsine or arccosine of a value greater than 1 or less than 1 Some mathematically valid functions would be ambiguous or meaningless For example functions of carrying capacity K should not contain K as an independent predictor of itself Functions of K should also not include A age or S sex as parameters because the condition of exceeding the carrying capacity
27. unmodeled population The numbers of additions and removals are specified according to the age and sex of animals Migration among populations VORTEX can model up to 50 populations with possibly distinct population parameters Each pairwise migration rate is specified as the probability of an individual moving from one population to another Migration among populations can be restricted to one sex and or a limited age cohort Emigration from a population can be restricted to occur only when the number of animals in the population exceeds a specified proportion of the carrying capacity Dispersal mortality can be specified as a probability of death for any migrating animal which is in addition to age sex specific mortality Because of between population migration and managed supplementation populations can be recolonized VORTEX tracks the dynamics of local extinctions and recolonizations through the simulation Appendix I 117 An Overview of Population Viability Analysis Using VORTEX VORTEX Version 9 User s Manual Output VORTEX outputs 1 probability of extinction at specified intervals e g every 10 years during a 100 year simulation 2 median time to extinction if the population went extinct in at least 50 of the simulations 3 mean time to extinction of those simulated populations that became extinct and 4 mean size of and genetic variation within extant populations Standard deviations across simulations and standa
28. which in turn will definitely be a subset of those processes that impact natural populations A number of variables affecting population dynamics and viability are not yet commonly examined in PVA models These include social and ecological determinants of dispersal complex social processes such as the role of non breeders in group stability and the impacts of other aspects of the social environment on reproductive success and survival competitive exploitative or mutualistic interactions with other species experiencing their own population dynamics and the effects of changes in the global environment To date most PVA models treat organisms as independent actors in spatially homogeneous physical biotic and social environments There is tremendous opportunity and need for elaboration of PVA models and it is likely that increasingly sophisticated models will also become more specific to the individual taxa and environments under study PHVA workshops must incorporate consideration of the assumptions of the PVA model used and the biases or limitations in interpretation that could result PHVAs consider only those threatening processes of which we have knowledge for which we can develop algorithms for modeling or other methods for analysis and for which we have some data As a result it is likely that PVAs will underestimate the vulnerability of most populations to extinction and that PHVA workshops will be less comprehensive than is desirable
29. 0 0022 Therefore ogy oe V0 0219 0 0022 0 140 which is the variation across years of the mean peak values for each curve in the left panel of the figure This calculation tells us that the contribution of demographic stochasticity to the total variance observed in our nine years of mortality data remember we removed the outlier from the analysis is quite small the variance attributable to environmental variability is almost 90 of the total variance in mortality This is shown graphically in the right panel of Figure D 1 In order for demographic stochasticity to make a significant contribution to the total observed variance the number of individuals sampled for a given rate n would have to be quite small on the order of a few tens The right panel of Figure D 1 also shows the frequency distribution obtained by including the catastrophe outlier in the calculation of overall mean and variance The inclusion of this single observation results in a significantly poorer fit to the data as the overall distribution of values the mean of all values in the left panel does not look much like a normal distribution This helps in part to illustrate why catastrophes events that are infrequent in occurrence yet severe in population impact are treated separately from more typical annual or seasonal fluctuations Finally it is instructive to note that each of the distributions in the right panel of Figure D 1 extend beyond 0 0 and or
30. 0 1 range is lt 0 000001 When modelling EV as a normal distribution the distribution must be truncated at 0 and 1 To avoid creating any bias in the mean demographic rate as a result of this truncation VORTEX always truncates the distribution symmetrically ECOLOGICAL BULLETINS 48 2000 For example if the mean is p 0 3 VORTEX truncates the distribution at 0 0 and 0 6 This truncation will cause the SD of the distribution to be very slightly less than that entered by the user Some PVA models use continuous distributions such as the normal or log normal to represent EV even when EV is large In such cases the necessary truncations can cause EV to be substantially less than intended by the user Moreover if the truncation is not symmetric then the mean demographic rate generated by the model can be strongly biased away from the input parameter References Ballou J D 1983 Calculating inbreeding coefficients from ped igrees In Schonewald Cox C M et al eds Genetics and conservation a reference for managing wild animal and plant populations Benjamin Cummings Menlo Park Cali fornia pp 509 520 Burgman M A Ferson S and Ak akaya H R 1993 Risk assessment in conservation biology Chapman and Hall Caswell H 1989 Matrix population models construction anal ysis and interpretation Sinauer Caughley G and Gunn A 1996 Conservation biology in theo ry and practice Blackwell ECOL
31. 1 0 As this is biologically implausible we need to truncate these distributions in order to allow their proper use in defining probabilities Partly for this reason VorTEx usually uses a binomial distribution which does not extend beyond 0 and 100 but which otherwise looks much like a normal distribution to represent EV For ease of calculation VorTEx sometimes does use a normal distribution when it is a very close approximation to the binomial but it then truncates the normal curve symmetrically about the mean to avoid creating any bias 36 Chapter 3 The Data Input Process VORTEX Version 9 User s Manual Box D Continued The above methods are a bit complex Because DS is usually quite small when the sample sizes n are at all large a quick somewhat generous estimate of EV is simply the total variation in rates observed across years treating DS as an insignificant contributor to the observed variation Finally keep in mind that the Vortex simulation program generates DS automatically as it determines whether each individual lives whether it breeds and what sex it is Unlike some other PVA programs you do not specify that DS should be added into the model and you cannot exclude it from the model or from real life You do need to specify the magnitude of EV however as EV results from external processes rather than being an intrinsic and inevitable part of all population dynamics The size of DS is a consequence of
32. 1981 Density dependence as related to life history strategy Ecology 62 602 610 Franklin I R 1980 Evolutionary change in small populations Pages 135 149 in Soul M E and B A Wilcox eds Conservation Biology An Ecological Evolutionary Perspective Sunderland MA Sinauer Associates Foose T J R C Lacy R Brett and U S Seal eds 1993 Kenyan Black Rhino Metapopulation Workshop Report Apple Valley MN Captive Breeding Specialist Group SSC IUCN Gilpin M E 1987 Spatial structure and population vulnerability Pages 125 139 in Soul M E ed Viable Populations for Conservation Cambridge Cambridge University Press Gilpin M E 1989 Population viability analysis Endangered Species Update 6 15 18 Gilpin M E and M E Soul 1986 Minimum viable populations processes of extinction Pages 19 34 in Soul M E ed Conservation Biology The Science of Scarcity and Diversity Sunderland MA Sinauer Associates Goodman D 1987 The demography of chance extinction Pages 11 34 in Soul M E ed Viable Populations for Conservation Cambridge Cambridge University Press Gunn A U S Seal and P S Miller eds 1998 Population and Habitat Viability Assessment Workshop for Peary Caribou and Arctic Island Caribou Rangifer tarandus Apple Valley MN Conservation Breeding Specialist Group SSC TUCN 124 Appendix IT Literature Cited VORTEX Version 9 User s Manual Hanski I A and M E Gi
33. 51 Kaiya Z S Ellis S Leatherwood M Bruford and U S Seal eds 1994 Baiji Population and Habitat Viability Assessment Report Apple Valley MN Captive Breeding Specialist Group SSC IUCN Kelly B T P S Miller and U S Seal eds 1999 Population and Habitat Viability Assessment Workshop for the Red Wolf Canis rufus Apple Valley MN Conservation Breeding Specialist Group SSC TUCN Kjos C O Byers P S Miller J Borovansky and U S Seal eds 1998 Population and Habitat Viability Assessment Workshop for the Winged Mapleleaf Mussel Quadrula fragosa Final Report Apple Valley MN Conservation Breeding Specialist Group SSC TUCN Kovacs T Z Korsos I Reh k K Corbett and P S Miller eds 2002 Population and Habitat Viability Assessment for the Hungarian Meadow Viper Vipera ursinii rakosiensis Apple Valley MN Conservation Breeding Specialist Group SSC IUCN Kumar A S Molur and S Walker eds 1995 Lion Tailed Macaque Population and Habitat Viability Assessment Report Apple Valley MN Captive Breeding Specialist Group SSC IUCN Lacy R C 1993 VORTEX A computer simulation model for Population Viability Analysis Wildlife Research 20 45 65 Lacy R C 1993 1994 What is Population and Habitat Viability Analysis Primate Conservation 14 15 27 33 132 Appendix III VorTEX Bibliography VORTEX Version 9 User s Manual Lacy R C 1996 Further population modelling of nort
34. 57000 lethal equivalents not subject to removal by selection EV in reproduction and mortality will be concordant First age of reproduction for females 2 for males 2 Maximum breeding age senescence 10 Sex ratio at birth percent males 50 Population l Population 1 Poanulation state varishles Vortex 9 21 CAPS NUM INS Date Time 10 24 03 10 43AM Figure 40 Input Summary section of Text Output At the top of the text display window are dropdown lists that let you move among the reports for the various Scenarios and Populations within Scenarios In the Input Summary all Populations in each Scenario are contained within the same text file so you could find them by scrolling down However the file can be very large so it is often faster to use the dropdown list to jump to the place where text on a Population starts Deterministic Calculations The second section of Text Output provides both text and a simple graph to display the deterministic projections of population size Figure 41 The text window shows the exponential rate of increase r the annual rate of change A and the per generation rate of change or net replacement rate RO as determined from life table analysis of the mean rates of reproduction and survival in your model The mean generation time and a stable age distribution calculated from age specific birth and death rates are 70 Chapter 4 Viewing Model Results VORTEX Version 9 User
35. AE a E o S 5 Reproduction Survival Copy input values from Population 1 E This Section z to subsequent populations Copy Input Values Vortex 9 21 Enter G if the catastrophe strikes this and other populations synchronously CAPS NUM INS Date Time 10 24 03 10 10AM 4 Figure 29 Catastrophes input section Global Local Each catastrophe is to be specified as global or local in scope this is applicable only when more than one population is modeled You are given considerable flexibility in how the scope of each catastrophe is specified so it is important to read the following information carefully in order to correctly model your metapopulation A global catastrophe will occur in the same years in all populations but the severity of effects can be entered as different or equal across populations Local catastrophes occur independently among the populations To cause a catastrophe to be regional in scope affecting only a subset of the populations you can specify that it is global but then set the severity factors to 1 0 see below for those populations which are not affected by that regional catastrophe 54 Chapter 3 The Data Input Process VORTEX Version 9 User s Manual You may also specify that a catastrophe is global for some populations but local for others In that case the catastrophe happens concurrently across the populations for which it is global but occurs indepen
36. Chicago IL University of Chicago Press Tilson R U S Seal K Soemarna W Ramono E Sumardja S Poniran C van Schaik M Leighton H Rijksen and A Eudey eds 1993 Orang utan Population and Habitat Viability Analysis Report Apple Valley MN Captive Breeding Specialist Group SSC TUCN Tilson R K Soemarna W Ramono S Lusli K Traylor Holzer and U S Seal eds 1992 Sumatran Tiger Population and Habitat Viability Analysis Report Apple Valley MN Captive Breeding Specialist Group SSC IUCN Tilson R K Soemarna W Ramono R Sukumar U S Seal K Traylor Holzer and C Santiapillai eds 1994 The Asian Elephant in Sumatra Population and Habitat Viability Analysis Report Apple Valley MN Captive Breeding Specialist Group SSC IUCN Tunhikorn S W Brockelman R Tilson U Nimmanheminda P Ratankorn R Cook A Teare K Castle and U S Seal eds 1994 Population and Habitat Viability Analysis Report for Thai Gibbons Hylobates lar and H pileatus Apple Valley MN Conservation Breeding Specialist Group SSC IUCN Wade P R 2002 Bayesian population viability analysis Pages 213 238 in Beissinger S R and D R McCullough eds Population Viability Analysis Chicago IL University of Chicago Press Walker S ed 1994 Manipur Brow Antlered Deer Sangai Population and Habitat Viability Assessment Apple Valley MN Conservation Breeding Specialist Group SSC IUCN Walker S and S
37. Phs S N binomial trials are then simulated by sampling from the uniform 0 1 distribution to obtain the desired result the frequency or proportion of successes If the value of N determined for a desired binomial distribution is larger than 25 a normal approximation is used in place of the binomial distribution This normal approximation must be truncated at 0 and at 1 to allow use in defining probabilities although with such large values of N s is small relative to p and the truncation would be invoked only rarely To avoid introducing bias with this truncation the normal approximation to the binomial when used is truncated symmetrically around the mean The algorithm for generating random numbers from a unit normal distribution follows Latour 1986 Environmental variation VORTEX can model annual fluctuations in birth and death rates and in carrying capacity as might result from environmental variation To model environmental variation each demographic parameter is assigned a distribution with a mean and standard deviation that is specified by the user Annual fluctuations in probabilities of reproduction and mortality are modeled as binomial distributions Environmental variation in carrying capacity is modeled as a normal distribution Environmental variation in demographic rates can be correlated among populations Catastrophes Catastrophes are modeled in VORTEX as random events that occur with specified probabilities A catastroph
38. R Chellam S Molur U S Seal D Sharma and S Walker eds 1995 Asiatic Lion Population and Habitat Viability Assessment Report Apple Valley MN Conservation Breeding Specialist Group SSC TUCN Asquith N M 2001 Misdirections in conservation biology Conservation Biology 15 2 345 352 Aurioles Gamboa D C Godinez Reyes M E Duran Lizarraga F J Garcia Rodrigurz C J Hernandez Camacho S Luque P S Miller and S Ellis eds 1999 Conservaci n An lisis y Manejo Planificado sobre los Pinnipedos de Mexico y An lisis de la Viabilidad de la Poblacion y del Habitat para el Lobo Marino de California Zalophus californianus californianus Apple Valley MN Conservation Breeding Specialist Group SSC AUCN Appendix III 129 VorTEX Bibliography VORTEX Version 9 User s Manual Ballou J D R C Lacy D Kleiman A Rylands and S Ellis eds 1997 Leontopithecus IT The Second Population and Habitat Viability Assessment for Lion Tamarins Leontopithecus Apple Valley MN Conservation Breeding Specialist Group SSC TUCN Barongi R J Ventocilla P S Miller and U S Seal eds 1996 Population and Habitat Viability Assessment for Baird s Tapir Tapirus bairdi Apple Valley MN Conservation Breeding Specialist Group SSC IUCN Beissinger S R 2002 Population viability analysis Past present future Pages 5 17 in Beissinger S R and D R McCullough eds Population Viability Analysis Chicago IL Un
39. Shannon A Woolfardt J Cooper R Lacy and S Ellis eds 2000 African Penguin Population and Habitat Viability Assessment Final Report Apple Valley MN Conservation Breeding Specialist Group SSC TUCN Wilson M H C B Kepler N F R Synder S R Derrickson F J Dein J W Wiley J M Wunderle A E Lugo D L Graham and W D Toone 1994 Puerto Rican parrots and potential limitations of the metapopulation approach to species conservation Conservation Biology 8 114 123 Xu H and H Lu 1996 A preliminary analysis of population viability for Chinese water deer Hydropotes inermis lived in Yancheng In Chinese Acta Theriologica Sinica 16 81 88 Yuan S D G Yazhen L Xiaoping Q Yang J Sale C Kirkpatrick J Ballou and U S Seal eds 1999 CBSG Guizhou Snub nosed Monkey Conservation and PHVA Workshop Report Apple Valley MN Conservation Breeding Specialist Group SSC IUCN Zhang X D Wang and K Wang 1994 The VORTEX model and its application on the management of the Chinese River Dolphin Lipotes vexillifer population Chinese Biodiversity 2 133 139 138 Appendix III VORTEX Bibliography VORTEX Version 9 User s Manual Appendix IV Reprints Lacy R C 2000 Structure of the VORTEX simulation model for population viability analysis Ecological Bulletins 48 191 203 Reprinted with permission of the publisher Lacy R C 2000 Considering threats to the viability of small populat
40. a species will change as a species declines Therefore it is important to consider carefully which PVA model is most appropriate for a par ticular analysis Lindenmayer et al 1995 Ak akaya and Sj gren Gulve 2000 An individual based simulation program that models the stochastic processes of small pop ulations in detail would probably not be the best model for examining viability of a population which numbers in the 40 tens of thousands Similarly a population based structured model which ignores factors such as fluctuations in sex ra tio mate availability and inbreeding would probably not be the most accurate model for a population which falls below 100 individuals Many perhaps all presently used PVA models assess only some of the threats facing small populations and therefore may underestimate probabili ties of extinction and difficulties in species recovery In this paper I will describe some of the threats to small populations that are not included in most PVA models This discussion will provide guidance as to when more de tailed individual based PVA models may be necessary to represent well the dynamics of small populations Most of the processes I will discuss are particularly important for species with low intrinsic growth rates and stable social sys tems and somewhat less so for those with high fecundity and little structure to the social or breeding system There fore these considerations will be most applicable
41. allow you to send the text to the Project Report print the text or save the text as a file that you would specify The Project Report will be described in detail later it is a simple word processor that allows you to start building a report of your analyses while you are working within the VORTEX program You can then access that report from MS Word or other software to further edit and refine it If you chose to print the text VORTEX will open the standard Windows Print utility If you save the text VORTEX saves it as a simple text file which could later be viewed edited or printed from NotePad MS Word or other word processing software Chapter 4 69 Viewing Model Results VORTEX Version 9 User s Manual 4 Vortex Stochastic Simulation of the Extinction Process File Edt Vortex Window Help JOG BeE S ls gt SS Page D WORTEXS ZPGS ZPG Ypi Project Settings Simulation Input Text Output Graphs and Tables Project Report Input Summary Deterministic Calculations Output Summary Other Output Send text to Report Print Save s Scenario to view zPat z Population to find Population 1 gt VORTEX 9 21 simulation of population dynamics ZPG1 l population s simulated for 100 years 100 iterations Extinction is defined as no animals of one or both sexes Inbreeding depression modeled with 3 14000 lethal equivalents per individual comprised of 1 57000 recessive lethal alleles and 1
42. and State Vars Population 1 Population 2 Reproductive System Population Supplemented v v Reproductive Rates First Year of Supplementation 10 Jortality Rates Last Year of Supplementation 50 atastrophes Interval Between Supplementations ate Monopolizati Optional Criterion for Supplementing Initial Population Size Labels and State Vars Dispersal Reproductive System Reproductive Rates Mortality Rates Mate Monopolization initial Poputation Size Canying Capacity Harvest Age 1 Supplemented Supplementation Adults Supplemented Copy input values from Population 1 This Section p to subsequent PAREA Age 1 Supplemented Adults Supplemented Copy Input values Vortex 9 21 Check this if individuals are added at regular intervals CAPS NUM INS Date Time 10 24 03 10 26AM 4 Figure 34 Supplementation input section Chapter 3 63 The Data Input Process VORTEX Version 9 User s Manual Saving your Input and Running the Simulation After you have completed entering values for all of the input parameters it is probably wise to save your project You would probably be disappointed if you spent a long time entering input values did not save them and then the program crashed during the simulation because one number was wrong To save your Project click on the save icon the disk on the toolbar or select Save or SaveAs from the File menu If y
43. and Tables Project Report Add Scenario Delete Scenario lt zPa2 gt Reorder ZPG1 ZPG2 cenario Settings pecies Description abelis and State Vars Population 1 Population 2 Mortality From Age Oto 1 enero Reproductive System SD in 0 to 1 Mortality Due to EY Mortality From Age 1to 2 PECCA RAE SD in 1 to 2 Mortality Due to EV ortality Rates Annual Mortality After Age 2 atastrophes SD in Mortality After Age 2 ate Monopolization nitial Population Size anying Capacity Mortality of Females as Mortality of Males as Copy from Females 2 oe S Zz c CARS a 2 o S Population 1 Population 2 Copy input values from Mortality From Age Oto 1 50 Population H SD in Oto 1 Mortality Due to EY Mortality From Age 1 to 2 This Section z SD in 1to 2 Mortality Due to EY to subsequent Annual Mortality After ge 2 populations SD in Mortality After Age 2 Copy Input Yalues Vortex 9 21 Enter annual mortality as a percent CAPS NUM INS Date Time 10 24 03 10 06AM Figure 28 Mortality Rates input section 52 Chapter 3 The Data Input Process VORTEX Version 9 User s Manual Be aware that if you enter a standard deviation for each mean mortality rate that is at least half of the survival rate 100 mortality rate in other words the coefficient of variation in survival is at least 50 in occasional yea
44. and Tables Project Report Times New Roman 7 fe Mi Car amp B Z U age 2S SS eee eee eee 509 of 1000 harvests of females could not be completed because of insufficient aumals 527 of 1000 harvests of males could not be completed because of meoufficiert animals Final expected heterozygosity was 0 4855 0 0569 SE 0 2545 SD Final observed heterozygosity was 0 5109 0 0684 SE 0 3061 SD Final ranuber of alleles wras 3 35 035SE 1 57 SD Number of lethal alleles per diploid 0 56 0 09 SE 0 40 SD Mean N all Z ZPG1 Population 1 Vortex 9 04 Enter a percent to define the annual probability of this catastrophe CAPS NUM INS Date Time 5 2 2003 6 04PM 4 Figure 14 The Project Report You have now completed your Quick Tour of VORTEX and we have looked at most of the main features of the program Spend some time exploring other aspects of the program change some of the input values run additional scenarios create some more tables and graphs Whenever you exit VORTEX the program will ask if you want to save your Project If you do all input output and report information will be saved so that it can be loaded again later 20 Chapter 2 Getting Started with VORTEX VORTEX Version 9 User s Manual Chapter 3 Creating a Project Data Input Creating a Project When you open VORTEX you must first choose whether to create a new Project or open an existing Project Figure 15 To create a n
45. and environmental variability is a subtle one even some professional population biologists have been confused by this Demographic stochasticity is the variation in an observed vital rate due to the sampling variation that is inherent because each individual an observation is an independent and random sample from a population with a given mean or probability Hence it is the variation in sample means X around a fixed population mean zz Environmental variation on the other hand is variation due to extrinsic factors that vary over time in the population mean itself i e u is different each year Putting this information together we conclude that the variation across years in the frequencies of births and deaths both in real populations and our simulated VorTex populations will have two components the demographic variation resulting from binomial sampling around the mean for each year and additional fluctuations due to environmental variability In actuality catastrophic events to be discussed in more detail later in the User s Manual also contribute to the overall observed variation across many years of data but they are treated separately from standard annual environmental variability Figure D 1 Left panel Expected values for a given annual demographic rate showing binomial sampling variance arising from demographic stochasticity with a sample size 7 of 100 individuals Right panel Frequency distribution of that same
46. certainty the best course of action is recognized management actions are designed in such a way that monitoring will allow testing of the adequacy of our model and understanding and corrective adjustments to management plans are made whenever the accumulating data suggest that the present course is inadequate to achieve the goals and that a better strategy exists Holling 1978 The urgency of the biodiversity crisis will not permit us ethically to refrain from aggressive conservation action until we have scientifically sound understanding of all the 108 Appendix I An Overview of Population Viability Analysis Using VORTEX VORTEX Version 9 User s Manual factors that drive population community and ecosystem dynamics PHVA provides a forum for making use of the information we do have in a well documented process that is open to challenge and improvement PHVA workshops can therefore assist wildlife managers in the very difficult and important job of using science to safeguard the future of wildlife populations In summary Population Viability Analysis PVA and Population and Habitat Viability Analysis PHVA refer to an array of interrelated and evolving techniques for assessing the survival probability of a population and possible conservation actions It might be useful to restrict the term PVA to its original meaning the use of quantitative techniques to estimate the probability of population persistence under a chosen model of populat
47. command at the top of the Input window This will delete the current Scenario A prompt will first warn you that you cannot recover from this action other than by re creating the Scenario again Reordering scenarios After you add and delete Scenarios from your Project you may find that the Scenarios are not listed in the order you would like them to have VORTEX provides a Scenario Manager Figure 39 which you access by clicking on the re order command next to the dropdown list of Scenario names The Scenario Manager lets you change the order of the Scenarios in your Project moving them up or down in the indexed list A feature not currently implemented will allow you also to specify that some Scenarios are to be considered to be grouped as sub scenarios of others moving them to higher or lower levels of a Scenario tree structure The level at which a Scenario is placed and the Scenario under which lower level Scenarios are nested has little or no meaning other than to the Sensitivity Analysis utility that has not yet been implemented Use buttons above to change the order or the grouping of the scenarios Close Figure 39 Scenario Manager window 68 Chapter 3 The Data Input Process VORTEX Version 9 User s Manual Chapter 4 Viewing Model Results Text Tabular and Graphical Output Once you have entered all of the necessary input parameters and given the command to run yo
48. created by VORTEX you may make the data inaccessible when you re open your Project Another file that you should not edit is the file with extension vpj This vortex project file is the master file that stores the data for your Project Any changes made to this file outside of the VORTEX program can cause your Project to be corrupted and possibly un openable In addition to the results made available to you within VORTEX the program stores other results in additional files that are placed into your Project directory Some of these additional files contain more detailed results often far more detailed than most users would care to examine These files typically are text files with semi colon delimiters formatted so that they can be opened directly into Excel and many other spreadsheet and database programs Which additional files are created depends on the settings you select in the Special Options of the Project Settings Available files include in which project is replaced by the name of your Project and scenario is replaced by the name of the Scenario project_scenario run A listing for each iteration of the year the population went extinct if it did go extinct and if it did not go extinct the final population size gene diversity mean inbreeding and number of founder alleles project_scenario ani A listing for each iteration of the animals living at the end of the iteration including their sex age inbreeding coef
49. definition of carrying capacity In fact some authors e g Caughley 1977 choose not to use the term altogether in their presentation of the mathematics of population growth In the context of wildlife management the habitat carrying capacity for a particular population can be defined as the maximum number of individuals that environment can sustain over time in the absence of unnatural disturbances and without inducing harmful trends in the abundance of the resources required by that population We can gain more insight into this concept by considering the familiar and admittedly simplistic logistic equation for population growth aN ry XO dt K where r is the intrinsic rate of population increase N is population size and K is carrying capacity Mathematically K can be thought of as the population size limit at which the rate of growth dN dt is equal to zero Some ecologists define K as a ratio of the total rate of food production in the habitat P to the per capita rate of food consumption necessary for survival M Since a population of size N must consume food resources at a rate of NM just to stay alive there are P NM resources available for the production of new individuals If NM exceeds P then resources available for reproduction become negative and the population must decrease in size When N is very small for example when a population is re established in its native habitat the potential growth rate is very close to
50. fate of the population at any given time in the future Such environmental variation should be incorporated into the model used to assess population dynamics and will generate a range of possible outcomes perhaps represented as a mean and standard deviation from the model In addition most biological processes are inherently stochastic having a random component The stochastic or probabilistic nature of survival sex determination transmission of genes acquisition of mates reproduction and other processes preclude exact determination of the future state of a population Such demographic stochasticity should also be incorporated into a population model because such variability both increases our uncertainty about the future and can also change the expected or mean outcome relative to that which would result if there were no such variation Finally there is uncertainty which represents the alternative actions or interventions that might be pursued as a management strategy The likely effectiveness of such management options can be explored by testing alternative scenarios in the model of population dynamics in much the same way that sensitivity testing is used to explore the effects of uncertain biological parameters Often the uncertainty regarding a number of aspects of the population biology current status and threats to persistence is too large to allow scientifically accurate and reliable projections of population dynamics Therefore
51. few per protected area Field surveys in Malaysia in 1995 found tracks of one juvenile among 35 sets of tracks and one of 21 adult fe males captured in the prior decade was pregnant AsRSG 1996 If the population were breeding as expected for a rhinoceros species ca 30 of adult females should be pregnant at any time and ca 15 of the animals should be under two years of age Although detailed studies of de mography have not been carried out in part because of the difficulty of studying secretive animals that are at low den sity in the forest it is plausible that the scarcity of mates is causing a near cessation of breeding over much of the frag mented range Even if some potential mates are available small popu 44 lations may provide little opportunity for mate choice The extent to which a reduced pool of possible mates may be causing breeding delays or failures in small natural popula tions has not been explored This problem could be exacer bated if the potential mates are all closely related to the choosing individual or to each other Ryan 2000 found that when given a choice of unfamiliar distantly related females in a Y apparatus male Peromyscus polionotus rhoad si mice preferred the less related female even when differ ences in kinship averaged only f 0 013 about the level of second cousins When subsequently paired with one or the other female from the choice test breeding was delayed and litter sizes w
52. it Always use parentheses to specify the order in which operations are to be performed Parentheses brackets and braces may be used interchangeably to indicate the order of operations Functions cannot contain any spaces or extraneous punctuation Case of function names and variables is ignored All letters that are entered in a function within the Function Editor are converted to upper case by VORTEX It can be difficult to correctly specify the function that describes the relationship you want for a demographic rate To help you confirm that you have specified the correct function VORTEX can display a simple x y Function Preview plot of any function entered into the Function Editor From the drop down list above the graph you must select which dependent variable from your function should be plotted along the x axis The plot will show the relationship to the selected x variable with each other dependent variable fixed at some simple value e g sex female K 100 N 100 numbers of males females juveniles and subadults 50 iteration 1 year 1 population 1 gene diversity 100 inbreeding 0 You can change the range and increment of the x axis if you wish The Function Preview graph will not display until you click the Update Graph command If you know how to read reverse Polish notation for functions you can click the command to Show Polish Notation in order to confirm that VORTEX is interpreting the pa
53. l ZPG1 Population 1 gp ZPG1 Population 1 c 2 ss Note if legend doesn t show make the window larger Add SE bars Add SD bars Graph Title Mean N all Font X Axis Title Years Y Axis Title lt i Print Graph Send to Report Export Graph Graph Line Thickness Vortex 9 21 caps NUM INS Date Time 10 24 03 9 23AM Figure 13 A Data Graph You should note that you have the option of adding bars to your graph to show standard errors SE of the means or standard deviations SD across the iterations Click on the Add SD bars command to see these bars Finally to wrap up our Quick Tour of VORTEX click on the Project Report tab This will take you to a note pad that contains information we have sent to the Report from other screens Figure 14 You will need to use the scroll bar or your cursor to move up and down through your Project Report Any information in the Project Report can be edited using standard Windows editing tools delete cut paste font settings etc The Project Report is saved in Rich Text Format and rtf file and it can be edited in Word or other programs Chapter 2 19 Getting Started with VORTEX VORTEX Version 9 User s Manual 4 Vortex Stochastic Simulation of the Extinction Process gt O x File Edit Vortex Window Help DseisBe amp ove AL f242PG C Yortex9 ZPG 2PG vpj Project Settings Simulation Input Text Output Graphs
54. no other species have been studied in sufficient detail to quantify the contributions of different types of alleles to inbreeding depression but the scant data available are not inconsistent with about half of the inbreeding effects being due to lethals in other species as well In summary if you don t know what to enter for inbreeding depression in Vortex use the default values of 3 14 lethal equivalents the median of 40 mammalian populations surveyed by Ralls et al 1988 with 50 of that due to lethal alleles 30 Chapter 3 The Data Input Process VORTEX Version 9 User s Manual VORTEX runs much more slowly when inbreeding depression is included and is modeled with less than 100 of the impact due to lethal recessives see below This is because the program will EF need to calculate and store all pairwise kinships among individuals in the population N2 kinships where N is the maximum population size attained Therefore if your population is expected to remain moderately large perhaps gt 250 so that inbreeding will be a rare event you may want to obtain much greater speed by assuming in your model that inbreeding has no impact on fitness VORTEX includes a detailed simulation of genetic change in the populations At the beginning of a simulation each founder individual is assigned two unique alleles at each of a number of loci Each offspring is then randomly assigned one of the two alleles from each parent at each locus VO
55. of genetic decay for comparison across scenarios and populations The mean observed heterozygosity reported by VORTEX is the mean inbreeding coefficient of the population 9 For each of the10 alleles at five non neutral loci that are used to model inbreeding depression each founder is assigned a unique lethal allele with probability equal to 0 1 x the mean number of lethal alleles per individual 10 Years are iterated via steps 11 through 25 below 11 The probabilities of females producing each possible size litter are adjusted to account for density dependence of reproduction if any 12 Birth rate survival rates and carrying capacity for the year are adjusted to model environmental variation Environmental variation is assumed to follow binomial distributions for birth and death rates and a normal distribution for carrying capacity with mean rates and standard deviations specified by the user At the outset of each year a random number is drawn from the specified binomial distribution to determine the percent of females producing litters The distribution of litter sizes among those females that do breed is maintained constant Another random number is drawn from a specified binomial distribution to model the environmental variation in mortality rates If environmental variations in reproduction and mortality are chosen to be correlated the random number used to specify mortality rates for the year is chosen to be the same percentile
56. population the observed variance around the mean survivorship of 0 733 was 0 047 The variance that would be expected from random binomial sampling based on this mean is 0 013 The difference V 0 034 or SD 0 184 can be attributed to environmental variation Mortality after the first year can similarly be determined from either data on banded birds of known age or from winter census reports from Aransas filed since 1938 young of the year are distinguishable from older birds upon arrival at Aransas Since 1938 a total of 2359 birds older than 1 year of age returned to Aransas out of a total of 2594 birds that departed Aransas the previous spring This yields an estimated annual mortality after the first year of 9 06 Among the banded birds 89 9 annual survival was observed in 386 bird years but band loss after several years could have accounted for some of the mortality recorded among banded individuals No variation was detectable statistically among mortality rates calculated separately for each age class beyond the first year The observed annual variation in survival rates from 1938 to 1990 was V 0 00255 the variation expected due to binomial sampling from a constant probability is V 0 00220 The difference can be attributed to environmental variation in the probability of surviving with V 0 00035 or SD 0 019 This value turned out to be very close to the intuitive estimate provided by workshop participants that annu
57. primary focus of concern In order to understand and predict the vulnerability of a wildlife population to extinction we need to use a model which incorporates the processes which cause fluctuations in the population as well as those which control the long term trends in population size Many processes can cause fluctuations in population size variation in the environment such as weather food supplies and predation genetic changes in the population such as genetic drift inbreeding and response to natural selection catastrophic effects such as disease epidemics floods and droughts decimation of the population or its habitats by humans the chance results of the probabilistic events in the lives of individuals sex determination location of mates breeding success survival and interactions among these factors Gilpin and Soul 1986 Models of population dynamics which incorporate causes of fluctuations in population size in order to predict probabilities of extinction and to help identify the processes which contribute to a population s vulnerability are used in Population Viability Analysis PVA For the purpose of predicting vulnerability to extinction any and all population processes that impact population dynamics can be important Much analysis of conservation issues is conducted by largely intuitive assessments by biologists with experience with the system Assessments by experts can be quite valuable and are often contrasted
58. s Manual 4 Vortex Stochastic Simulation of the Extinction Process File Edt Vortex Window Help Osc el S e Fs gt i Page D WORTEXS4 ZPG 2PG Ypi Project Settings Simulation Input Text Output Graphs and Tables Project Report Input Summary fe sil Output Summary Other Output Send text to Report Print Save s Send Graph to Report Print Export Scenario to view zp Population to display Population 1 5 Deterministic projections assume no stochastic fluctuations no inbreeding depression no limitation of mates no harvest and no supplementation Deterministic projections may not be meaningful if some rates change over time or are specified to be functions of other parameters Scenario ZPG1l Z 5 D _ oO i O a Population 1 Population 1 Deterministic population growth rate r 0 001 lambda 0 999 RO 0 997 Generation time for females CAPS NUM INS Date Time 10 24 03 10 454M Figure 41 Deterministic Calculations shown in Text Output also given See Box G for a brief description of these deterministic calculations The graph given with the Deterministic Calculations is fairly simple and crude but it shows the exponential growth or decline projected from the life table calculations up to the limit set by the carrying capacity The graph can be sent to your Project Report printed or exported to a bitmap bmp file for import into othe
59. small Caugh ley called for more theory to guide the declining popula tion approach more data to support the small population approach and better use of the strengths of the two ap proaches to guide conservation but he also questioned whether too much emphasis has been given to small popu lation processes in wildlife conservation Hedrick et al 1996 argued that the problems of small populations have at times been under appreciated but also that the process es causing population declines and the processes affecting populations that have become small are inter linked in complex ways so that PVA and conservation biology must encompass both of Caughley s paradigms The problems of small populations have received exten sive theoretical treatment e g Soul 1987 but further assessment of the factors affecting viability of very small populations is needed I will argue that we often underesti mate the importance of these factors in population viabili ty as the magnitude and even direction of some of these effects may be different than has been commonly sup posed Although I believe that the problems inherent in small populations are more numerous and more severe than is commonly recognized the same may be true of the causes of population decline However because additional threats to population viability arise as populations become small the kinds of PVA models that are needed for assess ing the status and recovery options for
60. small popula tions are considered rates of loss of genetic variation and accumulation of inbreeding can be much faster than has been suggested before These processes can be examined in detailed individual based PVA models Accurate data to parameterize these models however are often not available Thus we need to interpret cautiously PVA conclusions for populations that are small highly fragmented or projected for many generations R C Lacy rlacy ix netcom com Dept of Conservation Biology Daniel E amp Ada L Rice Center Chicago Zoological Society Brookfield IL 60513 USA There are many kinds of threats to the viability of populations of wildlife The processes which have driven many once abundant populations down to one or few small populations in scattered remnants of habitat include direct exploitation over harvest habitat destruction and fragmentation degradation of habitat quality introduc tion of exotic species and chains of extinction Caughley 1994 Often after precipitous declines occur conserva tion biologists and governmental agencies establish recov ECOLOGICAL BULLETINS 48 2000 ery actions to try to prevent local extirpation of populations or the ultimate extinction of the taxon As wildlife populations become smaller additional threats to stability and persistence arise which can exacer bate the difficulty of stopping or reversing a decline These problems of small populations generally result f
61. that a ran dom number is generated from the uniform 0 1 distribu tion or from a unit normal distribution Explanatory comments following pseudo code sec tions are preceded by More extensive explanations are given in notes following the code As an individual based PVA simulation model VOR TEX represents each individual in memory simulates life events such as sex determination breeding mortality and _ dispersal which could occur to each individual and mon itors the status of each individual and the population as a whole The characteristics tracked for each animal are sex alive dead status population membership age inbreeding coefficient and two alleles at each of six loci In addition VORTEX maintains a matrix of kinship coefficients be tween all pairs of living animals as this provides inbreeding coefficients for any offspring VORTEX models changes to a population as a series of discrete events that occur once per year or other time in terval The annual sequence of demographic events is ECOLOGICAL BULLETINS 48 2000 breeding mortality age 1 yr migrate disperse among populations harvest managed removals supplementa tion managed additions carrying capacity truncation census Fig 1 Occurrences of events are probabilistic demographic stochasticity emerges from chance variation in which individuals breed die and are of each sex Envi Start Read in parameters Set Iteration 1 ee
62. the Mantled Howler Monkey Alouatta palliata mexicana Apple Valley MN Conservation Breeding Specialist Group SSC IUCN Rylands A K Strier R Mittermeier J Borovansky and U S Seal eds 1998 Population and Habitat Viability Assessment Workshop for the Muriqui Brachyteles arachnoides Apple Valley MN Conservation Breeding Specialist Group SSC IUCN Seal U S ed 1992a Bali Starling Population Viability Assessment Report Apple Valley MN Captive Breeding Specialist Group SSC IUCN Seal U S ed 1992b Black Footed Ferret Recovery Plan Review Apple Valley MN Captive Breeding Specialist Group SSC TUCN Seal U S ed 1992c Genetic Management Strategies and Population Viability of the Florida Panther Felis concolor coryi Apple Valley MN Captive Breeding Specialist Group SSC TUCN Seal U S ed 1994a Attwater s Prairie Chicken Population and Habitat Viability Assessment Apple Valley MN Captive Breeding Specialist Group SSC IUCN Seal U S ed 1994b Houston Toad Population and Habitat Viability Assessment Report Apple Valley MN Conservation Breeding Specialist Group SSC TUCN Seal U S ed 1994c Population and Habitat Viability Assessment for the Greek Population of the Mediterranean Monk Seal Monachus monachus Apple Valley MN Captive Breeding Specialist Group SSC TUCN Seal U S ed 1996 Kirtland s Warbler Dendroica kirtlandii Population and Habitat Viabi
63. the predictions made from PVA models should be considered to be projections about what would most likely happen to the population if various hypotheses about the status of the populations and the threats are true Conservation and management decisions must be made based on the most plausible hypotheses about the population status before sufficient data could be collected to test those hypotheses scientifically An important advantage of PVA models is that they forced systematic consideration and specification of the assumptions and hypotheses that must be made in the absence of adequate data This facilitates careful reassessment and improvement in the analyses as better data become available Questions that can be explored with PVA models Below are some of the conservation and management questions that can be explored by Population Viability Analysis modeling References describing uses of VORTEX give many examples of these and other applications of PVA techniques to guide conservation Using the best current information on the biology of the taxon and its habitat are the populations projected to persist if conditions remain as they are now Beyond just the persistence of the population what is the most likely average population size range of population sizes across years and rate of loss of genetic variation If the population is at risk of extinction is the extinction expected to result primarily from negative average population growth mean de
64. to assist with wildlife management and endangered species recovery 2 Chapter 1 Introduction VORTEX Version 9 User s Manual gt Appendix II LITERATURE CITED provides a complete listing of the scientific literature referenced throughout this User s Manual gt Appendix III VORTEX BIBLIOGRAPHY includes what we hope is a reasonably complete list of references to papers that discuss VORTEX as a tool for population viability analysis and to those specific examples of the use of VORTEX in PVAs across a diverse taxonomic range Authors wishing to have their publications listed in future editions of this manual should email the citations to help vortex9 org gt Appendix IV REPRINTS provides copies of two papers that describe in detail the structure of the VORTEX model and some of the concepts behind the model Throughout the text you will find various aids that will enhance your overall use of VORTEX EF Brief explanatory notes that will help you remember important points clarify some commonly used terms etc Text boxes that will provide additional information on general concepts in population biology and genetics statistics and simulation modeling Case Studies that show you real examples of how data have been used to develop VorRTEX simulation models These case studies are gleaned from the many Population and Habitat Viability Assessment PHVA workshops conducted by CBSG over the past decade A Note about Regio
65. to mam mal and bird species and the bias toward these groups in examples below reflect my greater experience with PVA of these taxa Processes destabilizing small populations Shaffer 1981 categorized the stochastic threats to small populations demographic stochasticity environmental stochasticity natural catastrophes and genetic stochasticity These causes of uncertainty and fluctuation in population size interact but they are conceptually distinct Demographic stochasticity Demographic stochasticity is the random variation in the numbers of births number of deaths and sex ratio in a population that results from the fates of individuals being independent outcomes of probabilistic events of reproduc tion mortality and sex determination Shaffer 1981 The observed variation across years or across populations with constant probabilities would be distributed as binomial distributions If fates of individuals are independent then demographic stochasticity is intrinsic to the population and is a simple consequence of the sampling that occurs as individuals are subjected to the population rates Figure 1 shows the percent of whooping cranes Grus americana each year from 1938 to 1994 that failed to return the following year to the wintering grounds in Texas Al though some variation in mortality was due to environmen tal variation and likely catastrophes see below most of the variation in survival across years can be ac
66. v a 10 0 f 0 0 a 0 10 20 30 40 50 60 70 80 90 100 Year of Simulation 13 Regular pulses of a higher rate RATE Y 8 0 20 30 Background rate of 30 jumps to 50 every 8th 50 0 F year Note that the order of operators was left 45 0 to the VORTEX default left to right This is g 40 0 not a safe practice but it does work in this 35 0 case 2 300 25 0 8 200 1s0l a 10 0 L 5 0 0 0 O 10 20 30 40 50 60 70 80 90 100 Year of Simulation 94 Chapter 5 Using Functions in VORTEX 14 15 16 17 VORTEX Version 9 User s Manual Pulses of longer duration RATE C 8 lt 3 20 30 The rate jumps to 50 for a 3 year time span 50 0 every 8th year In this case parentheses were 45 0 L used wisely to be sure that the intended order of operators was followed 40 0 35 0 30 0 25 0 20 0 15 0 10 0 5 0 0 0 Demographic Rate 0 10 20 30 40 50 60 70 80 90 100 Year of Simulation Random pulses catastrophes RATE 50 20 SRANDCY R 100 lt 0 05 The background rate of 50 drops to 30 on 50 0 average once every 20 years A seeded 45 0 random number is needed otherwise the o 400l years in which the rate drops would be E aol independent among individuals effectively 2 30 0 the rate would continuously be 49 The seed 25 0 of Y R 100 causes a different seed to be 20 0 used for each year of each iteration if there 5 15 0 are
67. value for K could drop to zero during your simulation resulting in an unwanted extinction event If you re not convinced see Box C for an explanation of why this is so Trend in K VORTEX allows you to simulate changes in the carrying capacity Such changes may be positive or negative and result from human activities such as resource utilization or corrective management strategies or from intrinsic ecological processes such as forest succession To include a trend in carrying capacity check the box Then specify the time period during which the trend will occur and the annual rate of change in K The trend will begin in year and continue for the specified duration The program will model a liner trend over this time period Note more complex patterns of changing K can be specified by entering a function in the box for Carrying Capacity see Chapter 5 Chapter 3 59 The Data Input Process VORTEX Version 9 User s Manual Box F What Exactly Zs Carrying Capacity Anyway Carrying capacity rarely in the field of resource management has a term been so frequently used to the confusion of so many MacNab 1985 The definition and use of the concept of carrying capacity is one of the more tricky issues in population viability analysis and for that matter in much of population ecology Pick up any number of textbooks on ecology or wildlife management and you are likely to find that each one presents a slightly different formal
68. want to use Excel to generate your dispersal rate matrix rather than typing in all 1560 pairwise dispersal rates The commands to Make Cells Square and Make Cells Original Shape are simply there to help you show the grid in a format that is easier for you to view The fifth command available allows you to apply a multiplier to each non diagonal cell in the grid By entering a value and hitting Apply Multiplier of you can shift all of the dispersal rates upwards or downwards This makes it much easier to test a range of dispersal rates across Scenarios of your Project For example you might enter an initial set of rates and then apply multipliers of 0 2 and 4 in order to test no dispersal and 2x and 4x increases in dispersal VORTEX provides you with significant flexibility in defining dispersal rates for individuals within a metapopulation That is rates may be inversely proportional to distance directly proportional to habitat area or they may be defined through a more complex determining function However you have the task of calculating these rates for each pair of populations VORTEX does not calculate them for you based on a set of internal rules A considerable body of literature exists on the methods for estimating dispersal rates between populations Capture recapture studies can provide some of the best data for this process of estimation although experimental difficulties do exist see Ims and Yoccoz 1997 for more
69. ware tools as more people use the programs and compare the generated results to expectations from statistical theory and to results for simple and well known cases Also users of statistical software are expected to be sufficiently famil iar with the methods of statistical analysis to be able to choose appropriate models to apply to their problem to be able to provide the proper input and to be able to interpret the results Unlike the situation for statistical methods however there are not yet widely accepted and published accounts of standard methods for population viability analysis The methods of population based models e g Starfield and Bleloch 1986 Burgman et al 1993 are extensions of the methods of population ecology and demography e g Pie lou 1977 Caswell 1989 but many details of model con struction require decisions about algorithms and methods that are not fully delineated in general treatments The methods of individual based PVA models have been only cursorily described in the scientific literature Below is an outline of one widely used PVA software package VOR TEX ver 8 20 The basic approach taken in the VORTEX model is described in Lacy 1993 in Lindenmayer et al 2000 and other papers describing applications of VOR TEX and in the software manual Miller and Lacy 1999 Detailed documentation of the program flow and algo rithms is provided here so that users of VORTEX can con firm that the model is
70. with models used to evaluate population vulnerability to extinction Such a contrast is not valid however as any synthesis of facts and understanding of processes constitutes a model even if it is a mental model within the mind of the expert and perhaps only vaguely specified to others or even to the expert himself or herself A number of properties of the problem of assessing vulnerability of a population to extinction make it difficult to rely on mental or intuitive models Numerous processes impact population dynamics and many of the factors interact in complex ways For example increased fragmentation of habitat can make it more difficult to locate mates can lead to greater mortality as individuals disperse greater distances across unsuitable habitat and can lead to increased inbreeding which in turn can further reduce ability to attract mates and to survive In addition many of the processes impacting population dynamics are intrinsically probabilistic with a random component Sex determination disease predation mate acquisition indeed almost all events in the life of an individual are stochastic events occurring with certain probabilities rather than with absolute certainty at any given time The consequences of factors influencing population dynamics are often delayed for years or even generations With a long lived species a population might persist for 20 to 40 years beyond the emergence of factors that ultimately cause ext
71. you have specific data indicating a different genetic load you can enter it here Percent Due to Recessive Lethals Enter here the percent of the total genetic load quantified by the lethal equivalents you entered into the previous box that is due to recessive lethal alleles The number of lethal alleles per founder is limited to 10 therefore the product of the number of lethal equivalents and the percent of the total genetic load attributable to lethals cannot exceed this number The lethal alleles are distributed randomly among 10 autosomal loci thus the number of lethals per founder will be distributed approximately as a Poisson distribution A plausible value one that is consistent with data on Drosophila and a few other species that have been studied well would be 50 However cases have been reported in which nearly all of the genetic load is due to lethals while in other populations virtually none of the effects of inbreeding appears consistent with the action of recessive lethal alleles Lacy et al 1996 You may wish to test low and high values to see if it affects your simulations of population dynamics It probably won t because it is difficult to maintain a population for long at the very small population sizes at which effective purging of recessive lethal alleles would occur EV Concordance of Reproduction amp Survival Environmental variation EV is the annual variation in the probabilities of reproduction an
72. you need to create run and analyze scenarios that vary from your initial case for one or a few input parameters One way to do this would be to start from the beginning and create a new analysis in VORTEX However the program makes it very easy for you to copy all input from a prior Scenario into one or more new Scenarios in your Project In these newly copied Scenarios you can then change the few input parameters that you want to vary and re run the simulations for each case Adding Scenarios to Your Project To add a scenario from any Simulation Input window click on the Add Scenario command in the upper left The pop up window shown in Figure 37 will appear New Scenario Which data would you like the new scenario to have initially Create fi scenarios based on the scenario selected above General purpose scenarios Sensitivity Analysis Ok Cancel Figure 37 New Scenario window for adding Scenarios based on a prior Scenario Click on the existing Scenario that you want to use as a template for new Scenarios then select below the number of copies you wish to create of this Scenario and then click on OK You may notice that there 66 Chapter 3 The Data Input Process VORTEX Version 9 User s Manual is a disabled option for Sensitivity Analysis This option has not yet been implemented but it will in a later version provide you with a more automated way to create new Scena
73. 0 Pow 10 0 2 MAX 3 12 4 2 MIN 3 12 4 2 MOD 33 10 3 1 6 3 0412 10A0 20412 4 21 3 12 33 10 3 MOD 33 5 5 1 60 0 0 0 0 1 1 1 3 2 0 FALSE I 3 4 1 TRUE 3 4 3 4 AND 3 4 3 4 0R 3 4 3 gt 4 0 3 lt 4 3 gt 3 1 3 lt 3 1 SINC PI 2 0 COS PI 2 0 TAN PI 4 0 ASINC1 0 5707963 ACOS 0 0 5707963 ATAN 1 0 0 7853981 SIN PI 4 0 LNCE 1 0 10 gt 5 TRUE ITRUE FALSE 7071067 RAND 0 2341 or 0 8714 or 0 9151 or NRAND 0 512 or 0 716 or 2 376 or A seeded random number generator hence SRAND X provides a random number between 0 and 1 with a given seed value X A seeded random normal deviate hence SNRAND X returns a number from a 0 1 normal distribution with the seed value x Chapter 5 87 Using Functions in VORTEX VORTEX Version 9 User s Manual Using Random Numbers in Functions Random number generators can be used to create a wide variety of stochastic events for example a 5 year drought that occurs on average once every 30 years but the proper use of these functions requires careful consideration of how the seed values implicit as in RAND and NRAND or explicit as in SRAND and SNRAND determine when new random numbers are selected Repeated calls to the random number return the same value if the same seed is specified Random numbers produced with different even s
74. 0 A 1 0 10 20 30 40 50 60 70 80 90 100 Population Size N 46 Chapter 3 The Data Input Process VORTEX Version 9 User s Manual formulation Fowler 1981 suggests that density dependence in reproductive success can often be modeled quite well with a quadratic function that is with B 2 It is best to derive the values of P 0 P X A and B from a regression analysis of data on the breeding rate of your population If these data are unavailable but you can estimate P 0 and P K then you may want to explore several different combinations of A and B to come up with a curve that seems appropriate for your population You could use graphics or statistical software or even graph paper and a calculator to construct a range of hypothetical curves using different combinations of parameters as was done to produce Figure 24 In any event once you have decided on a particular set of parameters to use you should always graph the resulting curve to verify that it represents the mode of density dependent behavior you are looking for After you have entered the appropriate parameters as shown on Figure 25 below VORTEX can display a graph of the specified density dependence function for you so that you can verify the intended nature of the relationship Select the population from the drop down list and then hit the View command to see your graph Note you will need to specify at the bottom of the graphing box that you want to plot
75. 0 149 161 Alvarez K 1993 Twilight of the Panther Biology Bureaucracy and Failure in an Endangered Species Program Myakka River Publ Sarasota Florida Ballou J D 1983 Calculating inbreeding coefficients from pedigrees Pages 509 520 in Schonewald Cox C M S M Chambers B MacBryde and W L Thomas eds Genetics and Conservation A Reference for Managing Wild Animal and Plant Populations Menlo Park California Benjamin Cummings Ballou J D 1997 Ancestral inbreeding only minimally affects inbreeding depression in mammalian populations Journal of Heredity 88 169 178 Ballou J D R C Lacy D Kleiman A Rylands and S Ellis eds 1997 Leontopithecus II The Second Population and Habitat Viability Assessment for Lion Tamarins Leontopithecus Apple Valley MN Conservation Breeding Specialist Group SSC ITUCN Belovsky G E 1987 Extinction models and mammalian persistence Pages 35 57 in Soul M E ed Viable Populations for Conservation Cambridge Cambridge University Press Berger J 1990 Persistence of different sized populations an empirical assessment of rapid extinctions in bighorn sheep Conservation Biology 4 91 98 Bonaccorso F P Clark P S Miller and O Byers eds 1999 Conservation Assessment and Management Plan for the Tree Kangaroos of Papua New Guinea and Population and Habitat Viability Assessment for Matschie s Tree Kangaroo Final Report Apple Valley MN Conservation Breedin
76. 0 5 Set UpperLimit 1 200 Set LowerLimit Rate 1 Rate ELSE Set UpperLimit 2 Rate Set LowerLimit 0 END IF ELSE Add EV EVNRand to Rate Let Rate max LowerLimit Rate Let Rate min UpperLimit Rate END IF ELSE END FUNCTION ADJUSTRATE BEGIN FUNCTION MIGRATE FOR each living animal IF not in age range that migrates CONTINUE LOOP with next animal END IF IF not a sex that migrates CONTINUE LOOP with next animal END IF Set MigrationRand RAND Set pSource to population of current animal IF MigrationRand gt CumulativeMigrationProb pSource NumberPopulations CONTINUE LOOP with next animal Does not migrate END IF Obtain MigrationDensity by evaluating function or using specified constant parameter I See Note 3 IF PopulationSize pSource CarryingCapacity pSource lt MigrationDensity CONTINUE LOOP with next animal END IF Obtain MigrationSurvival by evaluating function or using specified constant parameter 1 See Note 3 Find to which population the animal migrates FOR up to 10 attempts to enter another population The limit of 10 attempts is imposed to prevent an infi nite loop from occurring when all populations are at carry ing capacity IF RAND gt MigrationSurvival Animal dies BREAK from LOOP CONTINUE with next animal END IF FOR each population pDestination IF MigrationRand lt CumulativeMigrationProb pSource pDest
77. 10 By condensing a series of mortality events from the very early stages of the mussel s life cycle the authors were able to define a system of reproduction that was amenable to the Vortex modeling system Other types of organisms that would benefit from this type of simplification include amphibians fish and even insects Sex Ratio at Birth Enter here a number between 0 0 and 100 0 to represent the average percentage of newborn offspring that are male This number is typically very near 50 signifying a roughly equal male female sex ratio at birth If relatively more or fewer males are born to a given female per year enter the appropriate percentage e g 55 for 55 males Density Dependent Reproduction Does the reproductive rate of your species change with changing population size That is is reproduction low when the population is small due to a difficulty in finding mates or conversely does reproduction drop off when the population is large more specifically at high density due to limited resources or territories intraspecific competition crowding stress etc If so check the box and then enter the subsequent parameters defining the nature of the density dependence If your population s reproduction is density dependent you will need to model this relationship VORTEX models density dependence with an equation that specifies the proportion of adult females that reproduce as a function of the total population size Normal
78. 100 or fewer years The above function is 10 0 equivalent to specifying a catastrophe with 5 0 F frequency 5 and severity 0 60 0 0 Wt E 0 10 20 30 40 50 60 70 80 90 100 Year of Simulation Random pulses independent among populations RATE 50 20 CSRAND Y R 100 100 SRAND P lt 0 05 The catastrophes are independent among populations because each population P sets a new and random seed for the random number generator which tests whether the catastrophe occurs Careful use of parentheses or brackets is critical in this function in order to ensure that the random number seeds work as intended Catastrophes affecting only selected age class es RATE 50 A lt 3 20 CSRAND Y R 100 lt 0 05 The catastrophe affects only individuals of ages 1 and 2 The 2 D graphs of this function do not illustrate the age dependent relationship The graphs against Y and R set A 1 and show the catastrophes affecting young individuals while the graph against A happens to display a year and iteration Y R 1 in which no catastrophe for any age occurs Chapter 5 95 Using Functions in VORTEX VORTEX Version 9 User s Manual 18 19 20 96 Multi year catastrophes RATE 50 20 SRAND Y 2 R 100 lt 0 10 The catastrophes have a 2 year impact 90 0 F because the seed value is converted to an 80 0 L integer giving pairs of subsequent years the o 700l same random number The frequency per ye
79. 143 158 Lacy R C 1993 1994 What is population and habitat viabil ity analysis Primate Conserv 14 15 27 33 Lacy R 1996 Further population modelling of northern white rhinoceros under various management scenarios In Foose T J ed Summary Appendix 3 Northern White Rhinoc eros Conservation Strategy Workshop International Rhino Foundation Cumberland Ohio pp 1 15 Lacy R C 1997 Importance of genetic variation to the viability of mammalian populations J Mammal 78 320 335 Lacy R C 2000 Structure of the VORTEX simulation model for population viability analysis Ecol Bull 48 191 203 Lacy R C and Lindenmayer D B 1995 A simulation study of the impacts of population subdivision on the mountain brushtail possum Trichosurus caninus Ogilby Phalangeri dae Marsupialia in south eastern Australia II Loss of ge netic variation within and between subpopulations Biol Conserv 73 131 142 Lacy R C and Ballou J D 1998 Effectiveness of selection in reducing the genetic load in populations of Peromyscus po lionotus during generations of inbreeding Evolution 52 900 909 Lacy R C and Miller P S 2001 Managing the human animal incorporating human populations and activities into PVA for wildlife conservation In Beissinger S and McCul lough D R eds Population viability analysis Univ of Chicago Press in press Lacy R C Alaks G and Walsh A
80. 167 p Miller P S and R C Lacy 1999 VORTEX Version 8 users manual A stochastic simulation of the simulation process Apple Valley MN Conservation Breeding Specialist Group SSC IUCN Mills L S S G Hayes C Baldwin M J Wisdom J Citta D J Mattson and K Murphy 1996 Factors leading to different viability predictions for a grizzly bear data set Conservation Biology 10 863 873 Mills M G L S Ellis R Woodroffe A Maddock P Stander A Pole G Rasmussen P Fletcher M Bruford D Wildt D Macdonald and U S Seal eds 1998 Population and Habitat Viability Assessment for the African Wild Dog Lycaon pictus in Southern Africa Final Workshop Report Apple Valley MN Conservation Breeding Specialist Group SSC IUCN Mirande C R Lacy and U Seal eds 1991 Whooping Crane Grus americana Conservation Viability Assessment Workshop Report Apple Valley MN Captive Breeding Specialist Group SSC IUCN Molur S R Sukumar and S Walker eds 1995 Great Indian One Horned Rhinoceros Population and Habitat Viability Assessment Report Apple Valley MN Conservation Breeding Specialist Group SSC IUCN Novellie P A P S Miller and P H Lloyd 1996 The use of VORTEX simulation models in a long term programme of re introduction of an endangered large mammal the Cape mountain zebra Equus zebra zebra Acta Ccologica 17 657 671 Odum A et al eds 1993 Aruba Island Rattlesnake Population and Hab
81. 1985 Carrying capacity and related slippery shibboleths Wildlife Society Bulletin 13 403 410 Maguire L A 1986 Using decision analysis to manage endangered species populations Journal of Environmental Management 22 345 360 Maguire L A R C Lacy R J Begg and T W Clark 1990 An analysis of alternative strategies for recovering the eastern barred bandicoot in Victoria Pages 147 164 in Clark T W and J H Seebeck eds Management and Conservation of Small Populations Brookfield IL Chicago Zoological Society Maier W L 1991 A fast pseudo random number generator Dr Dobb s Journal May 1991 152 7 Manansang J A MacDonald D Siswomartono P S Miller and U S Seal eds 1996 Population and Habitat Viability Assessment for the Babirusa Babyrousa babyrussa Apple Valley MN Conservation Breeding Specialist Group SSC IUCN Mirande C R Lacy and U Seal eds 1991 Whooping Crane Grus americana Conservation Viability Assessment Workshop Report Apple Valley MN Captive Breeding Specialist Group SSC TUCN Morton N E Crow J F and Muller H J 1956 An estimate of the mutational damage in man from data on consanguineous marriages Proceedings of the National Academy of Sciences USA 42 855 863 O Brien S J and Evermann J F 1988 Interactive influence of infectious diseases and genetic diversity in natural populations Trends in Ecology and Evolution 3 254 9 Odum A et al eds 1993 Arub
82. 1996 Hierarchical analysis of inbreeding depression in Peromyscus polionotus Evolu tion 50 2187 2200 Lande R 1988 Genetics and demography in biological conser vation Science 241 1455 1460 Lande R 1995 Mutation and conservation Conserv Biol 9 782 791 Lindenmayer D B and Lacy R C 1995 Metapopulation via bility of Leadbeater s possum Gymnobelideus leadbeateri in fragmented old growth forests Ecol Appl 5 164 182 Lindenmayer D B etal 1995 A review of the generic computer programs ALEX RAMAS space and VORTEX for model ling the viability of wildlife populations Ecol Model 82 161 174 ECOLOGICAL BULLETINS 48 2000 Lindenmayer D B McCarthy M A and Pope M L 1999 Arboreal marsupial incidence in eucalypt patches in south eastern Australia a test of Hanski s incidence function meta population model for patch occupancy Oikos 84 99 109 Lindenmayer D B Lacy R C and Pope M L 2000 Testing a simulation model for population viability analysis Ecol Appl 10 580 597 Lynch M and Walsh B 1998 Genetics and analysis of quanti tative traits Sinauer Margolis H 1996 Dealing with risk Why the public and the experts disagree on environmental issues Univ of Chicago Press Menges E S 2000 Applications of population viability analyses in plant conservation Ecol Bull 48 73 84 Miller P S 1994 Is inbreeding depression mo
83. 2 cenario Settin species caer Mate Monopolization abelis and State Vars Degree of Monopolization of Mating Opportunities Reproductive System Reproductive Rates ortality Rates Provide one of the following measures The program will calculate the equivalent values of the other two for you Population 1 Population 2 ee Males in Breeding Pool 50 50 ate Monopolization Males Successfully Siring Offspring 31 6 31 6 nitial Population Size Mean of Mates Successful Sire 1 6 1 6 arrying Capacity upplementation Copy input values from Population 1 z This Section to subsequent populations Copy Input Values don t know what of males are breeding Vortex 9 21 Enter the percent of males which are physically physiologically and socially capable of breeding Ud NUM INS Date Time 10 24 03 10 16AM 4 CAPS Figure 30 Mate Monopolization input section Initial Population Size In this section of input Figure 31 you specify the number of individuals at the start of your simulation Stable Age Distribution Specified Age Distribution You have two options for entering initial population sizes If you do not know the precise age class distribution in your population as is usually the case you can initialize your population according to the stable age distribution see Box G in Chapter 4 for a definition of and methods for calculating this distribution If you select the st
84. 20 pairs of the middle spotted woodpecker Dendrocopos medius which had been isolated 30 yr before Pettersson 1985 In Finland Sac cheri et al 1998 found that local populations of the Glanville fritillary butterfly Melitaea cinxia with lower het erozygosity indicative of greater inbreeding had lower egg hatching rate larval survival and adult longevity Ap parently as a consequence these populations had much higher probabilities of extinction Following Franklin 1980 and Soul 1980 only pop ulations with effective sizes below ca 50 have been com monly perceived to be at risk of significant inbreeding de pression To have an effective population size of 50 a typi cal natural population of a large mammal might need a total population size of ca 200 It is worth reconsidering the likely cumulative effects of inbreeding on the viability of such a population Inbreeding would accumulate at a rate of 1 per generation After 10 generations the 10 cumulative inbreeding may cause a 5 20 reduction in survival and in fecundity Ralls et al 1988 Lacy et al 1996 Lynch and Walsh 1998 The consequent reduction in population growth would be sufficient to cause low fe cundity species to decline Yet many wildlife managers with responsibility for populations of approximately this size assume that they can ignore effects of inbreeding and most PVA models for populations of such size omit the impacts of inbreeding on demography
85. 22 23 VORTEX Version 9 User s Manual Linear density dependence RATE 50 K N K The rate declines from 50 at N 0 to 0 when 50 0 N K 45 0 40 0 35 0 30 0 25 0 20 0 L 15 0 10 0 5 0 0 0 0 Demographic Rate 10 20 30 40 50 60 70 80 90 100 Population Size Density dependence used as the default for breeding in VORTEX RATE 50 20 N K A4 N C1 4N The rate peaks near 50 when N is small declines at higher densities and is 30 when N K At very small N the rate is also depressed For example it is reduced by 50 when N 1 and reduced by 25 when N 3 In terms of the coefficients that can be entered into the optional density dependence for breeding in VORTEX PCO 50 PCK 30 B 4 and A 1 Demographic Rate 0 10 20 30 40 50 60 70 80 90 100 Population Size Sex specific dispersal rates RATE D S M ORCRAND gt 0 35 If the above function is used for the Dispersal Modifier Function then 35 of the females are prevented from dispersing Thus dispersal rates for females are effectively reduced by 35 relative to male dispersal An unseeded random number is used so that dispersal will be determined independently each female Note that the dispersal rates entered subsequently D will be those applied to males with females having lower rates A similar approach can be used to create age specific dispersal rates or dispersal mortality C
86. 3 275 296 Matamoros Y G Wong and U S Seal eds 1996 Population and Habitat Viability Assessment Workshop for Saimiri oerstedi citrinellus Final Report Apple Valley MN Conservation Breeding Specialist Group SSC AUCN Mathews F and D W Macdonald 2001 The sustainability of the common crane Grus grus flock breeding in Norfolk Insights from simulation modeling Biological Conservation 100 3 323 333 McCann K A Burke L Rodwell M Steinacker and U S Seal eds 2000 Population and Habitat Viability Assessment for the Wattled Crane Bugeranus carunculatus in South Africa Apple Valley MN Conservation Breeding Specialist Group SSC IUCN McCann K K Morrison A Byers P Miller and Y Friedmann eds 2001 Blue Crane Anthropoides paradiseus A Population and Habitat Viability Assessment Workshop Apple Valley MN Conservation Breeding Specialist Group SSC IUCN 134 Appendix III VorTEX Bibliography VORTEX Version 9 User s Manual Miller P S 1996 Impacts of the Hawaiian longline fishery on the Pacific Ocean population of loggerhead turtles Caretta caretta An analysis using the VORTEX simulation modelling package Pages 105 132 in Bolten A B J A Wetherall G H Balazs and S G Pooley eds Status of Marine Turtles in the Pacific Ocean Relevant to Incidental Take in the Hawaii Based Pelagic Longline Fishery U S Department of Commerce NOAA Technical Memorandum NOAA TM NMFS SWECS 230
87. 50 populations A metapopulation is a group of populations which because they often occupy fragmented discontinuous habitat exchange individuals with varying frequency Note that because of the added complexities associated with metapopulations these models will often run considerably slower than the corresponding single population models EF If there is no exchange of individuals among populations i e dispersal in your model it maybe faster to run several individual simulations with each one modeling an isolated population instead of a more complex metapopulation model Chapter 3 27 The Data Input Process VORTEX Version 9 User s Manual Enter the number of populations that comprise your metapopulation model or enter 1 for a simulation composed of a single population If you intend to build a metapopulation model you will later need to specify dispersal rates and some other parameters Species Description The next section of input includes a set of basic questions about the species being modeled Figure 20 4 Vortex Stochastic Simulation of the Extinction Process File Edt Vortex Window Help Dem S v fs gt E 4ZPG D WORTEX9 ZPG ZPG vp Project Settings Simulation Input Text Output Graphs and Tables Project Report Add Scenario Delete Scenario lt ZA gt Reorder 2p ZPG2 cenario Settings See pecies Description Species Description abels and State Vars IV Inbreeding Dep
88. 7b How secure is the Lord Howe Island Woodhen A population viability analysis using VORTEX Pacific Conservation Biology 3 125 133 Bustamante J 1996 Population viability analysis of captive and released bearded vulture populations Conservation Biology 10 822 831 Cancino J P S Miller J Bernal Stoopen and J Lewis eds 1995 Population and Habitat Viability Assessment for the Peninsular Pronghorn Antilocapra americana peninsularis Apple Valley MN Conservation Breeding Specialist Group SSC IUCN 130 Appendix III VorTEX Bibliography VORTEX Version 9 User s Manual Chapman A Brook B W Clutton Brock T H Grenfell B T and Frankham R 2001 Population viability analysis on a cycling population a cautionary tale Biological Conservation 97 1 61 69 Clark T W G N Backhouse and R C Lacy 1991a The population viability assessment workshop A tool for threatened species management Endangered Species Update 8 1 5 Clark T W G N Backhouse and R C Lacy 1991b Report of a workshop on population viability assessment as a tool for threatened species management and conservation Australian Zoologist 27 28 35 Clark T W G N Backhouse and R C Lacy 2002 The population viability assessment workshop A tool for threatened species management Endangered Species Update 19 4 136 141 Combreau O F Launay and M Lawrence 2001 An assessment of annual mortality rates in adult sized migrant houbara bus
89. 8 30 2003 Project ZPG Scenario ZPGl Eater Opulation 1 Year 1 N Extinct 0 PLE 0 000 N Surviving 100 P S 1 000 Mean size all populations 7 44 i 0 Means across extant populations only Population size 7 44 i UL Expected heterozygosity 0 923 0 002 Observed heterozygosity 1 000 i 0 000 Number of extant alleles 14 08 0 26 Lethal alleles diploid 1 60 0 05 2 N Extinct re ai NE Surviving Vortex 9 21 CAPS NUM INS Date Time 10 24 03 10 47AM Figure 42 Output Summary section of Text Output The statistics reported in this file are gt The cumulative number of iterations populations that have become extinct or remain extant gt The probability of population extinction PE or survival equivalent to the proportion of iterations populations that have become extinct or remain extant gt The mean population size reported separately for all populations N all and only for those remaining extant N extant with standard error SE and standard deviation SD across iterations gt The mean stochastic growth rate r both with and without harvest or supplementation if applicable as well as across all years of the simulation Chapter 4 73 Viewing Model Results VORTEX Version 9 User s Manual gt gt gt The mean expected heterozygosity or gene diversity remaining in the extant populations with standard error and standard deviation acro
90. 94 Distribution and extinction patterns within a northern metapopulation of the pool frog Rana les sonae Ecology 75 1357 1367 Sj gren Gulve P and Ray C 1996 Using logistic regression to model metapopulation dynamics Large scale forestry extir pates the pool frog In McCullough D R ed Metap opulations and wildlife conservation Island Press Washing ton D C pp 111 137 Soul M E 1980 Thresholds for survival maintaining fitness and evolutionary potential In Soul M E and Wilcox B A eds Conservation biology An evolutionary ecological perspective Sinauer pp 151 169 Soul M E 1987 Viable populations for conservation Cam bridge Univ Press Starfield A M 1997 A pragmatic approach to modeling J Wildl Manage 61 261 270 Starfield A M and Bleloch A L 1986 Building models for conservation and wildlife management MacMillan New York Stephens P A and Sutherland W J 1999 Consequences of the Allee effect for behaviour ecology and conservation Trends Ecol Evol 14 401 405 Varvio S L Chakraborty R and Nei M 1986 Genetic varia tion in subdivided populations and conservation genetics Heredity 57 189 198 Vucetich J A and Creel S 1999 Ecological interactions social organization and extinction risk in African wild dogs Conserv Biol 13 1172 1182 Vucetich J A Peterson R O and Waite T A 1997 Effects of social
91. 9AM 7 Figure 10 The Output Summary section of Text Output The Input Summary section shows a text listing of all the input values used in this Scenario Deterministic Calculations show a text summary of the deterministic population growth that would be projected from the specified mean demographic rates if stochastic processes were not acting on the population This section also shows a simple graph of the deterministic population trajectory The Output Summary section gives a text description of the status of the population at each year of the simulations as well as summary 16 Chapter 2 Getting Started with VORTEX VORTEX Version 9 User s Manual statistics for the Scenario Other Output provides some tables with basic summary statistics for the Scenario and for each iteration Note that the sections of Text Output provide dropdown lists to allow you to move among Scenarios and Populations Buttons are also provided to allow you to save these texts to simple text files to print the text summaries or to send the summaries to the Project Report Send the Output Summary to the Report now so that we can view and edit it later as part of our Project Report All of the information shown on Text Output screens is stored automatically in text files that are EF placed into your project directory While you can access and edit these files using for example MS Notepad or Word it is better to first save the text to your own files so that they are
92. A should perhaps be reserved for its original yet still rather broad meaning Beginning in about 1989 Lacy et al 1989 Seal and Lacy 1989 Seal et al 1990 it became increasingly recognized that PVA can often be most usefully incorporated into a strategy for the conservation of a taxon if it is part of and often central to a conservation workshop that mobilizes collaboration among the array of people with strong interest in or responsibility for a conservation effort e g governmental wildlife agencies conservation NGOs and the local people who interact with the species or its habitat or with particular expert knowledge about the species its habitats or the threats it faces e g academic biologists conservation professionals other wildlife biologists experts on human demographics and resource use Conservation problems are almost always multi faceted involving not only complex dynamics of biological populations but also interactions with human populations the past present and future impacts of humans on habitats and human political social and economic systems Alvarez 1993 Bormann and Kellert 1991 Clark 1989 1993 Many people need to contribute knowledge expertise and ideas in order to achieve the recovery of threatened species Population viability analyses can provide a framework for incorporating the many needed kinds of knowledge into species conservation efforts because PVAs do allow the assessment of many kinds of fa
93. Antwerp Royal Zoological Society of Australia Royal Zoological Society of Scotland Saitama Children s Zoo San Antonio Zoo San Francisco Zoo Schonbrunner Tiergarten Sedgwick County Zoo Taipei Zoo Thrigby Hall Wildlife Gardens Twycross Zoo Union of German Zoo Directors Wassenaar Wildlife Breeding Centre Wilhelma Zoological Garden Woodland Park Zoo Zoologischer Garten Koln Zoologischer Garten Zurich Stewards 500 999 Aalborg Zoo Alice D Andrews Alameda Park Zoo Arizona Sonora Desert Museum Banham Zoo amp Sanctuary BioSolutions Division of SAIC Cotswold Wildlife Park Dickerson Park Zoo Dutch Federation of Zoological Gardens Fota Wildlife Park Givskud Zoo Granby Zoo Knoxville Zoo Knuthenborg Park Little Rock Zoo National Aviary in Pittsburgh National Zoological Gardens of Pretoria Odense Zoo Oregon Zoo Ouwehands Dierenpark Perth Zoo Potter Park Zoo Riverbanks Zoological Park Rolling Hills Refuge Conservation Center Staten Island Zoo Tierpark Rheine Wellington Zoo Welsh Mountain Zoo Wildlife World Zoo Inc John S Williams Zoologischer Garten Rostock Curators 250 499 Dr Edward amp Marie Plotka Emporia Zoo Lee Richardson Zoo Racine Zoological Society Roger Williams Park Zoo Rosamond Gifford Zoo at Burnet Park The Animal Park Gulf Breeze Tokyo Zoological Park Society Topeka Zoo Friends of Zoo de la Casa de Campo Sponsors 50 249 African Safari American L
94. Appendix IV for a detailed description of VORTEX program flow A dispersal survival rate Chapter 3 37 The Data Input Process VORTEX Version 9 User s Manual of 80 means that there is a 20 chance that an individual will die during the process of moving from population A to population B Dispersal Modifier Function Dispersal patterns can be very complex and determined by many factors VORTEX does not provide a full model of dispersal across complex landscapes but instead models movements among discrete populations with the user specifying the rate of movement between each pair of populations as you will do in a later Input section However this box provides you with the opportunity to customize dispersal in perhaps very complex ways Any function entered here will be used as a modifier of the rates to be entered later For example you could cause dispersal of males to be twice as high as the specified rate and twice as high as for females by entering D 1 S M The parameter D in the equation stands for the specified dispersal rate between any two populations Such dispersal modifier functions can be used to cause dispersal to be dependent on sex age inbreeding population density and many other characteristics of the individuals and populations With respect to dispersal or other aspects of population dynamics the standard VORTEX model may not match precisely the behavior of your species Often the difference
95. CBSG cares about saving species and their habitats However the initial development and continuing improvement of the software and manual do represent a significant commitment by these conservation organizations The rate at which improvements can be made is determined by the resources available to support that work If your budget allows it please consider making a donation to support the further development of Vortex If you find the software to be especially valuable to you consider donating perhaps US 100 a wild guess about the investment of resources per user that have gone into Vortex or more or less as you feel is appropriate If you find the manual to be especially helpful consider donating to the CBSG As a side benefit to US tax payers donations to either the Chicago Zoological Society or the CBSG are tax deductible Donations to the Chicago Zoological Society should be as a check written to the Chicago Zoological Society sent to Vortex donation Department of Conservation Biology Brookfield Zoo Brookfield IL 60513 USA Donations to the CBSG should be sent to Vortex donation CBSG 12101 Johnny Cake Ridge Road Apple Valley MN 55124 USA 4 Chapter 1 Introduction VORTEX Version 9 User s Manual Chapter 2 Getting Started with VORTEX System Requirements VORTEX version 9 was developed as a C program for the simulation code presented within an interface developed in MS Visual Basic To our knowledg
96. CN Species Survival Commission 1994 JUCN Red List Categories IUCN Gland Switzerland Kirkpatrick S and Stoll E 1981 A very fast shift register sequence random number generator Journal of Computational Physics 40 517 Kjos C O Byers P S Miller J Borovansky and U S Seal eds 1998 Population and Habitat Viability Assessment Workshop for the Winged Mapleleaf Mussel Quadrula fragosa Final Report Apple Valley MN Conservation Breeding Specialist Group SSC TUCN Krebs C J 1994 Ecology The Experimental Analysis of Distribution and Abundance 4 ed New York Harper Collins Lacy R C 1993a VORTEX A computer simulation model for Population Viability Analysis Wildlife Research 20 45 65 Lacy R C 1993b Impacts of inbreeding in natural and captive populations of vertebrates Implications for conservation Perspectives in Biology and Medicine 36 480 496 Lacy R C 1993 1994 What is Population and Habitat Viability Analysis Primate Conservation 14 15 27 33 Lacy R C 1997 Importance of genetic variation to the viability of mammalian populations Journal of Mammalogy 78 320 335 Lacy R C G Alaks and A Walsh 1996 Hierarchical analysis of inbreeding depression in Peromyscus polionotus Evolution 50 2187 2200 Lacy R C and J D Ballou 1998 Effectiveness of selection in reducing the genetic load in populations of Peromyscus polionotus during generations of inbreeding Evolution 52 900 909 Lacy
97. E amp Ada L Rice Center Chicago Zoological Society Brookfield IL 60513 USA VORTEX and like programs do exactly what they are told to do as constrained by the static single species mod els that provide their structure They can be useful for vari ous purposes so long as the user understands what the pro grams are doing Caughley and Gunn 1996 p 208 The complexity and multiplicity of processes influenc ing the dynamics of natural populations of animals and plants means that population viability analysis PVA models are also frequently complex Different models in corporate different population processes Individual popu lation processes can be modeled in various ways requiring different sets of driving variables using different equations to define the processes and providing different output to describe the population dynamics Users of PVA models should understand the basic structure of the models they use and it is important that models used for scientific studies and conservation efforts can be examined and rep licated Yet often the details of PVA computer programs ECOLOGICAL BULLETINS 48 2000 are not available to the users because the code is proprie tary information or otherwise not provided to users or simply because the task of reading and understanding the source code for large and complex programs is formidable One possible remedy to the problem of PVA users needing to understand the models
98. Hermaphroditic Read in FemaleBreedingAge Read in MaleBreedingAge Read in MaximumAge Read in SexRatio at birth Read in MaximumL itterSize Read in DensityDependentBreeding The pseudocode for modeling density dependent breed ing is not given below END FUNCTION READ _SPECIES_PARAMETERS BEGIN FUNCTION READ _MIGRATION_PARAMETERS Get input population structure and migration patterns Read in MigrationAges Read in MigrationSexes Read in MigrationSurvival Read in MigrationDensity FOR each population pSource FOR each other population pDestination Read in MigrationProb pSource pDestination END LOOP END LOOP END FUNCTION READ _MIGRATION_PARAMETERS BEGIN FUNCTION READ _POPULATION_PARAMETERS for popula tion p Read in ProportionFemalesBreeding p Read in BreedEV p Environmental variation is specified as a standard deviation 196 Read in Litter size distribution either as MeanLitterSize p and SDLitterSize p or as the fully specified distribution of ProbLitterSize p n FOR each age x up to FemaleBreedingAge Read in FemaleMortality p x Read in FemaleMortalityEV p x END age LOOP FOR each age x up to MaleBreedingAge Read in MaleMortality p x Read in MaleMortalityEV p x END age LOOP FOR each type of catastrophe c IF NumberPopulations gt 1 Read in GlobalOrLocalfp c END IF Read in CatastropheFrequency p c Read in CatastropheBreedSeverity p c
99. IF IF monogamous FOR each male in breeding pool m Set MaleUsed m FALSE Flag to indicate male is available for pairing END LOOP END IF IF hermaphroditic IF only one breeding female AND ProportionSelfing p 0 EXIT BREED END IF END IF FOR each female Dam in breeding pool Let BreedRand RAND GETBREEDRATE I BreedRate is probability of breeding for the female given by the user either as a constant ProportionFemalesBreeding or as a function of population size and other parameters See Note 3 IF BreedRate 0 CONTINUE LOOP with next breeding female END IF Find a mate IF hermaphroditic IF RAND lt ProportionSelfing p Let Sire Dam ELSE Choose a Sire at random from breeding pool WHILE Sire is Dam Choose a new Sire END WHILE END selfing IF ELSE ELSE not hermaphroditic Choose a Sire at random from the male breeding pool ECOLOGICAL BULLETINS 48 2000 IF monogamous WHILE MaleUsed Sire Choose a new Sire END WHILE Set MaleUsed Sire TRUE Flag Sire as unavailable for future Dams END IF END IF ELSE Find the litter size for that pairing IF MaximumLitterSize gt 0 Set CumulativeProbLitterSize 0 1 BreedRate FOR each possible litter size 7 Set CumulativeProbLitterSize n CumultativeProbLitterSize n 1 ProbLitterSize p n BreedRate END LOOP FOR each litter size 2 in decreasing order IF BreedRand gt CumulativeProbLitte
100. LocalMortEVNRand to same sign as LocalMortE VRand Set LocalKEVNRand NRAND Select random normal deviate for specifying EV in K ELSE EV in breeding is correlated with EV in mortality Set LocalMortEVRand LocalBreedEVRand Set LocalMortEVNRand LocalBreedEVNRand Set LocalKEVNRand LocalBreedEVNRand END EV correlation IF ELSE END FUNCTION LOCAL_EV_RANDS BEGIN FUNCTION CATASTROPHES for popula tion p FOR each type of catastrophe c IF Catastrophe is local in effect IF RANDO lt CatastropheFrequency p c II See Note 5 Set CatastropheFlag c TRUE Catastrophe has occurred ELSE Set CatastropheFlag c FALSE END catastrophe IF ELSE ELSE IF GlobalCatastropheRand lt CatastropheFrequency p c Set CatastropheFlag c TRUE ELSE Set CatastropheFlag c FALSE END catastrophe IF ELSE END Local Global catastrophe IF ELSE END catastrophe LOOP 198 END FUNCTION CATASTROPHES BEGIN FUNCTION BREED for population p Find breeders for the year FOR each living animal in the population IF sex female AND age gt FemaleBreedingAge Add female to breeding pool END IF IF not hermaphroditic IF sex male AND age gt MaleBreedingAge IF RAND Q lt ProportionMalesInBreeding ool p Add male to breeding pool END IF END IF END IF END animal LOOP IF no males selected for breeding pool but adult males do exist Add one male at random to breeding pool END
101. Molur eds 1994 Population and Habitat Viability Analysis PHVA Workshop for Indian Nepali Rhinoceros Zoo Outreach Organisation CBSG India Coimbatore Appendix III 137 VorTEX Bibliography VORTEX Version 9 User s Manual Wang Y S W Chu and U S Seal eds 1994 Population and Habitat Viability Assessment Workshop Report for the Asiatic Black Bear Ursus thibetanus formosanus Apple Valley MN Conservation Breeding Specialist Group SSC IUCN Wang Y S W Chu D Wildt and U S Seal eds 1995 Clouded Leopard Neofelis nebulosa brachyurus Population and Habitat Viability Assessment Apple Valley MN Conservation Breeding Specialist Group SSC AUCN Wei F Feng Z and Hu J 1997 Population viability analysis computer model of giant panda population in Wuyipeng Wolong Natural Reserve China International Conference on Bear Research and Management 9 2 19 23 Wemmer C A Than S T Khaing S Monfort T Allendorf J Ballou and S Ellis 2000 Thamin Population and Habitat Viability Assessment Final Report Apple Valley MN Conservation Breeding Specialist Group SSC AUCN Werikhe S L Macfie N Rosen and P S Miller eds 1998 Can the Mountain Gorilla Survive Population and Habitat Viability Assessment Workshop for Gorilla gorilla beringei Apple Valley MN Conservation Breeding Specialist Group SSC IUCN Whittington P R J M Crawford O Huyser D Oschadleus R Randall P Ryan L
102. ND IF END LOOP Set GeneDiversity p 1 ExpectedHomozygosity p Set ObservedHeterozygosity p 1 NumberHomozygotes PopulationSize p FOR each living animal in the population FOR each non neutral locus IF allele 1 at the locus is a lethal Increment NumberLethals END IF IF allele 2 at the locus is a lethal Increment NumberLethals END IF END locus LOOP END animal LOOP 201 Set LethalFrequencylp NumberLethals PopulationSize p END FUNCTION CALC_GENETIC_METRICS Note 1 Random integers from 0 to 64K are generated by the algorithm given by Kirkpatrick and Stoll 1981 The C code was modified from Maier 1991 Random real numbers between 0 and 1 are produced by first generating a random integer between 0 and 64K and then dividing that integer by 64K Random numbers from a normal dis tribution with mean 0 and SD 1 are generated by the polar algorithm supplied by Latour 1986 Binomially distributed numbers are generated by first calculating the cumulative probability distribution for the discrete out comes of the desired distribution then generating a ran dom real number and then assessing which binomial out come covers the portion of the distribution encompassing the random real number Note 2 VORTEX asks for the effects of inbreeding to be entered as a number of lethal equivalents per diploid ani mal with further specification of what proportion of this genetic load is due to
103. ND IF ELSE END age gt 0 IF END animal LOOP END FUNCTION MORTALITY BEGIN FUNCTION GETDEATHRATE Obtain DeathRate by evaluating mortality function for population and individual parameters I Most often the mortality function will simply return the mortality rate entered by the user for the age and sex of the current animal VORTEX provides the option however of making mortality a function of PopulationSize GeneDiversity Inbreeding and other variables ADJUSTRATE DeathRate LocalMortEV p LocalMortEVRand LocalMortEVNRand Adjust rate for local EV ADJUSTRATE DeathRate GlobalMortEV p GlobalMortEVRand GlobalMortEVNRand Adjust rate for global EV FOR each type of catastrophe c IF CatastropheFlag c TRUE Let DeathRate CatastropheSurvivalSeverity p c 1 DeathRate END IF END LOOP Sevi Ses END FUNCTION GETDEATHRATE BEGIN FUNCTION ADJUSTRATE Rate EV EVRand EVNRana Determine binomial parameter 7 for modeling EV II See Note 6 IF n lt 26 I Find the adjusted Rate from binomial EV FOR each BinomialOutcome 0 through n Add BinomialOutcome n to BinomialProportion Calculate BinomialProbability for BinomialProportion Add BinomialProbability to CumulativeBinomial IF EVRand lt CumulativeBinomial Set Rate Binomial Proportion BREAK from LOOP END IF END LOOP ELSE Use Normal distribution for EV and truncate symmetri cally to avoid bias IF Rate gt
104. OGICAL BULLETINS 48 2000 Kirkpatrick S and Stoll E 1981 A very fast shift register se quence random number generator J Comp Phys 40 517 Lacy R C 1993 VORTEX A computer simulation model for population viability analysis Wildl Res 20 45 65 Latour A 1986 Polar normal distribution Byte August 1986 131 132 Lindenmayer D B Lacy R C and Pope M L 2000 Testing a simulation model for population viability analysis Ecol Appl 10 580 597 Maier W L 1991 A fast pseudo random number generator Dr Dobb s Journal May 1991 152 157 Miller P S and Lacy R C 1999 VORTEX Ver 8 users manual A stochastic simulation of the simulation process IUCN SSC Conservation Breeding Specialist Group Apple Valley Minnesota Mills L S and Smouse E 1994 Demographic consequences of inbreeding in remnant populations Am Nat 144 412 431 Morton N E Crow J F and Muller H J 1956 An estimate of the mutational damage in man from data on consanguineous marriages Proc Nat Acad Sci USA 42 855 863 Pielou E C 1977 Mathematical ecology Wiley Starfield A M and Bleloch A L 1986 Building models for conservation and wildlife management MacMillan 203 Ecological Bulletins 48 39 51 Copenhagen 2000 Considering threats to the viability of small populations using individual based models Robert C Lacy Lacy R C 2000 Considering
105. PE 1 PE NumberIterations PopulationSize p GeneDiversity p Gene Diversity Heterozygosity expected under Hardy Weinberg equilibrium ObservedFeterozygosity p 1 mean inbreeding coefficient NumberAlleles p LethalFrequency p END year LOOP END population LOOP Calculate and report within population means of above summary statistics Call program for displaying graphical displays of trends in PopulationSize GeneDiversity Mean inbreeding coefficient 1 ObservedHeterozygosity Probability of population persistence to year Probability of extinction in that time interval Read in DoAnotherScenario IF DoAnotherScenario is FALSE BREAK from scenario LOOP 195 END IF END scenario LOOP END PROGRAM VORTEX BEGIN FUNCTION READ SPECIES _PARAMETERS Get input parameters from keyboard or input file de scribing simulation parameters inbreeding effects and ba sic species life history Read in Input Output file names Read in NumberOffterations Read in NumberOfYears Read in ExtinctionDefinition Extinction can be defined as no animals of one sex or as the population size falling below a specified minimum Read in NumberOfPopulations Read in InbreedingGeneticLoad Read in ProportionLoadDue ToLethals Read in EVCorrelationBetweenReproductionAndSurvival IF NumberOfPopulations gt 1 Read in EVConcordanceAmongPoulations END IF Read in NumberTypesOfCatastrophes Read in Monogamous Polygynous
106. RS I VORTEX describes dispersal between populations as migration END IF FOR each population p READ _POPULATION_PARAMETERS p END population LOOP FOR each population pSource 1 Calculate cumulative migration rates for each pairwise transition between populations Set CumMigrationProb pSource 1 MigrationProb pSource 1 FOR each destination population pDestination greater than 1 Set CumMigrationProb pSource p Destination CumMigrationProb pSource p Destination 1 MigrationProb pSource p Destination END pDestination LOOP END pSource LOOP Set NumberLethals InbreedingGeneticLoad ProportionLoadDue ToLethals Set LethalEquivalents InbreedingGeneticLoad 1 ProportionLoadDue ToLethab II See Note 2 FOR each population p Set GlobalBreedEV p BreedEV p EVConcordanceAmongPopulations Set LocalBreedEV p SQRT BreedEV p 2 GlobalBreedEV p 2 Partition Environmental Variation in breeding BreedEV into the component that is common to all populations GlobalBreedEV and the component that is specific to each population LocalBreedEV TotalEV 2 GlobalEV 2 LocalEV 2 Note EVs are given as standard deviations FOR each sex s FOR each age x up to age of breeding Set GlobalMortEV p s x MortEV p s x EVConcordanceAmongPopulations Set LocalMortEV p s x SQRT MortEV p s x 2 GlobalMortEV p s x 2 Partition EV in mortality M
107. RTEX normally models allele transmission at 5 loci that may contain lethal alleles allowing up to five unique and independent lethal recessive alleles per founder and also at one neutral locus with no impact on inbred progeny In the Special Options on the Project Settings screen you have the option of asking VORTEX to model alleles at a greater number of neutral loci Doing so will produce more precise results for genetic trends and the details of the emergent genetic patterns at the modeled loci can optionally be output to a file for further examination In its simplest form inbreeding depression is modeled in VORTEX as a reduction in the survival of offspring during the first year of life As a result the program generally underestimates the impact of inbreeding as it can also depress other components of fitness such as adult survival fecundity and or success in competition for mates More complex relationships between inbreeding and demographic rates can also be modeled see Chapter 5 for more on this subject Lethal Equivalents This box and the next ask you to specify the severity and nature of inbreeding depression in your simulated population Enter the average impact of inbreeding on first year survival quantified as a number of lethal equivalents per diploid individual As described more fully in Box B the default value of 3 14 is a summary statistic based on a survey of 40 captive mammalian populations Ralls et al 1988 If
108. Read in CatastropheSurvivalSeverity p c END catastrophe LOOP CALC _DETERMINISTIC_GROWTH p Calculate deterministic population growth rate genera tion time and stable age distribution from mean birth and death rates Effects of any catastrophes are averaged across years Read in ProportionMalesInBreeding ool p I See Note 4 IF initial numbers of animals are to be distributed according to the stable age distribution Determine initial numbers of animals in each age sex class The stable age distribution would rarely assign whole numbers to each age sex class Integral numbers are assigned that most closely match the desired distribution ELSE does not start at stable age distribution FOR each sex _ FOR each age up to MaximumAge Read in initial number of animals END LOOP END LOOP END stable age distribution IF ELSE Read in CarryingCapacity p K K may be specified as a function of year or other param eters See Note 3 Read in KEV p Read in Harvest p IF Harvest p Yes Read in First YearHarvest p LastYearHarvest p HarvestIntervallp FOR each age x up to FemaleBreedingAge For harvest all adults are treated in the same age cat egory Read in NumberFemales ToBeHarvested p x END LOOP FOR each age x up to MaleBreedingAge Read in NumberMales ToBeHarvested p x END LOOP ECOLOGICAL BULLETINS 48 2000 END IF Read in Supplement p IF Supplement p Ye
109. St Croix River in Minnesota and Wisconsin United States with individuals separated from one another by as much as 20 25 meters While no evidence points to a suppression of reproductive success at higher densities the mode of reproduction in these mussels suggests that Allee effects may play a major role in influencing reproduction as population size and density declines Kjos et al 1998 In fact reproductive success is thought to drop off rapidly as populations are reduced to below about 30 of the estimated carrying capacity To model this phenomenon P 0 P K 19 4 and A 4 the exponential steepness B is set to zero when reproductive success is unaffected at high densities This relationship is shown in the bottom panel of Figure VI 1 3 2 oO S D amp E 3 3 2 a n vj v a a Peary Caribou Rangifer tarandus Figure 26 Density dependence functions as modeled in VoRTEX for Peary caribou top panel Gunn et al 1998 and the winged mapleleaf Oo 1020 40 40 50 60 70 80 90 100 mussel bottom panel Kjos et al 1998 Population Density N k 100 Females Producing Brood Winged Mapleleaf Mussel Quadrula fragosa Reproductive Rates The next section of input Figure 27 asks for parameter values that specify reproductive rates Note that you decide when in the development of the next generation the birth is defined to occur For mammals you would probably use parturit
110. TROPHES p Determine if catastrophes occur that year Determine carrying Capacity K for year I See Note 3 Add LocalKEVNRand LocalKEV p to CarryingCapacitylp Adjust K for local EV Add GlobalKEVNRand GlobalKEV p to CarryingCapacity p I Adjust K for global EV BREED p Go through breeding cycle to produce offspring MORTALITY p Determine who dies that year END population LOOP Add 1 to the age of each animal IF NumberPopulations gt 1 MIGRATE ECOLOGICAL BULLETINS 48 2000 Determine which animals migrate between populations END IF FOR each population p IF year during which animals are to be harvested HARVEST p END harvest year IF END population LOOP FOR each population p IF year during which animals are to be supplemented SUPPLEMENT p END supplement year IF END population LOOP FOR each population p Tally PopulationSize p IF population is not extinct AND population was not extinct prior year Extinction can be defined by the user as the absence of one sex or as the population size falling below a specified lower limit rip log PopulationSize p PopulationSizePrior Year p I Calculate population growth rate 7 END IF IF not extinct AND PopulationSize p N gt CarryingCapacity p KY FOR each living animal IF RAND gt K N Stochastically kill excess above K Animal dies END IF _ END each animal LOOP END
111. U S Seal eds 1993 Population and Habitat Viability Assessment for the Pampas Deer Ozotoceros bezoarticus Apple Valley MN Captive Breeding Specialist Group SSC TUCN Appendix III 131 VorTEX Bibliography VORTEX Version 9 User s Manual Guichard C S Ellis Y Matamoros and U S Seal eds 2001 Andlisis de la Viabilidad de Poblacional y del Habitat del Manati en Mexico Apple Valley MN Conservation Breeding Specialist Group SSC IUCN Gunn A U S Seal and P S Miller eds 1998 Population and Habitat Viability Assessment Workshop for Peary Caribou and Arctic Island Caribou Rangifer tarandus Apple Valley MN Conservation Breeding Specialist Group SSC TUCN Haig S M and J D Ballou 2002 Pedigree analyses in wild populations Pages 388 405 in Beissinger S R and D R McCullough eds Population Viability Analysis Chicago IL University of Chicago Press Haig S M J R Belthoff and D H Allen 1993 Population viability analysis for a small population of red cockaded woodpeckers and an evaluation of enhancement strategies Conservation Biology 7 289 301 Hamilton S and H Moller 1995 Can PVA models using computer packages offer useful conservation advice Sooty shearwaters Puffinus griseus in New Zealand As a case study Biological Conservation 73 2 107 117 Heredia B P Gaona A Vargas S Ellis and U S Seal eds 1999 Taller Andlisis de la Viabilidad de Poblacion y del Habitat para
112. VORTEX by specifying the functional relationships There are two ways that you can enter a function rather than a constant for an input variable you can type the function directly into the input box for specifying the rate or you can open a Function Editor to help you develop the function to describe the relationship VORTEX provides an option and this option is the default for new Projects to have the Function Editor open automatically whenever you enter a as the first character in an input box for a demographic rate The other way to open the Function Editor is to click on the Function Editor icon on the toolbar If you type a function directly into an input box you must precede the function with an sign to distinguish the specification of a rate as a function rather than as a constant If you open the Function Editor by typing an in an input box and then develop a function within the Function Editor then the Function Editor will insert the function back into the active input box when you accept the function It is usually easier and safer to build a function first within the Function Editor and then send it over to the input screen Function Editor zi Function gt A 1 3 v gt 1075 le From o To 100 Incr f 1 Function Preview round In rand stand nrand snrand true false pi in abs Variables Age Population State Variable Pop
113. Version 9 21 VORTEX A Stochastic Simulation of the Extinction Process User s Manual Manual Written by Philip S Miller Conservation Breeding Specialist Group SSC IUCN Robert C Lacy Chicago Zoological Society Software Written by Robert C Lacy Max Borbat and JP Pollak A contribution of the IUCN SSC Conservation Breeding Specialist Group in collaboration with the Chicago Zoological Society VORTEX is provided at no cost in order to further conservation and science It is distributed without warranty of its suitability for any particular use and neither the program or this manual is guaranteed to be free of errors bugs or potentially misleading information It is the responsibility of the user to ensure that the software is appropriate for the uses to which it is put VORTEX is owned and copyrighted by the Chicago Zoological Society The software is not copy protected In addition to making back up copies individuals not for profit organizations and governmental agencies are hereby given licenses for making unlimited copies of VORTEX for the purpose of furthering conservation teaching and research Distribution of VORTEX is restricted to e distribution by the Chicago Zoological Society e distribution by the IUCN SSC Conservation Breeding Specialist Group e downloading of the program from the Internet http www vortex9 org vortex html by individuals not for profit organizations and governmental agenci
114. We need always to be cognizant of the limits of our understanding of wildlife populations and to include appropriate margins for error in our conservation strategies PVA is by definition an assessment of the probability of persistence of a population over a defined time frame Yet persistence of a population while a necessary condition for effective conservation of natural systems is often not sufficient Prevention of extinction is the last stand of conservationists but the goals should be higher conservation of functional biological communities and ecosystems PVA usually ignores the functional role of a species in a community but a PHVA workshop should consider much more than the prevention of the final biological extinction of the taxon A species such as the American Bison Bison bison can be functionally extinct in terms of no longer filling its original role in nature even as it is praised as a conservation success story and would be considered safe from extinction and viable The use of the PHVA process to help guide conservation decisions is not a singular event in which an analysis can be completed management actions recommended and implemented and conservation thereby assured The many uncertainties in the process mandate that PVA be used as a tool in an adaptive management framework and a PHVA workshop is just one stage of an effective conservation strategy In adaptive management the lack of knowledge adequate to predict with
115. Window Help JOciisea e Jaf f4Projecti not previously saved Project Settings Simulation Input Text Output Graphs and Tables Project Report Add Scenario Delete Scenario lt Scenario 1 gt wea Scenario 1 Scenario Settings abels and State Vars ispersal Rates Scenario Name Scenario 1 ortality Rates Number of Iterations fi oo atastrophes Number of Years ate Honopolization 1u nitial Population Size arrying Capacity Extinction Definition Only 1 Sex Remains Total N lt Critical Size Number of Populations Enter the critical size below which pseudo extinction is considered to have occurred FSS Sefeeeeees 5 5 S D e p alza 2 3 aja FIER 3 ej c i sis P 4 FF Part a amp HE 5 glg ale amp s S 3 Copy input values from Population 1 r This Section hed to all subsequent populations Copy Input Values Vortex 9 0 Enter a non empty scenario name CAPS NUM INS Date Time 5 2 2003 7 47PM Figure 18 Scenario Settings within Input showing a tooltip for the Extinction Definition It is important to remember that VORTEX will accept input values that are mathematically possible but biologically implausible While VORTEX provides help on many data input questions you may have such as when to enter the data as a proportion or as a percent the ultimate responsibility for entering valid data that will result in a meaningful model rests with you the u
116. X Wildlife Research 20 67 86 Lindenmayer D B V C Thomas R C Lacy and T W Clark 1991 Population Viability Analysis PVA The concept and its applications with a case study of Leadbeater s Possum Gymnobelideus leadbeateri McCoy Report to the Forest and Timber Inquiry Resource Assessment Commission Consultancy Series No FTC91 18 Canberra Australia 170 pp Lombard K B 1996 A population viability analysis of the Hawaiian Monk Seal Monachus schauinslandi M Sc dissertation University of Michigan Ann Arbor MI Lorek H and M Sonnenschein 1999 Modelling and simulation software to support individual based ecological modelling Ecological Modelling 115 2 3 199 216 Maehr D S R C Lacy E D Land O L Bass Jr and T S Hoctor 2002 Evolution of population viability assessments for the Florida panther A multiperspective approach Pages 284 311 in Beissinger S R and D R McCullough eds Population Viability Analysis Chicago IL University of Chicago Press Maguire L A R C Lacy R J Begg and T W Clark 1990 An analysis of alternative strategies for recovering the eastern barred bandicoot in Victoria Pages 147 164 in Clark T W and J H Seebeck eds The Management and Conservation of Small Populations Brookfield IL Chicago Zoological Society Majluf P E A Babcock J C Riveros M A Schreiber and W Alderete 2002 Catch and bycatch of sea birds and marine mammals in the small scale fisher
117. a Island Rattlesnake Population and Habitat Viability Assessment PHVA Workshop Apple Valley MN Captive Breeding Specialist Group SSC IUCN Pergams O R W R C Lacy and M V Ashley 1999 Conservation and management of Anacapa Island deer mice Conservation Biology in press 126 Appendix II Literature Cited VORTEX Version 9 User s Manual Petit S and L Pors 1996 Survey of columnar cacti and carrying capacity for nectar feeding bats on Cura ao Conservation Biology 10 769 775 Pielou E C 1977 Mathematical Ecology New York John Wiley and Sons Ralls K Ballou J D and Templeton A R 1988 Estimates of lethal equivalents and the cost of inbreeding in mammals Conservation Biology 2 185 93 Ricklefs R E 1979 Ecology 2 ed New York Chiron Robertson A 1960 A theory of limits in artificial selection Proceedings Royal Society of London 153B 234 49 Rohlf F J and R R Sokal 1981 Statistical Tables 2 ed New York W H Freeman and Company Ruggiero L F G D Hayward and J R Squires 1994 Viability analysis in biological evaluations Concepts of population viability analysis biological population and ecological scale Conservation Biology 8 364 372 Rylands A B 1993 1994 Population viability analyses and the conservation of the lion tamarins Leontopithecus of south east Brazil Primate Conservation 14 15 34 42 Samuels A and J Altmann 1991 Baboons of the Amboseli basin Demograph
118. a different population Demographically it will not matter whether you choose long term pairings or re arrangement of pairs each year Genetically there may be a small effect on the rate of loss of genetic diversity from the population fe Vortex Stochastic Simulation of the Extinction Process File Edt Vortex Window Help DOSH s BOS is EAZPG D VORTEX9 ZPG ZPG vpi iol x Project Settings Simulation Input Text Output Graphs and Tables Project Report Add Scenario Delete Scenario lt zPa2 gt Reorder ZPG1 ZPG2 cenario Settings species Description Reproductive System abeis and State Vars Monogamous Ce Hermaphroditic Reproductive System Long Term Monogamy Long Term Polygamy ortality Rates Age of First Offspring for Females 2 Soe Age of First Offspring for Males 2 nitial Population Size Maximum Age of Reproduction fi 0 anying Capacity Maximum Number of Progeny per Year Sex Ratio at Birth in Males Dispersal Reproductive Rates upplementation Carei Weien Population 1 Population 2 Population 1 z Density Dependent Reproduction This Section k Breeding at Low Density PIO i i ity to subsequent x a ca tying Capacity P K populations ee Parameter Steepness Parameter B Copy Input Values Vortex 9 21 Select this if the species is polygynous with new pairings each year CAPS NUM INS Dat
119. able age distribution you then enter the total Initial Population Size for each population VORTEX will assign individuals to each age sex class proportionate to the stable age distribution and will show that distribution in the grids If instead you choose to enter a Specified Age Distribution you will then enter the actual size of each age class for both males and females You may need to use scroll bars to view the older age classes in the grids As you enter these values you will notice that the total initial population size changes accordingly Chapter 3 57 The Data Input Process VORTEX Version 9 User s Manual 4 Vortex Stochastic Simulation of the Extinction Process File Edt Vortex Window Help Deel teega les gt E 4ZPG D WORTEX9 ZPG ZPG vpi Project Settings Simulation Input Text Output Graphs and Tables Project Report Add Scenario Delete Scenario lt zpa2 gt Reorder ZPG1 ZPG2 saminatm initial Population Size abels and State Vars Note Stable age distribution may not be meaningful if some demographic rates are functions of other parameters Reproductive System Start with g i Specified Age Distribution Reproductive Rates ortality Rates atastrophes ate Monopolization Initial Population Size arrying Capacity m Stable Age Distribution Population 1 Population 2 Initial Population Size 10 10 m Specified Age Distribution Female Ages upplementati
120. al South Africa Biochemical Systematics amp Ecology 29 6 563 583 Boyce M S 2002 Reconciling the small population and declining population paradigms Pages 41 49 in Beissinger S R and D R McCullough eds Population Viability Analysis Chicago IL University of Chicago Press Brito D and F A S Fernandez 2000 Metapopulation viability of the marsupial Micoureus demerarae in small Atlantic forest fragments in south eastern Brazil Animal Conservation 3 3 201 209 Brook B W M A Burgman and R Frankham 2000 Differences and congruencies between PVA packages The importance of sex ratio for predictions of extinction risk Conservation Ecology 4 1 6 online URL http www consecol org vol4 iss art6 Brook B W Cannon J R Lacy R C Mirande C and Frankham R 1999 A comparison of the population viability analysis packages GAPPS INMAT RAMAS and VORTEX for the Whooping Crane Grus americana Animal Conservation 2 23 31 Brook B W amp Kikkawa J 1998 Examining threats faced by island birds A PVA on the Capricorn silvereye using long term data Journal of Applied Ecology 35 491 503 Brook B W Lim L Harden R and Frankham R 1997a Does population viability analysis software predict the behaviour of real populations A retrospective study on the Lord Howe Island woodhen Tricholimnas sylvestris Sclater Biological Conservation 82 119 128 Brook B W Lim L Harden R and Frankham R 199
121. al decline but because of bad luck Chance or stochastic processes usually have little impact on long term population dynamics as long as the population is abundant and spread over a wide geographic range and a number of habitats Deterministic processes such as those listed above predominate in widespread still common species while local chance events impacting subsets of the population will average out across the broader diverse range When a population becomes small isolated and localized however chance events can become important even dominating the long term dynamics and fate of a population Appendix I 101 An Overview of Population Viability Analysis Using VORTEX VORTEX Version 9 User s Manual Many stages in the life history of an organism and the processes that define the history of a biological population are essentially stochastic sampling phenomena Births deaths dispersal disease sex determination and transmission of genes between generations all are largely probabilistic phenomena Small samples intrinsically have greater variance around the probabilistic mean or expectation than do large samples and therefore small populations will experience greater fluctuations in births deaths sex ratio and genetic variation than will larger populations The fundamental problem facing small populations is that the fluctuations they experience due to the multiple stages of sampling each generation make it increasingly likely th
122. al fluctuations in mortality rates would be about 2 Catastrophes In the next section of input Figure 29 you enter data to characterize catastrophes that might strike your populations Note that you must do this for each type of catastrophe you identified back in the Species Description section across each population comprising your metapopulation if you are modeling more than one population You toggle among the types of catastrophes by clicking on the buttons arrayed across the top of the Catastrophes window EF Don t forget to enter data for Catastrophe 2 if any and all further catastrophes after you have completed entering data for Catastrophe 1 Chapter 3 53 The Data Input Process VORTEX Version 9 User s Manual 4 Vortex Stochastic Simulation of the Extinction Process File Edt Vortex Window Help Osu Ba S os gt SS Page D AWORTEXS ZPG ZPG Ypi Project Settings Simulation Input Text Output Graphs and Tables Project Report Add Scenario Delete Scenario lt zPa2 gt Reorder 2ZPG1 ZPG2 cenario Settings pecies Description Catas trophes abels and State Vars Reproductive System Catastrophe 1 Catastrophe 2 Reproductive Rates ortality Rates Population 1 Population 2 atastrophes Global Local Global ate Monopolization Frequency 1 nitial Population Size arying Capacity Severity proportion of normal values Population 1 Population 2 2 Slsl 12 5
123. al population dynamics tell us about minimum population sizes Conservation Biology 4 324 327 Walker S and S Molur eds 1994 Population and Habitat Viability Analysis PHVA Workshop for Indian Nepali Rhinoceros Zoo Outreach Organisation CBSG India Coimbatore Werikhe S L Macfie N Rosen and P S Miller eds 1998 Can the Mountain Gorilla Survive Population and Habitat Viability Assessment Workshop for Gorilla gorilla beringei Apple Valley MN Conservation Breeding Specialist Group SSC IUCN Wright S 1977 Evolution and the Genetics of Populations Vol 3 Experimental Results and Evolutionary Deductions Chicago University of Chicago Press Zar J H 1996 Biostatistical Analysis 3 ed Englewood Cliffs Prentice Hall 128 Appendix II Literature Cited VORTEX Version 9 User s Manual Appendix III VORTEX Bibliography UUE We have attempted to compile an exhaustive list of articles and reports that use VORTEX as a tool in population viability analysis If we have missed any other examples or if you have published a contribution that you would like to add to the growing list please contact the Conservation Breeding Specialist Group see page 3 for details and we will update this Bibliography Ahlmann V K Collins and U S Seal eds 2000 Riverine Rabbit Bunolagus monticularis 4 Population and Habitat Viability Assessment Workshop Apple Valley MN Conservation Breeding Specialist Grou
124. al population size and request that the population be distributed according to the stable age distribution calculated from the life table Individuals in the starting population are assumed to be unrelated Thus inbreeding can occur only in second and later generations 8 Two unique alleles at a hypothetical neutral genetic locus are assigned to each individual in the starting population and to each individual supplemented to the population during the simulation VORTEX therefore uses an infinite alleles model of genetic variation The subsequent fate of genetic variation is tracked by reporting the number of extant neutral alleles each year the expected heterozygosity or gene diversity and the observed heterozygosity The expected heterozygosity derived from the Hardy Weinberg equilibrium is given by He 1 le in which p is the frequency of allele 7 in the population The observed heterozygosity is simply the proportion of the individuals in the simulated population that are heterozygous Because of the starting assumption of two unique alleles per founder the initial population has an observed heterozygosity of 1 0 at the hypothetical locus and only inbred animals can become homozygous Proportional loss of heterozygosity through random genetic drift is independent of the initial heterozygosity and allele frequencies of a population Crow and Kimura 1970 so the expected heterozygosity remaining in a simulated population is a useful metric
125. ally change a very useful analysis into something that is worthless It is strongly recommended that you periodically save your work and even save it under a new name in a new directory see below Hard disk space is cheap use it 8 Chapter 2 Getting Started with VORTEX VORTEX Version 9 User s Manual A Quick Tour of VORTEX The first screen you will see when you begin a new VORTEX session is shown in Figure 1 Ea Vortex Stochastic Simulation of the Extinction Process File Edt Vortex Window Help Dml CAPS NUM INS Date Time 10 24 03 8 57 AM Figure 1 The Vortex opening screen After admiring this artistic representation of the extinction vortex and appreciating the fact that the Chicago Zoological Society devoted a lot of resources to develop VORTEX for your use click on the Close graphic message to enter the program The next screen shown in Figure 2 asks what Project you wish to open Note in Figure 2 and many subsequent figures the image shown is just the sub window that is relevant to the point being made Select the Open Project tab so that we can use an existing sample Project A number of sample projects are copied into the Projects subdirectory when you install VORTEX More sample projects will be made available at http www vortex9 org vortex html and we encourage users to contribute their project files to this site so that others may explore those data sets
126. andom numbers See examples below Proper use of random number seeds can be difficult Think carefully about the effect of any seed that you use in a function to be certain that it will produce the same random numbers when you want them and independent random numbers otherwise Any variable e g A for age Y for year R for run P for population included within the seed will cause the same random number to be chosen for each case with the same value for those variables A Y R P For example if you specify SRANDCP within a function then each population will get an independent random number and that set of random numbers will be the same over all calls to evaluate that function such as for every year every run and every individual within each population If you specify SRAND P 100 Y then each population will get a new independent random number each year of the simulation but the set of random numbers will be the same across all runs of the simulation You would normally want to include the variable R in the random number seeds e g SRANDCCR 10000 CP 100 Y in order to cause the random numbers to be independent among runs of the simulation See the examples below for further information about random number seeds The seeds used by VORTEX will be converted to integers between 0 and 65536 Non integer seeds will be truncated hence SRAND 35 23 SRAND 35 89 and values above 64K will be wrapped the modulus taken
127. apleleaf mussel Quadrula fragosa has been reduced to only a few sites in the St Croix River between Minnesota and Wisconsion in the United States As is typical of nearly all freshwater bivalves this species reproduces by broadcasting a large number of larval offspring known as glochidia into the water column Kjos et al 1998 estimated that an adult female mussel produced a mean number of 171 000 glochidia in a typical breeding cycle Only those glochidia that locate and encyst within the gills of its host fish excyst following metamorphosis and then settle onto suitable substrate on the river bottom will survive to the subadult age class Because of the impossibility at least with today s computer systems of tracking such a large number of individual offspring VoRTEx cannot normally deal with such high levels of fecundity However this situation can be made much more tractable by simply redefining what is meant by reproduction instead of defining it in terms of the production of glochidia we can define it as the number of individuals that successfully settle onto suitable river bottom substrate Kjos et al 1998 estimated that only about 0 2 of the glochidia find and successfully encyst onto a host that about 15 of those successfully metamorphose and excyst and about 20 of those excysted juveniles settle onto suitable substrate In other words Final brood size 171 000 glochidia x 0 002 encyst x 0 15 excyst x 0 2 settle
128. apopulations Rather than modeling causal processes as is done in individual based models lo gistic models can use observed correlates of population transitions to generate predictive models of metapopulation trends Individual based models require detailed data on the factors driving population processes while logistic transition incidence models require detailed data on the important correlates of population transitions over significant periods of time Generalized analytical models can be extremely valua ble for discerning many broad trends e g Belovsky 1987 but they do not provide the situation specific repre sentations that are needed to assess local threats to specific small natural populations nor usually the time specific projections that are needed to understand non equilibrial systems Thus detailed and often individual based models are more appropriate for comparing management options for endangered species recovery and local conservation planning We should also retain some skepticism regarding the generality of theoretical results until they have been confirmed to apply to simulated or better real popula tions in which the unrealistic assumptions of the theoreti cal model have been relaxed There have been recent en couraging confirmations of the ability of PVA models to predict population dynamics Brook et al 2000 but more comparisons are needed among analytical results simulation results from models of varyin
129. ar sool is 10 so that the frequency of an onset of a 2 soo 2 year catastrophe is 5 os 5 40 0 e 30 0 o A 20t 10 0 0 0 0 10 20 30 40 50 60 70 80 90 100 Year of Simulation Multi year catastrophes with a decreased impact in year 2 RATE 50 10 CSRANDCY R 100 lt 0 05 8 CSRANDCCY 1 CR 100 lt 0 05 The second seed is the same as the first seed from the previous year Thus the catastrophe he f has a lesser impact severity 0 84 rather a anol i than 0 80 in the second year This approach S ol can also be used to model catastrophes which 2 300l impact survival in one year using a function a eal with an expression like that in the first 9 20 0 L brackets above and fecundity in the second 5 sol year using a function containing the S iooi expression in the second set of brackets 50l Note that in example 18 catastrophes 0 0 Ciena always start in even numbered years while in Be OE ES le AU TSD HOE AD BE lt 90 109 this example catastrophes can begin in any Year of Simulation year Random variation across years RATE 50 10 SNRANDCY R 100 This is the same as imposing a mean rate of 80 0 F 50 with environmental variation of SD 10 70 0 60 0 50 0 f 40 0 30 0 Demographic Rate 20 0 O 10 20 30 40 50 60 70 80 90 100 Year of Simulation Chapter 5 Using Functions in VORTEX 21
130. are indicated in the pseudo code by italicized labels Many of the variables are arrays e g a value stored for each population or for each age class or for each indi vidual as suggested by the loops within which they are calculated and used The indices of such arrays are indicat ed within brackets e g MortalityRate p s x for each population p sex s and age x VORTEX uses many more variables not shown in the pseudo code for facili tating calculations and accumulating sums sums of squares and other components needed for the basic statis tics reported in the output In the pseudo code loops are indicated with FOR and END LOOP statements or by WHILE and END WHILE statements Conditional actions are indicated by IF and END IF statements or by IF ELSE and END IF ELSE statements BREAK indicates that program flow exits from the bottom of a loop CONTINUE indicates that program flow jumps back to the next value at the top of the loop Multiplication is indicated by the asterisk symbol indicates exponentiation SQRT indicates the positive square root Function modules defined outside of the main body of the pseudo code program are labeled in the form FUNC TION O and are specified below the main VORTEX program The actual C code is subdivided into many smaller functions the pseudo code shows only the flow of the overall program and its largest modules The functions RAND and NRAND indicate respectively
131. at the populations will unpredictably decline to zero Once populations are small the probability that they will become extinct can become more strongly determined by the amount of fluctuations in population size than in the mean deterministic population growth rate Thus extinction can be viewed as a process in which once common and widespread populations become reduced to small isolated fragments due to extrinsic factors the small remnant populations then become subjected to large fluctuations due to intrinsic processes the local populations occasionally and unpredictably go extinct and the cumulative result of local extinctions is the eventual extinction of the taxon over much or all of its original range Gilpin and Soul 1986 Clark et al 1990 The stochastic processes impacting on populations have been usefully categorized into demographic stochasticity environmental variation catastrophic events and genetic drift Shaffer 1981 Demographic stochasticity is the random fluctuation in the observed birth rate death rate and sex ratio of a population even if the probabilities of birth and death remain constant Assuming that births and deaths and sex determination are stochastic sampling processes the annual variations in numbers that are born die and are of each sex can be specified from statistical theory and would follow binomial distributions Such demographic stochasticity will be most important to population viability perhaps only
132. ate the mean To complete our initial description of these data we must define a measure of variability in the data The most commonly used measure of variability is the variance usually denoted by s g2 XI X E n i f The n 1 in the denominator is a necessary correction factor to ensure that the estimate from the sample is an unbiased estimate of the variance in the population If we measured the variance on the entire population we would not need this correction and could simply use n in the denominator From this equation it is evident that s gets larger as the amount of variability about the mean increases The standard deviation s often abbreviated as SD is the positive square root of the variance and is another very common descriptor of variation in a sample of observations As you enter data into VoRTEx for your species you will be defining the variation in demographic rates in terms of standard deviations We can also describe variability through the use of the coefficient of variation here labeled CV in which sample variability is expressed as a percentage of the mean CV 100 X Finally the simplest measure of variability is the range of values observed in the sample Unfortunately the observed range is highly sensitive to the number of observations that are made 32 Chapter 3 The Data Input Process VORTEX Version 9 User s Manual Box C Continued The Binomial Distribution When summariz
133. aths exceeding mean births from large fluctuations in numbers from effects of accumulated inbreeding or from a combination of these factors Given that there is considerable uncertainty about several aspects of the species biology and its habitat is the population likely to persist across the plausible ranges of parameters that might characterize the population In particular how sensitive are the population dynamics to varying estimates of reproductive success juvenile survival adult survival effects of natural catastrophes initial population size carrying capacity of the habitat and dispersal among populations Are there critical values for any of these parameters which demarcate a transition from a population that would be considered viable to one that is not Which factors have the greatest influence on the projected population performance If important factors are identified management actions might be designed to improve these factors or ameliorate the negative effects How much change would be required in aspects of the population in order to ensure population survival Appendix I 113 An Overview of Population Viability Analysis Using VORTEX VORTEX Version 9 User s Manual What would be the effect of removing some individuals from the population Would there be a significant benefit from supplementing the population with individuals translocated from other populations or released from captive breeding stocks Can the populatio
134. ation 0 001 0 012 Population 2 0 001 0 011 Metapop 0 002 WithinPop 0 011 Population 0 001 0 010 CAPS NUM INS Date Time 10 24 03 10 57 AM Ui Figure 43 Scenario Summaries table in Other Output The other table in Other Output provides Iteration Summaries a tabulation for each iteration of the year of extinction if extinction occurs final population size and if extinction does not occur the final gene diversity mean inbreeding coefficient and number of founder alleles remaining The data in this Iteration Summary table can be used to analyze the full distribution not just the mean and SD of the times to extinction final population sizes and genetic statistics The Export button for the Other Output tables Chapter 4 75 Viewing Model Results VORTEX Version 9 User s Manual will export these tables as text files delimited with semi colons These files can be imported directly into Excel or other spreadsheet software for further analysis the column headers should transfer over Graphs and Tables Click on the Graphs and Tables tab to access a section that lets you build tables and graphs displaying results for a variety of summary statistics Figure 44 In the Data Specification tab of Graphs and Tables you specify what Scenarios Populations Years and Variables you want to put into the table that will be displayed at the right VORTEX then also creates a graph of the data in your table and gives y
135. ation becomes fixed for a random subset of the diversity of the original metapopulation This second process can be a benefit of ECOLOGICAL BULLETINS 48 2000 population subdivision but it becomes significant only af ter populations lose most of their gene diversity and be come highly inbred and it depends on no populations be coming extinct as a result of that inbreeding or other fac tors In individual based PVA models that model genetic changes the effects of subdivision on gene diversity are quite different because the PVA models do not unrealisti cally constrain the populations to be constant in size Smaller populations undergo greater fluctuations in number and therefore lose gene diversity much faster than if they were part of a larger breeding population As a con sequence of this greater demographic instability fragment ed metapopulations will usually lose genetic variation both heterozygosity and number of alleles per locus more rapidly than does a single more panmictic latge popula tion This trend occurs even when the effects of fragmenta tion are partly offset by dispersal among partly isolated populations In models of populations of mountain brush tail possums Trichosurus caninus Lacy and Lindenmayer 1995 found that both heterozygosity and number of alle les were reduced more quickly when metapopulations of 100 or 200 possums were fragmented into 2 5 or 10 sub populations that exchanged up to 5 of the
136. ation biology the science of scarcity and diver sity Sinauer pp 13 34 Goodman D 1987 The demography of chance extinction In Soul M E ed Viable populations for conservation Cambridge Univ Press pp 11 34 Gyllenberg M and Hanski I 1992 Single species metapopula tion dynamics a structured model Theor Popul Biol 42 35 61 50 Hedrick R W 1994 Purging inbreeding depression and the probability of extinction full sib mating Heredity 73 363 372 Hedrick P W and Miller P S 1992 Conservation genetics techniques and fundamentals Ecol Appl 2 30 46 Hedrick P W et al 1996 Directions in conservation biology comments on Caughley Conserv Biol 10 1312 1320 Jim nez J A et al 1994 An experimental study of inbreeding depression in a natural habitat Science 266 271 273 Keane B 1990 The effect of relatedness on reproductive success and mate choice in the white footed mouse Peromyscus leu copus Anim Behav 39 264 273 Keller L E et al 1994 Selection against inbred song sparrows during a natural population bottleneck Nature 372 356 357 Kindvall O 1996 Habitat heterogeneity and survival of the bush cricket Metrioptera bicolor Ecology 77 207 214 Lacy R C 1987 Loss of genetic diversity from managed popula tions interacting effects of drift mutation immigration se lection and population subdivision Conserv Biol 1
137. ation bottle ECOLOGICAL BULLETINS 48 2000 necks Moreover of the few PVA models which consider genetic effects e g INMAT Mills and Smouse 1994 VORTEX Lacy 2000 and see Menges 2000 for referenc es on plant PVAs usually an assumption is made that individuals at the start of the population projection are all unrelated and noninbred Thus we may under appreciate existing or imminent genetic problems in populations which have already lost much genetic variation Forexam ple early analyses of the remnant population of the Florida panther Felis concolor coryi assumed that prior inbreeding would not diminish reproductive rates Seal and Lacy 1989 even though a majority of the males had only one or no functional testicles Seal et al 1992 Golden lion tamarins Leontopithecus rosalia rosalia are now restricted to very small remnants of the original Atlantic coastal forest of Brazil have been reduced to a population of ca 350 an imals and scattered smaller populations Ballou et al 1998 have low genetic diversity Forman et al 1986 and show significant depression of juvenile survival when inbred Dietz et al 2000 Thus any PVA models that as sume tamarins presently have adequate genetic diversity may project perhaps incorrectly that the population could lose much more variation before genetic problems began to reduce population viability PVA modeling of small population processes As illustrated in the examples presen
138. ation programs Methods for Analyzing Population Viability An understanding of the multiple interacting forces that contribute to extinction vortices is a prerequisite for the study of extinction recolonization dynamics in natural populations inhabiting patchy environments Gilpin 1987 the management of small populations Clark and Seebeck 1990 and the conservation of threatened wildlife Shaffer 1981 1990 Soul 1987 Mace and Lande 1991 Appendix I 109 An Overview of Population Viability Analysis Using VORTEX VORTEX Version 9 User s Manual Shaffer 1981 suggested several ways to conduct PVAs Perhaps the most rigorous method and the one that would produce the most defensible estimates would be an empirical observation of the stability and long term fates of a number of populations of various sizes Berger 1990 presented a good example of this approach in which he observed that populations of bighorn sheep in the mountains of the western USA persisted only when the populations consisted of more than 100 animals A few other studies of wildlife populations have provided empirical data on the relationship between population size and probability of extinction e g Belovsky 1987 Thomas 1990 but presently only order of magnitude estimates can be provided for MVPs of vertebrates Shaffer 1987 More empirical studies are needed but the time and numbers of populations required for such studies are precluded in the cases of most spec
139. auisutaceoesecbiadcausiseneszecuddscdeaniens 78 Project Report aceenscasscicsusraeenccisdaweaseiiceicasvecasarcdbaecuteddssunsiasiadevudensens 81 Access to Other Stored Output s ssssssssnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn nnn 82 Chapter 5 Using Functions in Vortex s ssssssssnsnnnnnnnnnnnnnnnnnnnnnnnnnnnn 83 Introduction seiinsinvaadeacagnansccusidaiiwanbnadkinaivsntunnenpawedsed duaaenaannchunereaanen 83 Specification of Demographic Rates aS Functions ssssssssnnsnnnnnnnnnnnnn 84 Using Random Numbers in Functions ss sssssssssnnsnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnna 88 Notes Regarding Function Syntax and USe s ssssssssnnsnnnnnnnnnnnnnnnnnnnnnnn 88 Using Functions to Examine Genetic Evolution ssssssssnssnnnnnnnnnnnnnnnnn 90 Examples of Rate Functions s ssssssssssnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn nna 90 Appendix I An Overview of Population Viability Analysis Using VORTEX coestacvaaueiouedesinudexcuaaseusbaneeicudersueuvasiutedeeusenee 101 Introduction sssssssssonsnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn anann 101 The Dynamics of Small Populations ssssssssssssnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn 101 What is Population and Habitat Viability Analysis ssssssssssnnnnnnnnn 103 Population Viability Analysis PVA ssssssssnnnnunnnnnnnnnnnnnnnnnnnnnnnnnnnn 104 Population and Habitat Viability Analysis PHVA s sssssssssssnsnnnnn 106 Methods for Analyzi
140. aution new VORTEX users to stay away from creating such complex models How to Use This Manual By following the detailed instructions provided in the VORTEX User s Manual you should be able to construct surprisingly complex models of stochastic growth dynamics of wildlife populations In addition to this instruction the User s Manual provides you with supplementary information designed to help you get the most out of VORTEX and to see how it and related software packages are used in practical applications of conservation biology gt Chapter 2 GETTING STARTED WITH VORTEX gives you information on the program s modest system requirements and shows you how to install run and close the program gt Chapter 3 CREATING A PROJECT DATA INPUT provides a wealth of information on the types of biological data necessary for developing a VORTEX population model and the mechanics of entering data into the program gt Chapter 4 VIEWING MODEL RESULTS describes how to view your model results in text tabular and graphical form and how to work with output data files to assist in effective data analysis gt Chapter 5 USING FUNCTIONS IN VORTEX presents a detailed description of how to use this major but complex feature gt Appendix I ANOVERVIEW OF POPULATION VIABILITY ANALYSIS USING VORTEX gives a brief introduction to the principles of small population biology and describes in more general terms the use of population viability analysis
141. being used is for practi tioners to develop their own computer programs This would result in the user having a full understanding of a model that would be specifically designed for the analysis Development of user specific and case specific models is usually not practical however as many population biolo gists are not skilled computer programmers and the time required to develop a complex model is often prohibitive Moreover a complex computer program developed by and used by one person will sometimes contain serious pro gramming errors The testing of programs that are widely used may be a necessary prerequisite for reliable popula tion viability analyses to be employed effectively in biodi 191 versity conservation Finally the flexibility and expansive capabilities of generic PVA software to model a large diver sity of population processes will often lead PVA practition ers to consider threats to population viability that would otherwise have been neglected Widely available PVA software can serve the same role as do statistical analysis packages The ease of use flexible application to diverse needs and extensive prior testing fa cilitate many applications that would not otherwise be at tempted Ideally perhaps all users of statistical methods would write their own programs or otherwise study the code of the software entrusted for the analyses More prac tically confidence is gained in the reliability of generic soft
142. ble demographic rates can be specified to be functions of an individual s haplotype The final frequencies of haplotype will not be tallied by Vortex because VorTex doesn t even know that the Individual State Variable you created is a categorical variable However you can obtain a complete listing of all individuals at the end of the simulation including their state variables by selecting the Special Option from the Project Settings screen to Produce a file of all living individuals at the end of each iteration You can then analyze those data in whatever spreadsheet or other utility software you prefer 40 Chapter 3 The Data Input Process VORTEX Version 9 User s Manual Dispersal Rates This next section of input Figure 22 is accessible only if you specified in the Scenario Settings that your scenario is to have more than one population In the grid on this screen you enter dispersal rates to specify the probability that a given individual of the appropriate age sex class will disperse from population A to population B in a specific year That is a rate of 1 00 indicates a 1 probability that an individual will migrate from population A to population B Equivalently if a population consists of 100 one year old females with a dispersal rate between two populations of 1 then one of these females would on average be expected to disperse in that direction in any given simulation year Dispersal rates need not be symme
143. breeding and genetic drift are more rapid in a population that fluctuates in size than in a stable popula tion of the same mean size Together with other factors which can reduce breeding success in smaller populations this can cause the ratio of the effective population size to the total size N N to diminish as a population becomes smaller Hence while N might be 500 when N 1000 N may be 30 when N 100 and just 10 when N 50 In yet another example of the interaction between ge netic and demographic threats to population viability the joint effects of stochasticity in these two processes have been found to lead to consequences which can be opposite those predicted from purely genetic models A number of authors have reported that a subdivided population will retain more gene diversity over time than will a single pan mictic population because genetic drift will by chance fa vor different alleles in the various isolated populations Boecklen 1986 Varvio et al 1986 Lacy 1987 However the models on which this conclusion is based assume that populations are constant in size The apparently beneficial effect of subdivision is partly due to an artifact of the mod els in which model constraints create more equal distribu tion of reproductive success and therefore higher N when the population is divided into subunits of fixed size Barton and Whitlock 1997 and partly due to the protec tion of different alleles as each subpopul
144. by specification within functions rather than more simply as a parameter given to VORTEX is that you have greater control over how EV is implemented in the model For example it is possible to specify that EV is concordant between two populations but not with others RATE 50 10 SNRANDCY R 100 CP gt 2 100 SRANDC P In this function the overall mean demographic rate is 50 with annual fluctuations due to EV SD equal to 10 Populations 3 and greater will experience independent annual fluctuations while populations 1 and 2 will fluctuate synchronously The use of year Y in the seed for the random number causes a new random number to be used each year The use of R iteration or run in the seed causes the sequence of seed values to be different in each simulation The inclusion of P gt 2 100 SRANDCP within the seed causes a different sequence of random numbers to be chosen for each population after the first two have been evaluated The seeds must include Y R 100 to ensure that every year iteration is independent If you use Y R as the seed then year 3 of iteration 1 will have the same value as year 2 of iteration 2 etc In the simpler example of EV in K given above no seed was needed or specified so an independent random number will be selected each iteration each year and each population These examples show how elaborate and Chapter 5 89 Using Functions in VORTEX VORTEX Version 9 User s Manual non intuitive the
145. ccur because independent studies have generated discordant estimates Uncertainty can occur because environmental conditions or population status have been changing over time and field surveys were conducted during periods which may not be representative of long term averages Uncertainty can occur because the environment will change in the future so that measurements made in the past may not accurately predict future conditions Sensitivity testing is necessary to determine the extent to which uncertainty in input parameters results in uncertainty regarding the future fate of the population If alternative plausible parameter values result in divergent predictions for the population then it is important to try to resolve the uncertainty with better data Sensitivity of population dynamics to certain parameters also indicates that those parameters describe factors that could be critical determinants of population viability Such factors are therefore good candidates for efficient management actions designed to ensure the persistence of the population 112 Appendix I An Overview of Population Viability Analysis Using VORTEX VORTEX Version 9 User s Manual The above kinds of uncertainty should be distinguished from several more sources of uncertainty about the future of the population Even if long term average demographic rates are known with precision variation over time caused by fluctuating environmental conditions will cause uncertainty in the
146. conservation plans At low population densities the social systems of many species may be disrupted Such Allee effects are one type of density dependence in reproductive success Although the impor tance of understanding and modeling density dependence has been stressed by some authors Mills et al 1996 Brook et al 1997 most of the attention has been given to changes in demographic rates as the population ap proaches carrying capacity Yet it is not when a population is near carrying capacity that we need to be concerned about extinction Allee effects at the low end of density can be incorporated into several of the widely available ge neric PVA models e g RAMAS Space Akcakaya and Ferson 1992 VORTEX Lacy 2000 but this feature seems rarely to be used Individual based models can be tailored to provide detailed representations of specific so cial systems and this approach was used to look at how the interactions of stochastic processes and pack structure im pact viability of wolves Vucetich et al 1997 and wild dogs Vucetich and Creel 1999 Disruptions of the breeding system can occur for rea sons that range from the obvious to the subtle At very low population densities animals may be unlikely to encoun ter any potential mates when they are ready to breed and non selfing plants may not be adequately pollinated Menges 2000 Sumatran rhinoceroses Dicerorhinus su matrensis now exist at densities of only a
147. counted for by de mographic stochasticity Mirande et al 1991 The reduced variation in survival as the population grew in size from 18 birds in 1938 to ca 150 birds in the 1990s is clearly evident Demographic stochasticity has been recognized as a ECOLOGICAL BULLETINS 48 2000 Fig 1 Percent of whooping cranes observed each year on the wintering grounds which did not survive to return the following year In years with no bar shown no birds died Data from Mirande et al 1991 and pers comm Percent Mortality of Adult Birds Annual mortality of Whooping Cranes 1940 1945 1950 1955 1960 1965 1970 1975 1980 1985 1990 1995 potential threat to very small populations but the contri bution it can make to population instability has been un derestimated Based on simple calculations of the proba bility that all individuals will be of the same sex or die synchronously it has commonly been stated that demo graphic stochasticity can cause extinction only when pop ulations fall below ca 10 20 individuals Goodman 1987 Shaffer 1987 However processes that are not seri ous problems when acting alone can become significant contributors to population instability and decline when they act synergistically with other threatening processes The last five dusky seaside sparrows Ammospiza maritima nigrescens were all males an unfortunate but not overly sur prising event that effectively eliminated the taxon The probability tha
148. crease susceptibility to environmental perturbations and catastrophes Reduced population growth and greater fluctuations in numbers in turn accelerates genetic drift Crow and Kimura 1970 These synergistic destabilizing effects of stochastic process on small populations of wildlife have been described as extinction vortices Gilpin and Soul 1986 What is Population and Habitat Viability Analysis Analyses which have used the VORTEX simulation for guiding conservation decisions refer variously to Population Viability Analysis PVA Population and Habitat Viability Analysis PHVA Population Vulnerability Analysis Population Viability or Vulnerability Assessment and other variants on the name This diversity of terminology has caused some confusion among practitioners of the PVA or PHVA approach and probably even more confusion among wildlife managers who have tried to understand what analysis was being described and whether it could be a useful tool in their efforts to conserve biodiversity The diversity of perceptions about the PVA approach is not limited to its name Different people mean different things by PVA and the definitions and practice of PVA are constantly evolving We don t think it is not the case as has sometimes been suggested that some people are doing PVA correctly and others incorrectly but rather that people are using different if related kinds of analyses and labeling them with th
149. ctions that are underway and planned but an orang utan PHVA recognized that releases of confiscated pet orang utans are unlikely to have a conservation benefit for those populations which are facing habitat destruction not stochastic fluctuations and inbreeding For many species such as the whooping crane Grus americana the temporarily extinct in the wild black footed ferret Mustela nigripes and the Puerto Rican parrot Amazona vitatta only a single population persisted in the wild Although those populations may have been maintained or even increased for a number of years the principal threat was that a local catastrophe e g disease epidemic severe storm could decimate the population Clark 1989 Lacy et al 1989 Mirande et al 1991 The primary recovery actions therefore needed to include the establishment of additional populations Tragically some taxa such the eastern barred bandicoot Perameles gunnii in Australia may be critically threatened simultaneously by deterministic factors and stochastic processes Lacy and Clark 1990 PVA is formally an assessment of the probability of extinction but PVA methods often focus on other indicators of population health Mean and variance in population growth Lindenmayer and Lacy 1995a 1995b 1995c changes in range distribution and habitat occupancy Hanski and Gilpin 1991 1997 and losses of genetic variability Soul et al 1986 Lande and Barrowclough 1987 Seal 1992 Lacy a
150. ctors that threaten the persistence of populations Lacy 1993a Lindenmayer et al 1993 The Conservation Breeding Specialist Group CBSG of the IUCN s Species Survival Commission especially has advocated and used workshops centered on PVAs to provide guidance to conservation assessment and planning see references to CBSG workshops in Appendix III Over the past few years the PVA workshop as an approach to species conservation has expanded considerably beyond the quantitative analysis of extinction probabilities as advanced by Shaffer 1981 1990 Soul 1987 Gilpin 1989 Clark et al 1991 Boyce 1992 and others PVA workshops have incorporated consideration of resource use and needs by local human populations Seal et al 1991 Bonaccorso et al 1999 education programs for the local human populations Odum et al 1993 trade issues Foose et al 1993 and trends in human demographics and land use patterns Walker and Molur 1994 Herrero and Seal 2000 Recognizing that the conservation assessment workshops increasingly incorporated more than just the population biology modeling which still formed a core organizing and analysis framework for the workshop the CBSG has termed their workshops Population and Habitat Viability Analyses PHVA We would recommend that the term Population and Habitat Viability Analysis PHVA be used to describe the collaborative workshop approach to species conservation that centers on but encompasses mor
151. d Animal and Plant Populations Menlo Park CA Benjamin Cummings Shaffer M L 1981 Minimum population sizes for species conservation Bioscience 1 131 134 Shaffer M L 1987 Minimum viable populations Coping with uncertainty Pages 69 86 in Soul M E ed Viable Populations for Conservation Cambridge Cambridge University Press Shaffer M L 1990 Population viability analysis Conservation Biology 4 39 40 Simberloff D A 1986 The proximate causes of extinction Pages 259 276 in Raup D M and D Jablonski eds Patterns and Processes in the History of Life Berlin Springer Verlag Simberloff D A 1988 The contribution of population and community biology to conservation science Annual Review of Ecology and Systematics 19 473 511 Simmons M J and J F Crow 1977 Mutations affecting fitness in Drosophila populations Annual Review of Genetics 11 49 78 Sokal R R and F J Rohlf 1994 Biometry 3 ed New York W H Freeman and Company Soul M E ed 1987 Viable Populations for Conservation Cambridge Cambridge University Press Appendix IT 127 Literature Cited VORTEX Version 9 User s Manual Soul M M Gilpin W Conway and T Foose 1986 The millenium ark How long a voyage how many staterooms how many passengers Zoo Biology 5 101 113 Starfield A M and A L Bleloch 1986 Building Models for Conservation and Wildlife Management New York Macmillan Thomas C D 1990 What do re
152. d survival that arise from random variation in environmental conditions For a more detailed introduction to this topic refer to Boxes C and D EV impacts all individuals in the population simultaneously The sources of this environmental variation are outside the population examples include weather predator and prey population densities and parasite loads These factors can affect reproduction and survival independently or simultaneously Check this box if you think that good years for reproduction are also good years for survival Chapter 3 31 The Data Input Process VORTEX Version 9 User s Manual Box C A Brief Statistics Primer Many demographic characteristics among wildlife species e g birth and death rates litter size etc fluctuate randomly in magnitude from one year to the next In order to be able to describe this variability and to use VorTex most effectively you must have at least some basic knowledge of a few concepts in statistics Population Statistics vs Sample Statistics It is important to keep in mind the distinction between the value of a variable or statistic in a population and the value of the variable across a smaller set of observations sampled from that population Usually we do not know the true value for the entire population and that is something we wish to estimate by examining a sample from that population For some statistics such as the mean the best and unbiased estimate of the true populatio
153. ded by VORTEX Below are described all the input parameters requested on these screens Scenario Name Within each project you create scenarios that are defined by their sets of parameter values As you will see after you have defined one scenario often a Baseline or Best Guess scenario it is easy to create additional scenarios that change one or a few of the input values The default scenario name for a new project is just Scenario 1 On the Scenarios Settings screen you should change this to a more descriptive name Number of Iterations The answer to this question instructs VORTEX on how many times you wish to repeat the simulation given the data that you provide in the subsequent steps Each repetition is generally defined as a run or iteration Because VORTEX uses a random number generator to simulate random events in the life cycle no two iterations will be identical Thus to obtain a more complete picture of your simulated population you will want to generate multiple iterations of your model As a first step in the development of a sound population model you may want to make sure that the simulated population is behaving in a manner that is similar to your expectations To check this you can limit the number of iterations to just 10 or 20 If you wish to obtain a relatively crude picture or your results use 100 iterations Once you are comfortable with the model and wish to obtain a more rigorous de
154. demographic rate based on observed mean and variance of annual values Solid and dashed curves show the normal distributions that most closely fit the observed data with and without the catastrophic outlier while the dotted line shows the normal approximation to the binomial distribution expected solely from environmental variability and excluding the outlier The difference between the solid and dotted lines gives the variation attributable to demographic stochasticity Excluding outlier wee ae Including outlier Outlier x Lk 7 cx ae 10 20 20 30 40 50 60 70 80 Frequency Annual Demographic Rate Annual Demographic Rate Chapter 3 35 The Data Input Process VORTEX Version 9 User s Manual Box D Continued The left panel of Figure D 1 shows ten years of expected values of a given demographic rate say juvenile mortality in a simulated wildlife population Each bell shaped curve depicts the probability distribution we would expect from demographic stochasticity acting on that rate in that year Actually these little curves of demographic stochasticity would be binomial but the normal distributions are close enough for illustration purposes For example the expected rate yz in year 1 is 15 2 However when the fate of each juvenile in the population is considered it is possible that the actual rate may deviate from 15 2 solely from this sampling proces
155. dently in those populations for which it is local Normally the frequency of a global catastrophe would be set to be the same in each population affected by that global catastrophe However you can specify different frequencies for a global catastrophe among the populations In that case when the catastrophe hits a population it will also hit all other populations in which that catastrophe has at least as high a frequency of occurrence The catastrophe will sometimes occur in the populations that have higher frequencies while not occurring in populations with lower frequencies Case Study X A catastrophe sampler 1 Attwater s Prairie Chicken The impact of hurricanes was assessed by Seal 1994 in a Population and Habitat Viability Assessment for Attwater s prairie chicken Tympanuchus cupido attwateri an endangered bird that was reduced to just 3 disjunct subpopulations in coastal southeastern Texas Based on data from the National Oceanic and Atmospheric Administration it was assumed that hurricanes strike this area on average once every 70 years Species biologists indicated that populations in Refugio County dropped from 1 200 1 500 in the spring prior to Hurricane Beulah to approximately 250 in October following that storm Therefore it was assumed that catastrophic hurricanes would result in 80 mortality of the adult post fledging population This would translate into a severity factor with respect to survival of 0 20 Becaus
156. derations must be applied to all other demographic rates such as mortality age of first and last breeding etc In addition appropriate migration harvesting and supplementation rates must be established relative to the revised time cycle Extinction Definition VORTEX gives you three methods to define extinction of your population For most sexually reproducing species ultimate biological extinction is assured whenever the population has declined to the point that it no longer has individuals of both sexes In the first and most common choice extinction is simply defined as the absence of at least one sex You also have the option to assess the probability of a population dropping below a user defined threshold size termed quasi extinction The use of quasi extinction risk offers a useful alternative to the standard extinction risk If you chose to have the simulation tally quasi extinctions you need to specify the threshold critical size below which a population is considered extinct The simulation will however continue to run as the population may grow again to a size above this threshold Such recovery from quasi extinction would be tallied as a recolonization event A third option is available under Special Options on the Project Settings screen which defines extinction as any decline in population size Number of Populations VORTEX can model a single isolated population or a complex metapopulation composed of up to
157. derstand For example the typical representation of the growth of a wildlife population by an annual percent growth rate is a simplified mathematical model of the much more complex changes in population size Representing population growth as an annual percent change assumes constant exponential growth ignoring the irregular fluctuations as individuals are born or immigrate and die or emigrate For many purposes such a simplified model of population growth is very useful because it captures the essential information we might need regarding the average change in 110 Appendix I An Overview of Population Viability Analysis Using VORTEX VORTEX Version 9 User s Manual population size and it allows us to make predictions about the future size of the population A detailed description of the exact changes in numbers of individuals while a true description of the population would often be of much less value because the essential pattern would be obscured and it would be difficult or impossible to make predictions about the future population size In considerations of the vulnerability of a population to extinction as is so often required for conservation planning and management the simple model of population growth as a constant annual rate of change is inadequate for our needs The fluctuations in population size that are omitted from the standard ecological models of population change can cause population extinction and therefore are often the
158. ding age Maximum Number of Progeny per Year Enter the most individuals born to a given female during a year time cycle If your species produces more than one set of offspring in the form of litters clutches pods etc per year but you are using a year as your time cycle add each set together and then enter the total number born during the year You can enter the maximum number that has ever been recorded even though such an event may be quite rare and later on during the data input process you can then assign a low probability of occurrence to this maximum value You have the option of entering a mean and standard deviation for the distribution of offspring numbers rather than specifying the percentage of females producing each possible number of young see below This removes the limitation on the size of offspring numbers that can be modeled and therefore makes it much easier to model species with high fecundities To choose this option enter 0 for the maximum number Subsequent screens will allow you to specify the nature of this normal distribution see p 51 44 Chapter 3 The Data Input Process VORTEX Version 9 User s Manual EF When annual offspring numbers per female are not large for example on the order of five or fewer it is recommended to specify the exact distribution rather than using the optional normal distribution Case Study VI Modeling species with high fecundity The distribution of the winged m
159. dult mortality was only slightly greater than that expected due to random demo graphic stochasticity Mirande et al 1991 Figure 4 shows the population trends for the palila Loxioides bailleui a finch which is restricted to the ma mane forests on the slopes of the major volcanoes of the island of Hawai i Although some variation in population size may be caused by imprecise census estimates the spe cies clearly undergoes striking fluctuations in numbers even though the mean population size is ca 30 times great er than the current population of whooping cranes Palila must be sensitive to environmental variation probably Palila 1980 1993 tt 1 1990 1992 1982 1984 E E 43 with respect to both breeding and survival In part because of the much higher sensitivity to environmental variation PVA modeling projected a higher probability of extinction for palila Ellis et al 1992 than for the much smaller pop ulation of whooping cranes Mirande et al 1991 The contribution of environmental variation to extinction vor tices is well recognized Belovsky 1987 Goodman 1987 Foley 1994 but as with demographic stochasticity we may not always recognize how large the effect can be Disrupted breeding systems There is another cause of demographic instability in small populations but it does not fit easily within the categories of Shaffer 1981 is rarely considered in PVA models and may not be fully recognized in
160. e 1 13 1 69 2 06 2 33 2 53 2 70 2 85 2 97 3 08 3 47 3 74 3 93 4 09 4 32 4 50 Although environmental variation in birth and death rates can have a substantial impact on the viability of a population it is often difficult to obtain the data needed to estimate EV Long term field studies are needed in order to determine the amount of fluctuation that occurs in the demographic rates of your 50 Chapter 3 The Data Input Process VORTEX Version 9 User s Manual population If these data are available the standard deviation in mean birth rate can be simply calculated using the methods in Box C If your dataset is small but you are comfortable with making a rough quantitative estimate of the variability you can use the technique presented in Box E A common problem in estimating annual fluctuations in demographic rates is that the data might be so sparse that it is difficult or impossible to estimate the parameters on an annual basis If this is the case you might be forced to admit that the data are not sufficient to allow estimation of the variability around the mean values The only alternatives are to guess at the fluctuations in reproductive and mortality rates based on a general understanding of the natural history of the species or to omit environmental variability from the model altogether by entering 0 when each standard deviation is requested In this case you must recognize that a potentially important component of po
161. e it will install and run properly on computers with Pentium or newer processors running Win95 Win98 WinXP Win2000 or WinNT operating systems We believe that VORTEX will work properly with a diversity of Windows Regional settings for example it can use common European data formats However we cannot guarantee that it will work with all system configurations At this time the user interface of VORTEX is presented in American English At a future time versions in Spanish German French or other languages may be made available For many analyses VORTEX will use much of your computer s system resources Faster results and better performance will be obtained if you do not try to run other large applications such as MS Word Excel or Outlook at the same time that VORTEX is running The program may not run properly with less than 64 MB of system memory RAM and even more RAM will be required if you want to run other applications concurrently In addition the size of the populations that can be analyzed will be determined by the available RAM For example simulation of a population of 5000 living animals can require up to about 50 MB of RAM for storage of inbreeding calculations The program requires much more memory if you include inbreeding depression in your analyses so omitting inbreeding depression see Chapter 3 will allow analysis of larger populations and will run much faster Installation To install VORTEX from the CD P
162. e Fluctuations in rates can be estimated No catastrophic events of interest Catastrophic events modeled Only polygamous breeding Polygamous or monogamous breeding Random breeding Some adults excluded from breeding Non random distribution of fecundity Population starts at stable age distribution Starting population not at stable age distribution Constant sex ratio Unequal sex ratio No trends in habitat expected Trends projected in habitat quality or area No manipulation of animal numbers Managed removal supplementation or translocation Fish amphibian invertebrate or plant Bird mammal or reptile You have lots of money You have lots of time for buying software for running analyses and summarizing results Chapter2 7 Getting Started with VORTEX VORTEX Version 9 User s Manual Getting Around in VORTEX Your work in VORTEX will be structured as Projects and Scenarios A Project will contain all your input output and notes about a case that you are exploring Often a Project will contain all the analyses about a given species or population You could split your analyses of a species among multiple Projects but that would preclude you from easily copying input results or settings among the separate Projects containing your work On the other hand there is no advantage to combining work on different species or cases into one Project and it may be more useful and less confusing to keep distinct PVAs in separate VORTEX Projects It
163. e No Create initial individuals Set year t Determine annual modifiers for EV Determine if catastrophes occur Reproduction Mortality Harvest of individuals Supplement with new individuals Dispersal among populations ronmental variation in demographic rates is imposed by sampling rates from specified distributions during each simulated year Catastrophes which occur with specified probabilities cause one year reductions in reproduction and survival Genetic effects are modeled as reduced survi vorship of inbred individuals End Calculate and output mean census statistics Yes Iteration gt ni Increment iteration Yes t gt ny Increment year t Annual census of Demographic status Genetic variation Extinction status Remove excess individuals Fig 1 Flow chart of the primary components of the Vortex simulation Each step from Create initial individuals through Annual census is applied to each population in a modeled metapopulation year ny number of years simulated mp number of populations ni number of iterations N population size K carrying capacity EV environmental variation ECOLOGICAL BULLETINS 48 2000 193 VORTEX program pseudo code BEGIN PROGRAM VORTEX Initialize random number generator See Note 1 FOR each scenario READ SPECIES PARAMETERS IF NumberOfPopulations gt 1 READ _MIGRATION_PARAMETE
164. e Time 10 24 03 3 51AM 4 Figure 23 Reproductive System input section Chapter 3 43 The Data Input Process VORTEX Version 9 User s Manual VORTEX does not fully customize the details of mating systems because of the complexities of considering a wide variety of species and their particular characteristics More complex breeding systems can substantially impact genetic variation but are less likely to seriously alter the demographic performance of a population In the future VORTEX will also allow you to model a species with hermaphroditic breeding that is a species in which each individual is both male and female and can therefore potentially mate with any other individual including itself Presently this option is not yet enabled Age of First Reproduction for Females and Males VORTEX defines breeding as the time when the first offspring are born not the age of onset of sexual maturity or the age of first conception The program also assumes that breeding and for that matter all other events occurs at discrete intervals usually years but this can be described in terms of whatever you have defined as a suitable time cycle Thus breeding age must be entered as an integer value you cannot enter 2 5 years as the first age of breeding but must enter either 2 or 3 years In addition you should enter the median age of first breeding not the earliest age ever observed since the earliest observed age may not be typical of the
165. e generations of a simulation This diminishes the probability that inbred individuals in subsequent generations will be homozygous for a lethal allele Heterozygote advantage is modeled by specifying that juvenile survival is related to inbreeding according to the logarithmic model In S A BF in which S is survival F is the inbreeding coefficient A is the logarithm of survival in the absence of inbreeding and B is the portion of the lethal equivalents per haploid genome that is due to heterozygote advantage rather than to recessive lethal alleles Unlike the situation with fully recessive deleterious alleles natural selection does not remove deleterious alleles at loci in which the heterozygote has higher fitness than both homozygotes because all alleles are deleterious when homozygous and beneficial when present in heterozygous combination with other alleles Thus under heterozygote advantage the impact of inbreeding on survival does not diminish during repeated generations of inbreeding Unfortunately for relatively few species are data available to allow estimation of the effects of inbreeding and the magnitude of these effects apparently varies considerably among species Falconer 1981 Ralls et al 1988 Lacy et al 1993 and even among populations of the same species Lacy et al 1996 Even without detailed pedigree data from which to estimate the number of lethal equivalents in a 116 Appendix I An Overview of Population Viabilit
166. e hurricanes typically occur during late summer and autumn it was assumed that such an event would not affect reproductive success as breeding occurs in the spring Winged Mapleleaf Mussel Kjos et al 1998 identified major upriver chemical spills as the primary catastrophe impacting the last surviving populations of the winged mapleleaf mussel Quadrula fragosa A chemical spill of this type could occur as a result of for example an accident involving a vehicle carrying hazardous materials A detailed analysis by the Minnesota Department of Transportation suggests that the probability of such an event could be quite small see Kjos et al 1998 for a detailed description of the calculation A very conservative estimate of the probability was set at 0 20 i e it is thought to occur perhaps on average once every 500 years However if it were to occur it would have major effects on the mussel populations in the year that such an event occurs both reproductive success proportion of adult females breeding and survival spread out across all age classes would be reduced by 30 equivalent to a pair of severity factors equal to 0 70 Mountain Gorilla The primary catastrophic event modeled by Werikhe et al 1998 in their evaluation of mountain gorilla Gorilla gorilla beringei viability was the spread of disease from humans to gorillas As the extent of human gorilla interaction increases with rising human population pressures the lik
167. e order in which you select the years is shown in the list that accumulates on the right and this would be the order that the years show up in your data table Presumably you would want the years to be in ascending order in your table To re order the years click on the Sort Ascending command After you have selected and possibly sorted the years you want in your table click OK to send that selection to the Data Specification screen Selection of Populations or Variables is done in a similar way except that they are more straightforward to select because they are displayed in a single vertical list of check boxes After you have completed specification of your data table you can click on commands to print the table send it to your Project Report or export it to a text file delimited with semi colons Data Graphs If you click on the Data Graphs tab VORTEX will display a graph of the data that are in your table Figure 47 The dimension used for table columns is plotted as the x axis the dimension used for the rows of the 78 Chapter 4 Viewing Model Results VORTEX Version 9 User s Manual table will create separate lines on the graph the values displayed in the table will be the y axis of the graph To remember how the graph axes relate to the table lay out think of each row of the table as being plotted as a line on the graph with the columns place in the row being the dependent x axis variable and the value giv
168. e same or similar terms What analysis is correct depends on the need and the application Below we attempt to clarify what PVA is by suggesting a more consistent terminology and by describing the features that characterize the application of the PVA approach to conservation The perspective offered here is necessarily biased by personal experiences in conservation we will not attempt an exhaustive historical account of this field Population viability analysis originally described methods of quantitative analysis to determine the probability of extinction of a population Shaffer 1981 first defined a minimum viable population MVP as the size at which a population has a 99 probability of persistence for 1000 years but it might be more meaningful biologically to consider it to be the size below which a population s fate becomes determined largely by the stochastic factors that characterize extinction vortices One concept of population viability analysis is any methodology used to determine an MVP Shaffer 1990 More broadly PVA is the estimation of extinction probabilities and other measures of population performance by analyses that incorporate identifiable threats to population survival into models of the extinction process Brussard 1985 Gilpin and Soul 1986 Burgman et al 1993 Lacy 1993 1994 Shaffer s 1981 original term minimum viable population MVP has fallen into disfavor Soul 1987 even as the PVA approach has risen
169. e survival of inbred animals to model the effects of inbreeding depression Inbreeding depression is modeled as a loss of viability of inbred animals during their first year The severity of inbreeding depression is commonly measured by the number of lethal equivalents in a population Morton et al 1956 The number of lethal equivalents per diploid genome estimates the average number of lethal alleles per individual in the population if all deleterious effects of inbreeding were due entirely to recessive lethal alleles A population in which inbreeding depression is one lethal equivalent per diploid genome may have one recessive lethal allele per individual it may have two recessive alleles per individual each of which confer a 50 decrease in survival or it may have some other combination of recessive deleterious alleles which equate in effect with one lethal allele per individual VORTEX partitions the total effect of inbreeding the total lethal equivalents into an effect due to recessive lethal alleles and an effect due to loci at which there is heterozygote advantage superior fitness of heterozygotes relative to all homozygote genotypes To model the effects of lethal alleles each founder starts with a unique recessive lethal allele and a dominant non lethal allele at up to five modeled loci By virtue of the deaths of individuals that are homozygous for lethal alleles such alleles can be removed slowly by natural selection during th
170. e than a Population Viability Analysis in the narrow sense The concept of a PHVA continues to expand and evolve as it should considering the need for more holistic and flexible approaches to conservation e g Ruggiero et al 1994 Thus in the usage I recommend PVA is a quantitative analysis of the probability of population persistence under defined sets of assumptions and circumstances PHVA is a workshop process that brings to bear the knowledge of many people on species conservation eliciting and assessing multiple options for conservation action principally by using the tool of PVA as a way evaluate present threats to population persistence and likely fates under various possible scenarios Population Viability Analysis PVA Two defining characteristics of a PVA are an explicit model of the extinction process and the quantification of threats to extinction These features set PVA apart from many other analyses of the threats facing species including for example the IUCN Red Books of Threatened Species As a methodology to estimate the probability of extinction of a taxon PVA necessarily must start with an understanding or model of the extinction process Clark et al 1990 104 Appendix I An Overview of Population Viability Analysis Using VORTEX VORTEX Version 9 User s Manual Generally the model of extinction underlying a PVA considers two categories of factors deterministic and stochastic Deterministic factors those tha
171. e will occur if a randomly generated number between zero and one is less than the probability Appendix I 115 An Overview of Population Viability Analysis Using VORTEX VORTEX Version 9 User s Manual of occurrence Following a catastrophic event the chances of survival and successful breeding for that simulated year are multiplied by severity factors For example forest fires might occur once in 50 years on average killing 25 of animals and reducing breeding by survivors 50 for the year Such a catastrophe would be modeled as a random event with 0 02 probability of occurrence each year and severity factors of 0 75 for survival and 0 50 for reproduction Catastrophes can be local impacting populations independently or regional affecting sets of populations simultaneously Genetic processes VORTEX models loss of genetic variation in populations by simulating the transmission of alleles from parents to offspring at a hypothetical neutral non selected genetic locus Each animal at the start of the simulation is assigned two unique alleles at the locus Each offspring created during the simulation is randomly assigned one of the alleles from each parent VORTEX monitors how many of the original alleles remain within the population and the average heterozygosity and gene diversity or expected heterozygosity relative to the starting levels VORTEX also monitors the inbreeding coefficients of each animal and can reduce the juvenil
172. eal U S R C Lacy K Medley R Seal and T J Foose eds 1991 Tana River Primate Reserve Conservation Assessment Workshop Report Apple Valley MN Captive Breeding Specialist Group SSC TUCN Seal U S J Manansang D Siswomartono T Suhartono J Sugarjito eds 1996 Komodo Monitor Varanus komodoensis Population and Habitat Viability Assessment Workshop Report Apple Valley MN Conservation Breeding Specialist Group SSC IUCN 136 Appendix III VorTEX Bibliography VORTEX Version 9 User s Manual Seal U S S Walker and S Molur eds 1995 Barasingha Population and Habitat Viability Assessment Report Apple Valley MN Conservation Breeding Specialist Group SSC IUCN Sillero Zubiri C J Malcolm S Williams J Marino Z Tefera K Laurenson D Gottelli A Hood D Macdonald D Wildt and S Ellis 2000 Ethiopian Wolf Conservation Strategy Workshop Final Report Apple Valley MN Conservation Breeding Specialist Group SSC IUCN Soberon R P Ross and U S Seal eds 2000 Cocodrilo Cubano An lisis de la Viabilidad de la Poblacion y del Habitat Borrador del Informe Apple Valley MN Conservation Breeding Specialist Group SSC TUCN Soemarna K R Tilson W Ramono D W Sinaga R Sukumar T J Foose K Traylor Holzer and U S Seal eds 1994 The Sumatran Rhino in Indonesia Population and Habitat Viability Analysis Report Apple Valley MN Captive Breeding Specialist Group SSC IUCN
173. ear effects Vv VVVVV Note that VORTEX includes within the basic data entry screens the option to model reproduction as a density dependent function and an option to model carrying capacity as having a linear change over a Chapter 5 83 Using Functions in VORTEX VORTEX Version 9 User s Manual specified number of years Easy access to these two particular functions are provided because they are needed more frequently than are detailed functional dependencies of most other rates Even for these two rates however you can specify these functions to have almost any shape if you use the function editor to specify the rates For most users and for most purposes there will be no need or desire to model demographic rates as functions it is usually fully adequate to specify fixed demographic rates rather than functions Specification of rates as functions can be difficult the appropriate form of the function is rarely known the function parameters are usually very difficult to estimate and it is not trivial to enter a function correctly If alternative functions need to be examined in sensitivity testing the number of combinations of input parameters to be explored can quickly become overwhelming Consequently we would not recommend that novice users or students use the function option within VORTEX Specification of Demographic Rates as Functions Dependencies of demographic rates on population and individual parameters are entered into
174. eed in a given year this assumes of course that animals can breed throughout their normal lifespan A more detailed example is presented below in Case Study VIII EV in Breeding Environmental variation EV in reproduction is modeled by the user entering a standard deviation SD for the percent females producing litters of offspring see Box C for a refresher on some basic concepts in statistics and their calculation VORTEX then determines the percent breeding for a given year by sampling from a binomial distribution with the specified mean and standard deviation Chapter 3 49 The Data Input Process VORTEX Version 9 User s Manual Case Study VIII Using interbirth intervals to estimate annual adult females breeding In a risk assessment for the Ugandan population of the eastern subspecies of chimpanzee Pan troglodytes schweinfurthii Edroma et al 1997 used interbirth interval IBI data from a number of well studied populations in Uganda and neighboring countries The mean IBI for these populations was set at 5 years However the early death of an infant will cause the IBI for a given female to shorten dramatically Data suggest that if an infant dies at 6 months of age the IBI will be reduced to about 2 years This rapid response means that the effect of infant mortality on population growth may be quite small so long as the mother is not killed or harmed by the same forces responsible for the death of her infant In addition i
175. el Lince Ib rico Lynx pardinus Apple Valley MN Conservation Breeding Specialist Group SSC TUCN Herrero S P S Miller and U S Seal eds 2000 Population and Habitat Viability Assessment Workshop for the Grizzly Bear of the Central Rockies Ecosystem Ursus arctos horribilis Apple Valley MN Conservation Breeding Specialist Group SSC IUCN Hosack D A P S Miller J J Hervert and R C Lacy 2002 A population viability analysis for the endangered Sonoran pronghorn Antilocapra americana sonoriensis Mammalia 66 2 207 229 Howells O and G E Jones 1997 A feasibility study of reintroducing wild boar Sus scrofa to Scotland Are existing woodlands large enough to support minimum viable populations Biological Conservation 81 77 89 Jackson S M 1999 Preliminary predictions of the impacts of habitat area and catastrophes on the viability of Mahogany Glider Petaurus gracilis populations Pacific Conservation Biology 5 1 56 62 Jennings M R Beiswinger S Corn M Parker A Pessier B Spencer and P S Miller eds 2001 Population and Habitat Viability Assessment for the Wyoming Toad Bufo baxteri Apple Valley MN Conservation Breeding Specialist Group SSC IUCN de Jong Y A P R van Olst and R C C M de Jong 1997 Feasibility of reintroduction of the Eurasian lynx Lynx lynx on De Veluwe the Netherlands by using the stochastic simulation programme VORTEX Zeitschrift fuerSaugetierkunde 62 44
176. elihood of passing human diseases to gorillas is thought to be markedly higher Data from discussions with primate veterinarians at the PHVA Workshop led to the construction of the following major disease events e Influenza like disease 10 annual probability of occurrence 5 reduction in survivorship no effect on reproduction e Severe but not pandemic viral disease 10 annual probability of occurrence 25 reduction in survivorship 20 reduction in the proportion of adult females breeding e Hypothetical viral disease with chronic cyclicity targeting the organ reproductive system 4 annual probability of occurrence 25 reduction in survivorship 100 reduction in the proportion of adult females breeding i e no reproduction during a catastrophe year Chapter 3 55 The Data Input Process VORTEX Version 9 User s Manual Frequency Once the scope of the catastrophe is identified you need to define the probability that a given catastrophe will occur in a particular year Enter this as a percent from 0 0 to 100 0 For example a value of 1 0 means that there is a 1 chance that this particular event will occur in any one year Stated another way a catastrophe given a frequency of occurrence of 1 0 means that in a simulation lasting 100 years this event is expected to occur one time on average Severity proportion of normal values For each catastrophe you need to define the severity with respect to reproduction percentage
177. emory and a warning message is given In this case it is possible that the analysis may have to be terminated because the simulated population exceeds Nmax Because Nmax is often several fold greater than the likely maximum population size in a simulation a warning that it has been adjusted downward because of limiting memory often will not hamper the analyses 5 The deterministic growth rate of the population is calculated from mean birth and death rates that have been entered Algorithms follow cohort life table analyses Ricklefs 1979 Generation time and the expected stable age distribution are also calculated Life table calculations assume constant birth and death rates no limitation by carrying capacity no limitation of mates no loss of fitness due to inbreeding depression and that the population is at the stable age distribution The effects of catastrophes are incorporated into the life table analysis by using birth and death rates that are weighted averages of the values in years with and without catastrophes weighted by the probability of a catastrophe occurring or not occurring 6 Iterative simulation of the population proceeds via steps 7 through 26 below 118 Appendix I An Overview of Population Viability Analysis Using VORTEX VORTEX Version 9 User s Manual 7 The starting population is assigned an age and sex structure The user can specify the exact age sex structure of the starting population or can specify an initi
178. en in the table being the dependent y axis variable Need Stochastic Simulation of the Extinction Process File Edt Vortex Window Help Dem re os 4ZPG D AWORTEXS ZPG ZPG Ypi Project Settings Simulation Input Text Output Graphs and Tables Project Report Data Specification Data Graphs Graph Options Legend Text Position M ean N a 11 ZPG1 Population 1 ZPG2 Population 1 ZPG2 Population 2 ZPG2 Metapopulation Note if legend doesn t show make the window larger Add SE bars Add SD bars Graph Title Mean N all Font J ZPE Popuksian 1 X Axis Title Years 77 t P ZPS1 Poputsian 1 ZPGS2 Papubsian2 Graph Line Thickness a ih 1 i i 1 ZPS2 Metapapubaion 100 Print Graph Send to Report Export Graph Vortex 9 21 CAPS NUM INS Date Time 10 24 03 1 45PM Figure 47 Data Graphs window The initial size of the Data Graphs window that opens up will often force your graph to be squeezed into a fairly small window and often the legend will not be displayed because it doesn t fit in the small window To see a better image of the graph click on the corner of the Project window and drag it out to a larger size On the Data Graphs window you are provided with several Graph Options for changing the look of your graphs You can change the text or position of the legend the text or font of the main title or the axis titles and the line t
179. ental variation in mortality catastrophe frequency and severities carrying capacity dispersal dispersal mortality occurrence of harvest and supplementation and definition of extinction can be specified to be functions of the above population and individual variables The flexibility to specify population rates as functions rather than as fixed constants has been added to VORTEX so that users can model specific population dynamics that might be known to be appropriate for some species or that are of interest in a theoretical analysis With some creativity and perhaps considerable effort VORTEX can now model many of the kinds of population dynamics that can be envisioned As just a few examples gt it might be known that carrying capacity will change at some determined date in the future gt it might be believed that reproductive rates will change over time perhaps due to some management action the density dependence observed in reproduction might not fit the shapes of the curves allowed in previous versions of VORTEX mortality rates might change over time or respond in a complex way to population density inbreeding might impact fecundity adult survival or might affect the two sexes differently dispersal might be age and sex dependent fecundity mortality or the effects of catastrophes might be age dependent environmental variation might occur with a periodicity that is longer than a year or catastrophes might have multi y
180. equential seeds will not be correlated The unseeded forms RAND and NRAND set their own unique or nearly so seed each time they are called The very first use of a random number generator in VORTEX uses a seed based on the number of seconds elapsed since the turn of the century Each call to an unseeded random number generator also sets a new seed for the next call for an unseeded random number Thus two identically configured computers starting the same simulation at exactly the same second on their clocks would produce identical results for an analysis This synchrony may require however that all memory storage locations including hard disk caches and even the hard disk contents are identical on the two systems because they will affect the time required for each read or write to the disk The specification of random number seeds allows synchronization of sequences of random numbers This can be used to create synchrony of events such as catastrophes or environmental variation across populations or autocorrelations among years time lags or cycles If several different demographic rates are specified by functions containing random number generators perhaps to trigger separate catastrophes impacting survival and fecundity care must be taken to create the desired synchrony or lack of synchrony If two functions contain the same seed values they will return the same random number Seed values must be distinct to create independence of r
181. er of lethal alleles that was specified for the starting population 23 The population growth rate is calculated as the ratio of the population size in the current year to the previous year 24 If the population size N exceeds the carrying capacity K for that year additional mortality is imposed across all age and sex classes The probability of each animal dying during this carrying capacity truncation is set to N K N so that the expected population size after the additional mortality is K 25 Summary statistics on population size and genetic variation are tallied and reported 26 Final population size and genetic variation are determined for the simulation 27 Summary statistics on population size genetic variation probability of extinction and mean population growth rate are calculated across iterations and output Appendix I 121 An Overview of Population Viability Analysis Using VORTEX VORTEX Version 9 User s Manual 122 Appendix I An Overview of Population Viability Analysis Using VORTEX VORTEX Version 9 User s Manual Appendix II Literature Cited Akcakaya H R 1997 RAMAS Metapop Viability Analysis for Stage Structured Metapopulations Version 2 0 Setauket NY Applied Biomathematics Altmann J D Schoeller S A Altmann P Muruthi and R M Sapolsky 1993 Body size and fatness of free living baboons reflect food availability and activity levels American Journal of Primatology 3
182. erations that do not become extinct with SE and SD across iterations gt The final age sex composition of the extant populations and gt The mean population growth rate with SE and SD across iterations When harvesting or supplementation are included in your model VORTEX will report the mean population growth rate for years without harvest or supplementation for years with harvest or supplementation and averaged across all years Additional summary information will be provided when you have built a metapopulation model For example the output file will also include the same set of summary data for the global metapopulation and will also present a set of within population means These means are unweighted averages across populations while the standard deviations are means of the individual standard deviations of the populations Population sizes and genetic metrics are averaged across only those populations that survived some simulations Similarly times to extinction recolonization and re extinction are averaged across only those populations that had some extinctions Finally if any recolonization events occurred during the simulation VORTEX will report the frequency of recolonization the mean time to recolonization and the frequency and mean time to population re extinction if appropriate Also given for metapopulations will be some tables of genetic distances and identities with standard errors to show the amount of genetic di
183. ere smaller when the only available partner was the one that had been less preferred Species with complex social systems may be especially vulnerable to problems resulting from low population density For example striped back wrens Campylorhynchus nuchalis have very low breeding success unless they have at least two adult non breeding helpers sharing in defense against nest predators and breeding success is related strongly to the number of such helpers Rabenold 1990 If such a population were to decline in numbers recruit ment could stop when few birds remained to serve as help ers One population was rescued from demographic de cline when immigrants from nearby populations joined remnant breeding groups Rabenold et al 1991 Presum ably extirpation of the local population would have oc curred if there had not been nearby sources of immigrants Inbreeding depression and loss of genetic diversity At least two kinds of genetic problems can impact the vi ability of small populations reduction of fitness of indi viduals resulting from inbreeding and loss of genetic di versity due to random genetic drift Lacy 1997 There has been much written about e g Frankel and Soul 1981 Schonewald Cox et al 1983 Hedrick and Miller 1992 Frankham 1995a but also much debate over e g Lande 1988 1995 Caughley 1994 Caro and Laurenson 1994 Hedrick et al 1996 the importance of genetics to conser vation of wildlife population
184. es for their own research and conservation applications e redistribution without charge of the unmodified executable program for the purposes described above Unauthorized redistribution of VORTEX in whole or in part by any for profit organization or for any profit making purposes is expressly forbidden Cover Artwork Linda Escher Escher Illustrations Citation of this manual Miller P S and R C Lacy 2003 VORTEX A Stochastic Simulation of the Extinction Process Version 9 21 User s Manual Apple Valley MN Conservation Breeding Specialist Group SSC IUCN Citation of the software program Lacy R C M Borbat and J P Pollak 2003 VORTEX A Stochastic Simulation of the Extinction Process Version 9 Brookfield IL Chicago Zoological Society Additional printed copies of VORTEX User s Manual and installation CDs can be ordered through the IUCN SSC Conservation Breeding Specialist Group 12101 Johnny Cake Ridge Road Apple Valley MN 55124 USA Send checks for US 75 00 for printing and shipping costs payable to CBSG checks must be drawn on a US bank Funds may be wired to First Bank NA ABA No 091000022 for credit to CBSG Account No 1100 1210 1736 Lower costs for bulk orders may be arranged The CBSG Conservation Council These generous contributors make the work of CBSG possible Benefactors 20 000 and above Chicago Zoological Society Minnesota Zoological Gardens Omaha s Henry Doorly Zoo SeaWorld Inc To
185. esources have been provided over the years by the Chicago Zoological Society and the CBSG to support the development and continual improvement of VORTEX Neither organization recovers these costs of development nor receives any funding to provide ongoing support to VORTEX users Chapter 1 3 Introduction VORTEX Version 9 User s Manual Nevertheless we are committed to doing everything we can to help you get the most out of your VORTEX modeling experience Towards this end we suggest the following support options gt This User s Manual We hope that we have provided you with all of the information necessary to navigate your way through the program gt Tooltips and Input Prompts Most icons commands menus and input boxes have tooltips that pop up with explanatory messages when the cursor is paused over them In addition during input prompts will appear at the bottom of the window when the user clicks on a data entry box gt On screen Help Chapters 1 5 of this manual are provided in the Help menu of the program gt The VORTEX Listserver To help VORTEX users in their use of the program for PVA a VORTEX Users email discussion group Listserve has been established The VORTEX Listserve facilitates the exchange of ideas questions answers and suggestions among the many users of VORTEX The listserve also provides a medium for announcing updates bug fixes and suggestions provided by CBSG or by the program s developer To g
186. et information about the listserve or to subscribe go to https listhost uchicago edu mailman listinfo vortex Because there is no registration of VORTEX users the listserve is only way we can assure that users will hear about updates bug fixes and other announcements gt VORTEX on the Web Explore the VORTEX home page at http www vortex9 org vortex html to download updated programs or documentation files to report program bugs or to obtain other information pertinent to the effective use of VORTEX gt Contact the CBSG Office As a last resort if you are unable to solve your problem by the means suggested above you can reach the CBSG Office directly to get help Our contact information is Telephone 1 952 997 9800 Fax 1 952 432 2757 E mail office cbsg org We urge you to read the entire User s Manual not only to better your understanding of VORTEX but also to enhance your appreciation of the perils facing small populations of threatened wildlife For a more in depth treatment of population viability analysis and models for use in risk assessment we recommend Starfield and Bleloch 1986 and Burgman et al 1993 as excellent introductions to these topics A Note about Cost Vortex is provided free of charge because of the commitment of the Chicago Zoological Society to making it widely available to further biodiversity conservation Similarly the manual developed by the CBSG is provided for downloading because the
187. ethal equivalents and the cost of inbreeding in mammals Conserv Biol 2 185 193 Ronce O Perret F and Olivieri I 2000 Evolutionarily stable dispersal rates do not always increase with local extinction rates Am Nat 155 485 496 Ryan K K 2000 Causes and consequences of male mate choice in a monogamous oldfield mouse Peromyscus polionotus Ph D thesis Univ of Chicago Saccheri I et al 1998 Inbreeding and extinction in a butterfly metapopulation Nature 392 491 494 ECOLOGICAL BULLETINS 48 2000 Schonewald Cox C M et al eds 1983 Genetics and conser vation A reference for managing wild animal and plant pop ulations Benjamin Cummings Menlo Park California Seal U S and Lacy R C 1989 Florida panther population viability analysis Report to the U S Fish and Wildlife Service IUCN SSC Captive Breeding Specialist Group Ap ple Valley Minnesota Seal U S etal 1992 Genetic management strategies and popu lation viability of the Florida panther Fels concolor coryi Report to the U S Fish and Wildlife Service IUCN SSC Captive Breeding Specialist Group Apple Valley Minnesota Shaffer M L 1981 Minimum population sizes for species con servation BioScience 31 131 134 Shaffer M 1987 Minimum viable populations coping with uncertainty In Soul M E ed Viable populations for conservation Cambridge Univ Press pp 69 86 Sj gren Gulve P 19
188. ever be brought back to the islands for release While this position derives from a reasonable concern for disease transmission much of the decline of Hawaii s native birds is thought to be due to introduced avian diseases as much as from any political or philosophical stand any justification for the restriction must be questioned in light of the fact that wildlife agencies import and release without quarantine 1000s of exotic gamebirds onto the islands annually Once experts are assembled problems stated and goals set data gathered and assumptions specified then the PHVA process can proceed with what I describe as PVA in the narrow sense estimation of the probability of population persistence The available data are used to estimate the parameters that are needed for the model of population dynamics to be applied Often data are not available from which to estimate certain key parameters In those cases subjective and objective but non quantified information might be solicited from the assembled experts values might be obtained from data on related species or a factor might simply be omitted from the model While such a non precise process might consist simply of intuitive judgements made by experts it is important to specify how values for the parameters in the model were obtained The resulting limitations of the analyses should be acknowledged and a decision made if how by whom and when the missing data would be collected so that more
189. ew Project double click on the Blank Project or click on the Blank Project and then hit OK The Open Project tab will allow you to browse to find an existing project The Recent Projects tab will allow you to select from a list of the 10 most recent Projects that you have worked on You can get to these same options to create a new Project or open an existing Project from either the menu or the tool bar at the top of the VORTEX screen x grteenennennennennennenneneeneaneny ject Open Project Recent Projects or Blank Project r Description J Show this dialog when the program starts Ok Cancel Figure 15 The welcome window for starting a VORTEX Project If you choose to start with a Blank Project the only input values that will be pre filled are a few that are necessary to define the basic Project and Scenario properties It is often easier to start a new Project by opening an existing Project and then changing those input parameters that are different However be sure to go through every input screen to confirm that you have set the input parameters to the new values and be sure to save the Project under a new name When you chose to create a new Project you next need to specify a Project name and you have the option of recording your name as the Project creator Figure 16 Chapter 3 21 The Data Input Process VORTEX Version 9 User s Manual You can also specify the directory i
190. ewborn individual and c a transition function Transition fin the change in state if any each year of the simulation These functions are entered in the same way as other functions that can be used to specify demographic rates see Chapter 5 Case III Using an Individual State Variable to model transmission of mitochondrial DNA haplotypes Mitochondrial DNA haplotypes are inherited from the maternal parent This matrilineal transmission can be modeled by creating an Individual State Variable IS1 labeled mtDNA To assign randomly one of 10 haplotypes encoded 1 through 10 to the founder individuals specify a Initialization Function of CEIL RAND 10 The maternal inheritance is defined simply with the birth function of IS1 because the individual state parameters for use in the birth function are set at birth to be the values from the maternal parent pending redefinition in the birth function In the absence of mutation the transition function also would be IS1 to preserve the value for each individual across years To model mutation to one of the original haplotypes with mutation rate 0 0001 the transition function could be set to RAND lt 0 00011 CEIL RAND 10 The mutation rate used in the function has to be elevated by 10 to account for the cases in which mutation would be to the existing haplotype leaving the value unchanged Once the mtDNA haplotype is defined as an individual state varia
191. exponential If the population exceeds its carrying capacity the number of individuals will be reduced until N lt K The carrying capacity then can be thought of as representing a stable equilibrium population size Many population ecologists describe the gradual approach towards this equilibrium in terms of damped oscillations in population growth Empirically one could estimate the habitat carrying capacity for a given animal species by calculating the total food supply appropriate for that species that is available in the habitat and dividing that value by the rate of that species consumption of its available food supply for a detailed discussion of this technique see Hobbs and Swift 1985 For example Petit and Pors 1996 estimated population sizes flower availability and nectar output for each of three species of columnar cacti on Cura ao Carrying capacities for the two species of nectar feeding bats dependent on these cacti could then be estimated based on the daily availability of mature flowers and the field energy requirements of the bats with additional energy requirements associated with pregnancy and lactation taken into account If detailed data such as these are unavailable a rough estimate of habitat carrying capacity can be generated using long term data on population size If the size of the population of interest appears to be relatively constant over the period of observation and in the absence of significant human
192. f population survival under alternative scenarios for future conservation action 9 implementation of optimal actions for assuring accomplishment of conservation goals 10 continued monitoring of the population 11 reassessment of assumptions data models and options and 12 adjustment of conservation strategies to respond to the best information available at all times There are many uncertain aspects of population dynamics especially of endangered taxa including few data on species biology and habitats uncertain political and social climate for implementing conservation actions and the unpredictability inherent in small populations due to the many stochastic forces that drive population dynamics The rapid development of PVA as a research and management tool and the concurrent but not always parallel expansion of the scope of what conservation threats options and actions are considered in PHVA workshops has led to confusion Different people can describe rather distinct kinds of analyses with the same terminology while others use different terms to describe nearly identical approaches The ever changing concepts of PVA and PHVA are confusing but the flexibility of the processes is also their strength Current tools are inadequate to address fully the challenges of stemming the losses of biodiversity The PVA PHVA framework allows and encourages rapid application of new tools data and interpretations into increasingly effective conserv
193. f population dynamics that would result from some generalized life history It is most usefully applied to the analysis of a specific population in a specific environment In the program explanation that follows demographic rates are described as constants specified by the user Although this is the way the program is most commonly and easily used VORTEX does provide the capability to specify most demographic rates as functions of time density and other parameters see Chapter 5 Demographic stochasticity VORTEX models demographic stochasticity by determining the occurrence of probabilistic events such as reproduction litter size sex determination and death with a pseudo random number generator For each life event if the random value sampled from a specified distribution falls above the user specified probability the event is deemed to have occurred thereby simulating a binomial process Demographic stochasticity is therefore a consequence of the uncertainty regarding whether each demographic event occurs for any given animal The source code used to generate random numbers uniformly distributed between 0 and 1 was obtained from Maier 1991 based on the algorithm of Kirkpatrick and Stoll 1981 Random deviates from binomial distributions with mean p and standard deviation s are obtained by first determining the integral number of binomial trials N that would produce the value of s closest to the specified value according to No
194. fed Vortex Stochastic Simulation of the Extinction Process File Edt Vortex Window Help DEH re i sf EiZPG D WORTEX9 ZPG ZPG vpj iof x fT Simulation Input Text Output Graphs and Tables Project Report Project Name ZPG Send all to Report Users Names Usor Names User Add User Name Remove User Name Special options sample analysis of a population that has a deterministically projected zero population growth but which is small enough to be vulnerable to extinction Rescued by supplementation Same parameters as the default parameters in the DOS version of Vortex Project Notes Project created on 10 10 03 24 44 Pat and fast saved 10 10 03 21346 PH Vortex 9 21 NUM INS Date Time 10 24 03 3 07AM 4 CAPS Figure 4 The Project window Chapter 2 11 Getting Started with VORTEX VORTEX Version 9 User s Manual EF Get into the habit of adding Notes to your Projects to document what you are doing You will be glad that you did when you later need to tell others what you did in your analyses Also on the Project Settings screen is a button that will send the Project Settings information to your Project Report Your Report is a note pad utility much like MS Notepad that lets you build documentation of your Project We will take a look at the Project Report soon for now click on the Send all to Report button to capture the settings information in your Report EF Send
195. few examples of interactions among threatening processes that can reduce population viability often in unexpected and unexpectedly strong ways Increased dispersal among patches of habitat is usually assumed to help stabilize a metapopulation Increased dis persal can restore genetic variation to previously inbred populations can reduce demographic fluctuations within local populations can rescue demographically weak popu lations Brown and Kodric Brown 1977 and can lead to recolonization of temporarily extirpated local populations However the metapopulation dynamics of small partly isolated and frequently extirpated populations can be highly dependent on spatial temporal and behavioral as pects of the population structure Fahrig and Merriam 1994 For example ifa metapopulation declines to a level at which many of its constituent local populations are very small or extinct then the benefits of dispersal can be re placed by disadvantages Uncompensated emigration from isolated populations can depress local population growth Fahrig and Merriam 1985 and suitable habitat that is temporarily empty can act as a population sink where ani mals fail to find mates Gyllenberg and Hanski 1992 Consequently increased dispersal can accelerate decline of sparsely populated metapopulations Lindenmayer and Lacy 1995 This collapse into a metapopulation vortex may be more likely if dispersal behaviors evolved in a physical and biotic env
196. fferentiation that existed between populations at the end of the simulations Other Output The fourth section of Text Output provides two summary tables in grid formats Figure 43 One table provides a line of basic summary statistics for each Population of each Scenario that has been run The summary statistics tabulated are the number of iterations Runs the deterministic growth rate det r 74 Chapter 4 Viewing Model Results VORTEX Version 9 User s Manual the mean stochastic growth rate stoc r experienced in the simulations the SD of the stochastic population growth SD r and final values at the end of the simulation for many of the descriptive statistics listed above in the Output Summary If a Scenario has been run several times then the table will show the results from these multiple sets of simulations Comparing results across repeated sets of simulations can indicate whether the number of iterations was large enough to give results that are sufficiently stable precise for your purposes You can also get an indication of this by looking at the reported standard errors 4 Vortex Stochastic Simulation of the Extinction Process File Edt Vortex Window Help Osee 42 e B lees E4ZPG D WORTEX9 ZPG ZPG Ypi Project Settings Simulation Input Text Output Graphs and Tables Project Report Scenario Summaries Iteration Summaries Send to Repor t Print Export Seenaio __ifiune E NES EEREN Popul
197. ficient and genotypes at the modeled loci project_scenario gen A listing of final allele frequencies and probabilities of allele persistence averaged across the iterations for the first locus modeled project scenario Iter gp A listing in GenePop format of the individuals alive at the end of the iteration including their sex age inbreeding coefficient and genotypes at the modeled loci 82 Chapter 4 Viewing Model Results VORTEX Version 9 User s Manual Chapter 5 Using Functions in VORTEX Introduction VORTEX provides the option of modeling demographic rates as functions of population or individual parameters The population descriptors that can be used as variables in the functions include time year in the simulation iteration population population size carrying capacity numbers of juveniles animals in the first age class subadults greater than 1 year but not yet breeding age adult females adult males all females or all males and gene diversity expected heterozygosity Individual characteristics that can be entered as variables in these functions include ID sex age number of mates 0 or 1 for females and monogamous males possibly more for polygamous males inbreeding coefficient and genotypes at modeled loci Almost all demographic rate parameters such as the percent of females breeding each year environmental variation in breeding litter clutch size sex ratio mortality rates environm
198. functions can become when you want to create even moderately complex models of population dynamics Using Functions to Examine Genetic Evolution The parameters available for use in functions defining demographic rates include an individual s paternally inherited allele V and the maternally inherited allele Z of the normally non selected locus which is monitored for tracking genetic diversity The symbols for these variables V and Z have no intuitive meaning but are rather the result of few letters remaining available for denoting additional parameters for functions By specifying that demographic rates are functions of the alleles carried by an individual it is possible to model a wide variety of genetic processes impacting population dynamics including the effect and fate of alleles that confer alternative life history strategies e g lower fecundity but higher survival balancing disruptive or directional selection for alleles impacting demography hybrid vigor or outbreeding depression caused by introgression of alleles from a distinct taxon or geographic population and genetically based individual variation in demographic rates When the initial population is created and when the population is supplemented with any new individuals the founders are assigned unique alleles sequentially Hence the first individual of the Population 1 is assigned alleles 1 and 2 the second individual is assigned alleles 3 and 4 and so on Final f
199. g Specialist Group SSC TUCN Bormann F H and S R Kellert 1991 Ecology Economics and Ethics The Broken Circle New Haven Yale University Press Boyce M S 1992 Population viability analysis Annual Review of Ecology and Systematics 23 48 1 506 Brussard P 1985 Minimum viable populations how many are too few Restoration and Management Notes 3 21 25 Burgman M S Ferson and H R Ak akaya 1993 Risk Assessment in Conservation Biology New York Chapman and Hall Appendix II 123 Literature Cited VORTEX Version 9 User s Manual Caswell H 2001 Matrix Population Models 2 ed Sunderland MA Sinauer Caughley G 1977 Analysis of Vertebrate Populations London John Wiley and Sons Charlesworth D and B Charlesworth 1987 Inbreeding depression and its evolutionary consequences Annual Reviews of Ecology and Systematics 18 237 268 Clark T W 1989 Conservation Biology of the Black Footed Ferret Philadelphia Wildlife Preservation Trust International Clark T W 1993 Creating and using knowledge for species and ecosystem conservation Science organizations and policy Perspectives in Biology and Medicine 36 497 525 Clark T W R M Warneke and G G George 1990 Management and conservation of small populations Pages 1 18 in Clark T W and J H Seebeck eds Management and Conservation of Small Populations Brookfield Illinois Chicago Zoological Society Clark T W G N Backhouse and R C
200. g detail experi mental data and observations on natural populations For a variety of reasons PVA models for small popula tions may need to be highly specific with respect to how they model breeding systems dispersal behavior and ge netic processes Simple generalizations of population ge netics theory may be misleading because most of that the ory was based on large sample approximations For exam ple generalizations about effects of dispersal among small populations often have assumed that an infinite number of such populations exist Many metapopulation models as sume that the system has reached extinction recoloniza tion equilibrium Variation in demographic rates num bers of individuals and other population statistics rarely follow a normal distribution Effects of threatening proc esses on populations are rarely linear or log linear and threshold effects in which there are sharp discontinuities in effects are possible The effects of multiple threats are often synergistic rather than additive Many of the parameters required to build specific de tailed models of small population dynamics can only be estimated well with long term and extensive data It is clearly difficult to obtain large samples from small popula tions and conservation action may have to precede long term field studies in order to ensure that the populations persist long enough to permit extended study Obtaining a complete enumeration of a sma
201. g the impacts of population dynamics on genetic structure e invoke other options that may from time to time be made available usually on a test basis or for special circumstances To use this option you would need to know the undocumented codes for using these additional options To begin entering the values for the parameters that will specify the Scenarios of your Project click on the Simulation Input tab Getting Help when Entering Input Data VORTEX will accept most of the input that you provide as long as the values are biologically possible and within the rather wide limits set by the program see above When entering input data brief hints about the values to be entered will be displayed in a line at the bottom of the Project screen These messages appear when you click on a data entry box and sometimes they will appear as pop up tooltip messages when your cursor passes over a data entry box for more than a few seconds Figure 18 If you try to enter a value for input that is of an incorrect type e g a letter when a number is required or outside the acceptable bounds e g a negative number for a mortality rate then VORTEX will usually display a message that the value is invalid and it will force you to enter a valid value before you proceed with data entry Chapter 3 23 The Data Input Process VORTEX Version 9 User s Manual 4 ortex Stochastic Simulation of the Extinction Process lox File Edit Yortex
202. gain resumes the decline at a rate of 5 per year after year 25 4 Exponential decline RATE 50 0 98AY The rate declines by 2 each year Demographic Rate Demographic Rate Demographic Rate 50 0 45 0 40 0 35 0 30 0 25 0 20 0 15 0 10 0 5 0 0 0 50 5 MINC5 Y CCY 25 CY gt 25 50 0 45 0 40 0 35 0 30 0 25 0 20 0 15 0 10 0 5 0 0 0 50 0 45 0 f 40 0 35 0 30 0 f 25 0 20 0 15 0 10 0 5 0 0 0 VORTEX Version 9 User s Manual a O O 10 20 30 40 50 60 70 80 90 100 Year of Simulation O 10 20 30 40 50 60 70 80 90 100 Year of Simulation O 10 20 30 40 50 60 70 80 90 100 Year of Simulation Chapter 5 91 Using Functions in VORTEX VORTEX Version 9 User s Manual 5 Exponential decline with inbreeding RATE 50 EXP 2 0 I 100 The rate declines from 50 in non inbred 50 0 animals down to 6 7 in fully inbred animals I 45 0 100 Note that the inbreeding coefficient 40 0 I is expressed as a percent An equation like 35 0 this might be used to specify a decline in 30 0 L 25 0 f 20 0 15 0 10 0 5 0 0 0 fecundity due to inbreeding Demographic Rate 10 20 30 40 50 60 70 80 90 100 Inbreeding Coefficient 6 Age dependent fecundity with linear decline after the onset of breeding RATE A gt 5 50 C A 5 2 Breeding begins with a ra
203. geny You can use a Normal distribution approximation or you can fully specify the probabilities of each number of progeny When you use the Normal approximation VORTEX will randomly select a number of progeny for each breeding female by sampling from a normal distribution with the specified mean and standard deviation and then choosing the closest whole number of offspring to the value sampled The distribution will be symmetrically truncated if necessary in order to prevent the specification of negative litter sizes and to prevent bias in the sampling of the distribution If you have data on the percents of females producing each possible number of progeny and if the maximum number produced is not very large then it is more accurate to enter that exact distribution You accomplish this by entering the percentage i e a number between 0 0 and 100 0 for each specified size up to the maximum For example if the maximun litter size is 5 but the average litter is comprised of just 2 individuals you would enter a much higher percentage of females producing smaller litters say 60 produce a litter of 2 but only 5 produce a litter of 5 The total must add to 100 and the final value will be entered automatically by the program in order to sum to 100 Copy input values from When modeling a metapopulation you often will want to use the same values for most input parameters across all of the populations On the left side of the Simulation EF Inp
204. ges from 0 to more than 30 but it is usually in the range of 1 to 5 Isn t it depressing to know that you probably carry from 1 to 5 alleles which would be fatal Chapter 3 29 The Data Input Process VORTEX Version 9 User s Manual Box B Continued Figure B 1 Expected juvenile survival as a function of inbreeding coefficient under alternative levels of inbreeding depression severity defined as the number of lethal equivalents LE per haploid genome see text for details Juvenile Survival 0 3 Inbreeding Coefficient F genetic defects if you had two copies of any one of those alleles Aren t you glad that you are diploid To date no clear patterns have emerged to suggest that certain taxonomic ecological or other categories of species typically have high or low number of lethal equivalents it seems to be largely a matter of chance whether a population is severely affected by inbreeding or not How does VorTEx use lethal equivalents VorTEXx simulates inbreeding depression in two ways because different genetic mechanisms of inbreeding depression can have different consequences for population viability Recessive lethal alleles are rather efficiently removed from a population by natural selection when inbreeding occurs As a result many individuals may die in the early generations of inbreeding but when they die they take their lethal alleles with them to the grave and subsequent generations of ind
205. gly cautioned to not expect to be able to build and use meta models without the assistance of an expert Lacy and Miller 2002 discuss the conceptual need to link PVA models with other kinds of knowledge Individual State IS Parameters VORTEX provides the user with the option of creating up to nine Individual State parameters that define characteristics of individuals These state parameters may represent any feature of the organism that can be specified or coded by a numeric value For example dominance status might be encoded as Dominant 1 0 Subdominant 2 0 and Subordinate 3 0 Ora state variable might be used to represent some measure of body condition Or two state variables might be used to track the x and y coordinates of each individual s location on a landscape To create one or more individual state variables check the box then indicate how many variables you will be creating For each variable you then enter into the table a label which can be any text that will help you to remember what parameter you were representing The VORTEX program however will track the Individual State variables with the labels IS1 IS2 etc as indicated in the first column of the table For each IS variable you need to enter three functions or constants to define a an initialization function Init fn the starting value for each individual at the beginning of the simulation b a birth function Birth fn the value for each n
206. hapter 5 97 Using Functions in VORTEX VORTEX Version 9 User s Manual 24 25 26 27 98 Alleles confer differential reproductive rates RATE 40 10 V 2 10 2 2 In this case half of the alleles specifically 50 0 F r those with even numbers cause an increment 45 0 AN of 10 in the breeding rate of their carriers An g 40 0 i individual that is homozygous for an even 35 0 1 numbered allele will have a breeding rate 2 300 equal to 60 while those homozygous for an S 25 0 odd numbered allele will have a rate equal to 4 20 0 f 40 B oT 10 0 f 5 0 0 0 10 20 30 40 50 Allele Identifier Overdominance for survival all unique founder alleles RATE 20 10 v Z An infinite alleles model in which homozygotes have a mortality of 30 while the rate for heterozygotes is 20 Overdominance for survival two functionally distinct founder alleles RATE 20 10 v 2 Zz 2 A two allele model in which homozygotes with two odd or two even alleles have a mortality of 30 while the rate for heterozygotes is 20 Outbreeding depression for breeding rate upon introgression from supplemented individuals RATE 50 10 C V lt 20 Z gt 19 With ten initial founders and with some 50 0 l i number of individuals from another source 45 0 L used as supplements at a later stage the o 40 0 breeding rate is 50 for an individual which S ol carries both of its alleles from t
207. he initial 2 300 founders or both from the source population S 250l of the supplements vs 40 for individuals gt 20l which are heterozygous carrying an allele asol from each source a ool 5 0 0 0 0 10 20 30 40 50 Allele Identifier Chapter 5 Using Functions in VORTEX VORTEX Version 9 User s Manual 28 Genetically based individual variation in breeding success RATE 50 5 CSNRAND R 100 V SNRANDCCR 100 Z In this case breeding rates vary around a mean of 50 with a standard deviation equal to 5 SQRT 2 Demographic Rate 70 0 F 60 0 50 0 40 0 30 0 20 0 f 10 0 F 0 0 0 10 20 30 40 50 Allele Identifier 29 Density dependence relative to the average density across populations 1 and 2 RATE 50 C KKC1 KK 2 NNC1 NN 2 KK 1 KK 2 Note the use of KK p and NN p to indicate K and N for population p Chapter 5 99 Using Functions in VORTEX VORTEX Version 9 User s Manual 100 Appendix I An Overview of Population Viability Analysis Using VORTEX VORTEX Version 9 User s Manual Appendix I An Overview of Population Viability Analysis Using VORTEX Introduction This Appendix presents an overview of processes threatening the health and persistence of wildlife populations the methods of population viability analysis the VORTEX simulation program for PVA and the application of such techniques to wildlife conservation Much of the fo
208. he simulation Furthermore you are allowed to both harvest and supplement individuals in a fashion independent of one another unrelated to both each other and to any other individual in the recipient population Consequently supplementation is a means of increasing genetic diversity as well as total numbers of individuals within a population EF VORTEX assumes that the individuals that are being added to the recipient population are If you want to supplement your population s check the Population Supplemented box You must then provide the values on the subsequent lines to define the nature of the supplementation First Last Year of Supplementation The supplementation can begin and end at any time during the stipulated length of the simulation Enter the years in which you wish to begin and end supplementation For example if you wish to begin supplementing in year 20 and end in year 50 enter 20 and 50 for these two questions respectively No supplementation will be allowed before or after the time frame that you have specified Interval Between Supplementations If you wish to supplement every year within the specified time frame enter 1 If you wish to supplement every other year enter 2 Optional Criterion for Supplementing You can specify here some criteria that will restrict supplementation to occur only if the population status meets certain conditions You enter this as a function see Chapter 5 For example if you enter
209. he x axis of your graph Figure 12 Specify Years Ordering ane he B 7 3 Order Selections a you would a5 Year 0 like to use 10 V Year 10 siira Year 20 T E Year 30 Ea v Year 40 _ 40 v Year 50 50 v Year 60 Select All o 7 Year 70 Unselect All 3a Year 80 peu Z Year 90 v E Sort A di Sort D di gt or Descending 90 y hi Sort Ascending ort Descendin Ok Cancel Figure 12 Specification of years as the columns for tabular output To specify years you can Select All select individual years by clicking on their boxes or select rows all years in a decade or columns years in decadal intervals from the table For example to select years 0 10 20 click on the number 0 at the top of the first column Do this now The method by which years are selected may be a little confusing at first but once you learn how it works it does allow very rapid and flexible specification of sets of years If you add years to your selection in a non sequential order you will want then to sort them by clicking on one of the sort buttons on the right After you have selected the years you want click on OK EF When changing your selection of reporting years you may obtain better results if you Unselect All before making your new selection rather than unchecking multiple boxes
210. hern white rhinoceros under various management scenarios Appendix 3 in Foose T J ed Summary Northern White Rhinoceros Conservation Strategy Workshop Cumberland OH International Rhino Foundation Lacy R C 2000 Structure of the VORTEX simulation model for population viability analysis Ecological Bulletins 48 191 203 Lacy R C and T W Clark 1990 Population viability assessment of the eastern barred bandicoot in Victoria Pages 131 146 in Clark T W and J H Seebeck eds The Management and Conservation of Small Populations Brookfield IL Chicago Zoological Society Lacy R C and T W Clark 1993 Simulation modeling of American marten Martes americana populations Vulnerability to extinction Great Basin Naturalist 53 282 292 Lacy R C N R Flesness and U S Seal eds 1989 Puerto Rican Parrot Population Viability Analysis Report to the U S Fish and Wildlife Service Apple Valley MN Captive Breeding Specialist Group SSC TUCN Lacy R C and D B Lindenmayer 1995 A simulation study of the impacts of population subdivision on the mountain brushtail possum Trichosurus caninus Ogilby Phalangeridae Marsupialia in south eastern Australia II Loss of genetic variation within and between subpopulations Biological Conservation 73 131 142 Lane S J and J C Alonso 2001 Status and extinction probabilities of great bustard Otis tarda leks in Andalucia southern Spain Biodiversity amp Conservation 10 6
211. hickness You can also toggle between a line graph and a bar graph although for many kinds of data that would be plotted only one of these two graphs would be reasonable Command buttons are provided to allow you to Print the graph send it to the Project Report or Export the graph to a bitmap bmp file You can also add error bars to show standard errors SE around the plotted means or standard deviations SD across iterations The SE and SD options are available only for those plotted variables for which they would be applicable E g there is no error around deterministic growth rates Chapter 4 79 Viewing Model Results VORTEX Version 9 User s Manual While these basic Graph Options will be adequate for many purposes VORTEX also provides you with access to a much more extensive graphing utility To fine tune your graphs right click on the graph and select Properties That will bring up an Advanced Graph Properties window that gives you considerable control over almost all aspects of the graph Figure 48 Advanced Graph Properties i x Error Bar Background Legend Labels Graph Title Mean N fall Bottom Title Years r Left Title Title OoOO O C Horizontal Up C Down m Right Title Title C Up Horizontal Cancel Apply Now Help Figure 48 Advanced Graph Properties It is always good to watch the VORTEX website for upgrades The Tables and Graphs section of
212. ic stability and change International Journal of Primatology 12 1 19 Sapolsky R M 1982 The endocrine stress response and social status in the wild baboon Hormones and Behavior 15 279 292 Sapolsky R M 1986 Endocrine and behavioral correlates of drought in the wild baboon American Journal of Primatology 11 217 227 Seal U S ed 1992 Genetic Management Strategies and Population Viability of the Florida Panther Felis concolor coryi Apple Valley MN Captive Breeding Specialist Group SSC TUCN Seal U S ed 1994 Attwater s Prairie Chicken Population and Habitat Viability Assessment Apple Valley MN Captive Breeding Specialist Group SSC TUCN Seal U S and R C Lacy eds 1989 Florida Panther Population Viability Analysis Report to the U S Fish and Wildlife Service Apple Valley MN Captive Breeding Specialist Group SSC IUCN Seal U S J D Ballou and C V Padua eds 1990 Leontopithecus Population Viability Analysis Workshop Report Apple Valley MN Captive Breeding Specialist Group SSC IUCN Seal U S R C Lacy K Medley R Seal and T J Foose eds 1991 Tana River Primate Reserve Conservation Assessment Workshop Report Apple Valley MN Captive Breeding Specialist Group SSC IUCN Selander R K 1983 Evolutionary consequences of inbreeding Pages 201 215 in Schonewald Cox C M S M Chambers B MacBryde and W L Thomas eds Genetics and Conservation A Reference for Managing Wil
213. ies threatened with extinction exactly those for which estimates of population vulnerability are most urgently needed A more elegant and general approach to PVA is to develop analytical models of the extinction process that will allow calculation of the probability of extinction from a small number of measurable parameters Goodman s 1987 model of demographic fluctuations and applications to conservation of the classic population genetic models of loss of genetic diversity by genetic drift Franklin 1980 Soul et al 1986 Lande and Barrowclough 1987 are valuable efforts in this direction Unfortunately our understanding of population biology is not yet sufficient to provide fully adequate analytical models of the extinction process For example none of the existing analytical models incorporate all three of demographic environmental and genetic fluctuations and thus they do not begin to model the array of extinction vortices described by Gilpin and Soul 1986 Moreover the analytical models make extremely simplifying assumptions about a number of the intricacies of population structure For example social groupings or preferences are often assumed to be invariant or lacking resulting in random mating and dispersal is usually assumed to be random between all sites the island model or only to occur between adjacent sites the stepping stone model Much more work is needed either to develop more complex and flexible models or to de
214. impact one can fairly safely assume that the population is at or near its carrying capacity If this equilibrium is observed in the presence of major human influences such as a strong hunting pressure then historical data could be consulted to determine if this stable size is indeed natural or purely artificial One could also calculate K for a given habitat using population density data from undisturbed habitats elsewhere in the species range 60 Chapter 3 The Data Input Process VORTEX Version 9 User s Manual Harvest In this section VORTEX gives you the option of removing individuals during a simulation Figure 33 4 Vortex Stochastic Simulation of the Extinction Process File Edt Vortex Window Help OSes eS los gt E ZPG D WORTEXS ZPG ZPG vpi iol x Project Settings Simulation Input Text Output Graphs and Tables Project Report Add Scenario Delete Scenario lt zPG2 gt Reorder ZPG1 ZPG2 cenario Settings pecies Description abelis and State Vars Harvest Population Population 2 Reproductive System Population Harvested Reproductive Rates First Year of Harvest ortality Rates A atastrophes Optional Threshold for Harvest ate Monopolization Initial Population Size ing Capacity Number of Females of each age to be Harvested Population1 Population 2 Age 1Harvested 1 Adults Harvested 1 a 3
215. in popularity Shaffer stressed that an MVP was an estimate of the population size below which the probability of extinction was unacceptably high that different populations would have different MVPs and that the MVP determined for a population would depend on the threatening factors that were considered However the term implied to some people that there was a well defined number below which extinction was certain and above which persistence was assured Re emphasizing the probabilistic nature of the extinction process a number of conservation biologists have focused on methods for estimating the probability of extinction over defined time periods for a designated population exposed to a specific scenario of environmental conditions threats to persistence and future management actions and other foreseeable events Brussard 1985 Starfield and Bleloch 1986 Soul 1987 Simberloff 1988 Gilpin 1989 Shaffer 1990 Boyce 1992 Burgman et al 1993 Thus Population Viability Analysis or the synonymous Population Viability Assessment and Population Vulnerability Analysis came to describe any of the array of methods for quantifying the probability of extinction of a Appendix I 103 An Overview of Population Viability Analysis Using VORTEX VORTEX Version 9 User s Manual population Although PVA has been extended by some to encompass a broader approach to conservation see below the term Population Viability Analysis or PV
216. in populations that are smaller than a few tens of animals Goodman 1987 in which cases the annual frequencies of birth and death events and the sex ratios can deviate far from the means Environmental variation is the fluctuation in the probabilities of birth and death that results from fluctuations in the environment Weather the prevalence of enzootic disease the abundances of prey and predators and the availability of nest sites or other required microhabitats can all vary randomly or cyclically over time The fluctuations in demographic rates caused by environmental variation is additive to the random fluctuations due to demographic stochasticity Thus the difference between the observed variation in a demographic rate over time and the distribution describing demographic variation must be accounted for by environmental variation Catastrophic variation is the extreme of environmental variation but for both methodological and conceptual reasons rare catastrophic events are analyzed separately from the more typical annual or seasonal fluctuations Catastrophes such as epidemic disease hurricanes large scale fires and floods are outliers in the distributions of environmental variation As a result they have quantitatively and sometimes qualitatively different impacts on wildlife populations A forest fire is not just a very hot day Such events often precipitate the final decline to extinction Simberloff 1986 1988 For example one of
217. ination BREAK from LOOP Animal will try to migrate to pDestination END IF END LOOP IF Population pDestination at carrying capacity IF tried 9 times before to find an open population ECOLOGICAL BULLETINS 48 2000 Animal dies Never found an open population into which to migrate BREAK from LOOP CONTINUE with next animal END IF IE CumulativeMigrationProb p Destination NumberPopulations 0 Animal dies Cannot migrate away from pDestination BREAK from LOOP CONTINUE with next animal END IF Set MigrationRand RAND Set pSource pDestination I Moves on from population pDestination old pDestination becomes current pSource WHILE MigrationRand gt CumulativeMigrationProb pSource NumberPopulations Set MigrationRand RAND I Must migrate somewhere so draw a new random number END WHILE END IF END LOOP Change animal s population to pDestination Adjust tallies of population sizes Increment size of pDestination decrement size of pSource END animal LOOP END FUNCTION MIGRATE BEGIN FUNCTION HARVEST for population p FOR each age x I HARVEST lumps all animal above breeding age as a single class IF NumberMales p x lt NumberMalesToBeHarvested p x All males age x die ELSE WHILE number harvested lt NumberMalesToBeHarvested p x Choose at random a living male in age class x Male dies END WHILE END IF ELSE END LOOP FOR each age x
218. inction Humans can synthesize mentally only a few factors at a time most people have difficulty assessing probabilities intuitively and it is difficult to consider delayed effects Moreover the data needed for models of population dynamics are often very uncertain Optimal decision making when data are uncertain is difficult as it involves correct assessment of probabilities that the true values fall within certain ranges adding yet another probabilistic or chance component to the evaluation of the situation The difficulty of incorporating multiple interacting probabilistic processes into a model that can utilize uncertain data has prevented to date development of analytical models mathematical equations developed from theory which encompass more than a small subset of the processes known to affect Appendix I 111 An Overview of Population Viability Analysis Using VORTEX VORTEX Version 9 User s Manual wildlife population dynamics It is possible that the mental models of some biologists are sufficiently complex to predict accurately population vulnerabilities to extinction under a range of conditions but it is not possible to assess objectively the precision of such intuitive assessments and it is difficult to transfer that knowledge to others who need also to evaluate the situation Computer simulation models have increasingly been used to assist in PVA Although rarely as elegant as models framed in analytical equations computer si
219. information An example of estimating dispersal rates from molecular data is described in Case Study IV Case Study IV Estimating migration rates from DNA sequence data The Anacapa Island deer mouse Peromyscus maniculatus anacapae is endemic to the Anacapa islands off the coast of California near Los Angeles Pergams et al 1999 conducted a population viability analysis to develop a comprehensive management plan involving the potential for captive breeding reintroduction or translocation of individuals following eradication of introduced rats Nucleotide sequences were obtained from the mitochondrial DNA mtDNA cytochrome oxidase subunit II gene of mice sampled across each of the three Anacapa Islands Based on the average amount of nucleotide sequence divergence among mice from the different islands the authors were able to directly calculate an estimate of gene flow Nm where N is the average size of a pair of islands and m is the average rate of migration between those islands per generation see Nei 1982 for details For example Nm between Middle and West Anacapa was calculated to be 7 27 individuals per generation Since a generation in Anacapa Island deer mice is only 84 days and assuming a time cycle of 21 days for the analysis the number of individuals migrating between the two islands is 7 27 0 25 1 8175 per time cycle The average population size across Middle and West Anacapa Islands was estimated to be 19 044 mice so
220. information to your Report whenever you think that you may want it documented It is easy to delete parts of the Report but it is hard later to see something that you never sent The last item on the Project Settings screen is a Special Options button These options are ones that most users will never need to use so we won t look at them now Click now on the Simulation Input tab to take you to the screen shown in Figure 5 fea Vortex Stochastic Simulation of the Extinction Process File Edt Wortes Window Help Ose s Be S lls o Page D WORTEXS 2ZPG ZPG Ypi Project Settings Simulation Input l Text Output Graphs and Tables Project Report Add Scenario Delete Scenario lt zp gt Reorder ZPE ZPG2 cenario Settings pecies Description abels and State Vars Reproductive System Scenario Name PGI Reproductive Rates ortality Rates Number of Iterations fi oo atastrophes Number of Years ate Honopolization m nitial Population Size anying Capacity Scenario Settings Extinction Definition Only 1 Sex Remains Total N lt Critical Size Number of Populations fi upplementation Copy input values from Population 1 Vortex 9 21 Enter a non empty scenario name caps NUM INS Date Time 10 24 03 9 13AM Figure 5 The Simulation Input window 12 Chapter 2 Getting Started with VORTEX VORTEX Version 9 User s Manual Simulation Input is arranged as 13 scree
221. ing When the simulations are complete close the window before doing anything else The results of the simulation you just completed are now stored with your Project on the computer There are two modes in which you can view the results Text Output and Graphs and Tables Go to Text Output by clicking on its tab Within the Text Output section are four tabbed subsections Input Summary Deterministic Calculations Output Summary and Other Output Figure 10 EJ Vortex Stochastic Simulation of the Extinction Process File Edt Yortex Window Help Deute Page D WORTEXS 2ZPG ZPG Ypi Project Settings Simulation Input Text Output Graphs and Tables Project Report Input Summary Deterministic Calculations Output Summary Other Output Send text to Report Print Save s Scenario to view zPG1 Population to find Population 1 Results from VORTEX 9 21 simulations completed Fri Oct 24 09 18 30 2003 Project ZPG scenario ZPG1l Population 1 Population 1 Year 1 N Extinct 0 PLE 0 000 N Surviving 100 P S 1 000 Mean size all populations 7 44 0 Means across extant populations only Population size 7 44 0 17 Expected heterozygosity 0 923 0 002 Observed heterozygosity 1 000 i 0 000 Number of extant alleles 14 086 0 26 Lethal alleles diploid 1 60 0 05 2 N Extinct 2 P E Vortex 9 21 caps NUM INS Date Time 10 24 03 91
222. ing a dataset consisting of a number of individual observations it is useful to present that summary graphically in the form of a frequency distribution usually in the form of a bar graph Often we are dealing with data on a dichotomous variable such as alive or dead breeding or not breeding male or female and we are interested in tallying 4l a sae the frequency of each possibility in a sample of n observations also known as cases or trials The probability 3p of any given case belonging to one or the other category is denoted p and q with p q 1 The frequency of samples consisting of 0 1 2 or n observations of a specific category in a sample of n cases is described by a binomial distribution Figure C 1 shows a pair of binomial distributions forn 5 Figure C 1 The binomial distribution for sample size n 5 and a p q 0 5 and b p 0 4 q 0 6 The bars give the probabilities p X of obtaining a particular number of observations of the first category For example with p 0 4 and q 1 p 0 6 the probability of obtaining a sample consisting of one observation out of a possible 5 in the first category is 0 259 If n observations are sampled from a population with X belonging to one category and n X in the other then the population parameter p the proportion of the observations that is in the first categor
223. ion as the point at which offspring are tallied For oviparous species however you can start to tally offspring at egg laying or at hatching or at fledging or at any other developmental stage that makes sense to you and for which you can specify the demographic rate parameters For amphibians you may choose to start each animal s life in the VORTEX model at metamorphosis Whenever you define an individual s life to begin you must make sure that the first year mortality rates you specify in the next input section are appropriate for the choice you made about when to start recording offspring For example if you tally offspring starting at hatching then the clutch sizes you specify on this screen will be in terms of the number of hatches and your first year mortality will be from hatching through the subsequent 12 months If you choose to start offspring at fledging then the clutch size will be specified in terms of the number of fledglings and survival will be from fledging onwards 48 Chapter 3 The Data Input Process VORTEX Version 9 User s Manual 4 Vortex Stochastic Simulation of the Extinction Process File Edt Vortex Window Help DEH amp S e Ff gt E ZPG D WORTEX9 ZPG ZPG vpi Project Settings Simulation Input Text Output Graphs and Tables Project Report Add Scenario Delete Scenario lt zpa2 gt Reorder ZPG1 ZPG2 cenario Settings A species Description Reproductive Rates abe
224. ion dynamics a specified set of biological and environmental parameters and enumerated assumptions about human activities and impacts on the system PHVA refers to a workshop approach to conservation planning which elicits and encourages contributions from an array of experts and stakeholders uses PVA and other quantitative and non quantitative techniques to assess possible conservation actions and strives to achieve consensus on the best course of action from competing interests and perspectives incomplete knowledge and an uncertain future Many of the components of PVAs and PHVAs even when used in isolation can be effective educational and research tools To be a useful framework for advancing the conservation of biodiversity however PHVA must incorporate all of 1 collection of data on the biology of the taxon status of its habitat and threats to its persistence 2 quantitative analysis of available data 3 input of population status and identifiable threats to persistence into analytical or simulation models of the extinction process 4 assessment of the probability of survival over specified periods of time given the assumptions and limitations of the data and model used 5 sensitivity testing of estimates of extinction probability across the range of plausible values of uncertain parameters 6 specification of conservation goals for the population 7 identification of options for management 8 projection of the probability o
225. ions behind the selected management options and for assessing the success of conservation efforts Closely parallel to the testing of uncertainties in the present situation is the testing of options for management PVA modeling allows one to test the expected results of any given management action under the assumptions of the model and within the limitations of present knowledge on the computer Appendix I 107 An Overview of Population Viability Analysis Using VORTEX VORTEX Version 9 User s Manual before implementation in the field This process can guide selection of the management options most likely given current knowledge to be effective and will define target recovery goals that should be obtained if our knowledge is adequate and the recommended actions are followed A PHVA workshop on the Black Rhinoceros in Kenya s 11 rhino sanctuaries Foose et al 1993 suggested that periodic movement of rhinos between fenced sanctuaries to reduce inbreeding and demographic fluctuations would be necessary to stabilize the populations in the smaller parks Moreover the modeling provided estimates of the rate at which the larger populations would be able to provide surplus animals for translocation It would be an error to assume that any PVA model incorporates everything of interest A PVA simulation program can only include those processes that are known to the programmer This will likely be a subset of what might be known to the field biologists
226. ions using individual based models Ecological Bulletins 48 39 51 Reprinted with permission of the publisher Appendix IV 139 Reprints Ecological Bulletins 48 191 203 Copenhagen 2000 Structure of the VORTEX simulation model for population viability analysis Robert C Lacy Lacy R C 2000 Structure of the VORTEX simulation model for population viability analysis Ecol Bull 48 191 203 The structure of the VORTEX computer simulation model for population viability analysis is outlined The program flow is described here in order to provide a detailed specification of the structure of a widely used population viability analysis model VORTEX is an individual based simulation program that models the effects of mean demographic rates demographic stochasticity environmental variation in demographic rates catastrophes inbreeding depression harvest and supplementation and metapop ulation structure on the viability of wildlife populations The model facilitates analysis of density dependent reproduction and changing habitat availability and most demo graphic rates can optionally be specified as flexible functions of density time popula tion gene diversity inbreeding age and sex VORTEX projects changes in population size age and sex structure and genetic variation as well as estimating probabilities and times to extinction and recolonization R C Lacy rlacy ix netcom com Dept of Conservation Biology Daniel
227. ir residents each year Rates of genetic decay slowed as dispersal rates were increased but the individual based stochastic model consistently showed that population subdivision caused faster genetic decay from the metapopulation a result not predicted from many analytical genetic models Characteristics of highly vulnerable species an l Summarizing this discussion of the threats to viability of small populations we can identify some of the characteris tics of populations that lead to the most complicated population dynamics as populations become small and which therefore might require the most detailed and indi vidual based PVA models Especially vulnerable species would include those with non breeding helpers such as striped back wrens and naked mole rats species with co operative foraging such as many parrots and social carni vores and species with group defense behaviors such as musk ox and many primates Species with precise mecha nisms for mate choice such as many bird species could have demographic and genetic problems when that choice becomes limited Monogamous species will have depressed reproduction when there is demographic stochasticity in the sex ratio Species with low fecundity are particularly vulnerable to inbreeding depression Mills and Smouse 1994 be cause they can withstand less depression of survival before population growth rates become negative and because they will recover more slowly from popul
228. ironment that was different from the current landscape For example in largely contiguous habitat with local competition for breeding territories the optimal dis persal pattern might be for subadults to always disperse and to disperse in a random direction When habitat is highly fragmented and often unoccupied however it might be adaptive to remain near the natal site unless local densities are very high Ronce et al 2000 and to develop dispersal behaviors that more efficiently locate suitable habitat for example habitat with an excess of inhabitants of the opposite sex Many metapopulations may be occu pying recently fragmented landscapes for which their evolved dispersal strategies are suboptimal In PVA mod els it might be important to consider that dispersal strate gies that are stabilizing at one population density can be come destabilizing at different population densities Disruption of breeding systems represents another ex ample of interactions between processes As populations become small individuals may become closely related to most or all potential mates In a number of species indi viduals have been observed to avoid mating with genetic relatives Keane 1990 Inbreeding avoidance in a small population could lead to frequent failures to locate any suitable mates The suppression of breeding might be con 46 sidered a form of inbreeding depression but it may not be recognized as such since the individuals ma
229. is a population level phenomenon and K is assessed once for each population each year If K is a function of inbreeding I the value of I applied in the function will be the mean for the population The total length of a function cannot exceed 512 characters Functions cannot contain more than 24 numerical constants or more than a total of 128 constants plus variables plus operators Often you can find an alternative form that is shorter Many of the variables that can be used in rate functions will themselves change during each year of the simulation In order to avoid unresolvable interdependencies of parameters and rates the population size N and sizes of subsets J F M U X W and gene diversity G used in function evaluations are the numbers that were tallied at the last pre breeding season census Even without specifying rates as functions many of the rates used in VORTEX can be specified to be different for different years sexes ages or inbreeding levels e g age specific mortality inbreeding depression in juvenile mortality linear trends in K etc Be aware that the effects of any functions entered are imposed on top of such dependencies that might be given in the standard input format For example EV in carrying capacity could be specified via standard input or via a function of the type K 100 10 NRAND thereby giving an annual level of EV in K equal to a standard deviation of 10 The advantage of creating EV
230. is probably a good idea to specify a new directory for storing each Project and this is the default in VORTEX although you can store all your work in one directory if you wish Each Scenario within a Project contains a discrete set of input values and if it has been run output Thus for a given species Project you may decide to test several or even many different Scenarios each of which would have an alternative set of input values representing an alternative view of the population For example different Scenarios may represent various plausible input values to be explored during sensitivity testing or may represent alternative management options that might be applied to a population The VORTEX interface has separate screens windows or tabs for Project Settings Simulation Input Text Output Graphs and Tables and a Project Report Each of these are specific to an open Project and you can toggle among the Scenarios of a Project within the input and output screens You can open concurrently multiple VORTEX Projects within a VORTEX session although there may only rarely be cases in which it is useful to have more than one Project open at the same time A caution It is almost inevitable that VORTEX contains some bugs and it may be that you will make some mistakes while working with VORTEX Thus it is possible that after you spend hours working on a VORTEX Project the program will suddenly crash It is also possible that you will accident
231. itat Viability Assessment PHVA Workshop Apple Valley MN Captive Breeding Specialist Group SSC TUCN Ounsted M K Soemarna W Ramono U S Seal A Green Rudyanto and R Ounsted eds 1994 The White Winged Wood Duck in Sumatra Population and Habitat Viability Analysis Report Apple Valley MN Captive Breeding Specialist Group SSC IUCN Paolo C and L Boitani 1991 Viability assessment of the Italian wolf and guidelines for the management of the wild and a captive population In Italian Ricerche de Biologia della Selvaggina 89 1 58 Parysow P and D J Tazik 2002 Assessing the effect of estimation error on population viability analysis an example using the black capped vireo Ecological Modelling 155 2 3 217 229 Pergams O R W 1998 Genetic morphological and population viability analysis of California Channel Island deer mice M Sc thesis University of Illinois at Chicago Phillips M N Fascione P Miller and O Byers eds 2000 Wolves in the Southern Rockies A Population and Habitat Viability Assessment Final Report Apple Valley MN Conservation Breeding Specialist Group SSC TUCN Pinder L and U S Seal eds 1994 Population and Habitat Viability Assessment Report for Cervo do Pantanal Blastocerus dichotomus Apple Valley MN Conservation Breeding Specialist Group SSC IUCN Plissner J H and S M Haig 2000 Viability of piping plover Charadrius melodus metapopulations Biological Con
232. iversity of Chicago Press Beissinger S R J R Walters D G Catanzano K G Smith J B Dunning S M Haig B R Noon and B M Smith 2002 The use of models in avian conservation Current Ornithology 17 in press Belovsky G E C Mellison C Larson and P A Van Zandt 2002 How good are PVA models Testing their predictions with experimental data on the brine shrimp Pages 257 283 in Beissinger S R and D R McCullough eds Population Viability Analysis Chicago IL University of Chicago Press Berry H M Bush B Davidson O Forge B Fox J Grisham M Howe S Hurlbut L Marker Kraus J Martenson L Munson K Nowell M Schumann T Shille K Venzke T Wagener D Wildt S Ellis and U Seal eds 1997 Population and Habitat Viability Assessment for the Namibian Cheetah Acinonyx jubatus and Lion Panthera leo Workshop Report Apple Valley MN Conservation Breeding Specialist Group SSC AUCN Bonaccorso F P Clark P S Miller and O Byers eds 1999 Conservation Assessment and Management Plan for the Tree Kangaroos of Papua New Guinea and Population and Habitat Viability Assessment for Matschie s Tree Kangaroo Final Report Apple Valley MN Conservation Breeding Specialist Group SSC IUCN Bowland A E K S Bishop P J Taylor J Lamb F H van der Bank E van Wyk and D York 2001 Estimation and management of genetic diversity in small populations of plains zebra Equus quagga in KwaZulu Nat
233. ividuals have fewer lethal alleles to cause inbreeding depression This process is often referred to as purging the genetic load of lethal alleles See Hedrick 1994 Ballou 1997 and Lacy and Ballou 1998 On the other hand selection is ineffective at purging inbreeding depression when the inbreeding depression results from a general advantage of heterozygotes over all homozygotes or to a lesser extent when it is caused by recessive sub lethal alleles To model the effects of lethal alleles which can be removed by selection during generations of inbreeding VorTEXx assigns to each individual at the start of a simulation some unique lethal alleles If inbred descendants happen to receive two copies of the same lethal allele they are killed To model the component of inbreeding depression that is not effectively reduced by selection VORTEX calculates the inbreeding coefficient of each individual and then applies an exponential equation like the one above but using just a part of the total lethal equivalents to determine how much that individual s survival is reduced To incorporate these two mechanisms of inbreeding depression VorTEX needs to know i e you need to tell it how much of the overall inbreeding depression lethal equivalents to assign to lethal alleles vs other genetic mechanisms As mentioned above for Drosophila flies it has been reported that about half of the lethal equivalents are due to actual lethal alleles Almost
234. ject Settings Simulation Input Text Output Graphs and Tables Project Report Data Specification Data Graphs Columns 5 able s Table 1 Rows Pisurvive N extant SE N extant i Populations H Population 1 0 4000 7 95 0 68 ZPG2 Population 2 0 3300 9 42 0 98 Metapopulatior 0 4600 14 09 1 25 Year Year 100 Print Table Sendto Report Export Table Scenar Columns ZPG1 ZPG2 Plsurvive N exl N A Z O NA Z Vortex 9 21 CAPS NUM INS Date Time 10 24 03 1 32PM _ Figure 45 An example of a Table with Variables as Columns VORTEX can display a multi part table with results from a different Scenario shown in each part You select which Scenario s you want to examine by checking the boxes in the grid on the lower left of the screen To then specify which Years Populations and Variable s you want in your table you need to specify the Columns and Rows in the grid in the lower left and pick from the dropdown list which Variable Year Population is to be tabulated The specification of Columns and Rows can be done by Chapter 4 77 Viewing Model Results VORTEX Version 9 User s Manual typing the numbers of the desired Years or Populations into the grid under Columns or Rows as appropriate Alternatively you can click on the button for Rows or Columns That will open up a window for specification of the Years Populations or Variables as app
235. lace the VORTEX installation CD into the appropriate disk drive and then run the SETUP program Either double click on SETUP from Windows Explorer or go to START gt RUN and then enter D SETUP EXE in which D is your CD drive To install VORTEX from the Internet Go to http www vortex9 org vortex html and download the current version of the installation program Save this downloaded file to any temporary directory of your hard disk or to your desktop Double click on the downloaded file to unzip the installation package files Unzip them to the directory where you saved the downloaded file or to any directory of your choosing other than the directory to where you wish to install VORTEX Run the SETUP program Either double click on SETUP from Windows Explorer or go to START gt RUN and then enter Chapter2 5 Getting Started with VORTEX VORTEX Version 9 User s Manual C TEMP SETUP EXE in which C temp is the drive and directory where you placed the installation files You may want to put a short cut to VORTEX on your Desktop VORTEX is copyrighted but not copy protected You can make as many copies as you wish and you may give copies of the program to others free of charge You may not sell the program or any components of it or otherwise represent it as your personal property Running VORTEX Start VORTEX by double clicking on a short cut icon or by double clicking on the VORTEX program itself To exit the VORTEX prog
236. lation management Pages 87 123 in Soul M E ed Viable Populations for Conservation Cambridge Cambridge University Press Latour A 1986 Polar normal distribution Byte August 1986 131 2 Lindenmayer D B and R C Lacy 1995a Metapopulation viability of Leadbeater s Possum Gymnobelideus leadbeateri in fragmented old growth forests Ecological Applications 5 164 182 Lindenmayer D B and R C Lacy 1995b Metapopulation viability of arboreal marsupials in fragmented old growth forests Comparison among species Ecological Applications 5 183 199 Lindenmayer D B and R C Lacy 1995c A simulation study of the impacts of population sub division on the mountain brushtail possum Trichosurus caninus Ogilby Phalangeridae Marsupialia in south eastern Australia I Demographic stability and population persistence Biological Conservation 73 119 129 Lindenmayer D B T W Clark R C Lacy and V C Thomas 1993 Population viability analysis as a tool in wildlife conservation policy A review with reference to Australia Environmental Management 17 745 758 Mace G M and R Lande 1991 Assessing extinction threats Toward a re evaluation of IUCN threatened species categories Conservation Biology 5 148 157 Mace G et al 1992 The development of new criteria for listing species on the IUCN Red List Species 19 16 22 Mace G and S Stuart 1994 Draft IUCN Red List Categories Version 2 2 Species 21 22 13 24 MacNab J
237. lation is large and the percent of animals killed is high then these two ways of modelling the effects of poaching will yield the same results the deterministic component of poaching dominates the population dynamics If the population is small or the percent of animals killed is very low then the numbers killed in a stochastic model and in nature might vary substantially from year to year the stochastic nature of poaching further destabilizes the population Which of the various deterministic and stochastic factors are important to consider in a PVA will depend on the species biology the present population size and distribution and the threats it faces For example orang utans may be threatened by forest destruction and other largely deterministic processes but inbreeding and randomly skewed sex ratios resulting from highly stochastic processes are unlikely to be problems at least not on a species wide basis On the other hand even if the remnant Atlantic coastal rainforest of Brazil is secured for the future the populations of golden lion tamarins Leontopithecus rosalia which can persist in that remnant forest are not sufficiently large to be stable in the face of stochastic threats Seal et al 1990 Rylands 1993 4 Ballou et al 1997 The identification of the primary threats facing a taxon via a comprehensive PVA is important for conservation planning For example tamarin populations might be stabilized by the translocations and reintrodu
238. leles the relationship between inbreeding and survival might be expected to be roughly an exponential decline of this form By observing the relationship between survival and inbreeding the coefficient b in the above equation can be measured The value b is a measure of the severity of the effects of inbreeding not in terms of how inbred the population is as that is measured by F but rather in terms of how much fitness is depressed for any given level of inbreeding and it is the number of recessive lethal alleles per haploid genome that would cause the observed rate of inbreeding depression This concept is called the number of lethal equivalents in the population A population with 4 0 lethal equivalents per diploid individual b 2 0 might have 4 lethal alleles per individual or it might have 8 alleles per individual which each cause 50 reduction in survival when homozygous or it might have 2 lethal alleles and four 50 lethals or any other combination of deleterious alleles which have the same total effect VoRTEX uses this concept of lethal equivalents to quantify the severity of depression of first year survival due to inbreeding Thus the user must specify how many lethal equivalents characterize the population under study For only a few species however has the number of lethal equivalents been measured in careful breeding studies Among those species that have been studied the number of lethal equivalents per diploid 2b ran
239. lis and State Vars Population1 Population 2 Adult Females Breeding 50 Reproductive System EV in Breeding 125 Reproductive Rates lortality Rates atastrophes ate Monopolization nitial Population Size r Normal Distribution arrying Capacity Population 1 Population 2 Specify the distribution of number of offspring per female per year C Use Normal distribution approximation Specify exact distribution upplementation Standard Deviation Copy input values from Population 1 This Section Population 1 Population 2 to subsequent populations Copy Input Values ad My note about the Reproductive Rates Vortex 9 21 Enter the probability of each number of progeny the last row will be filled in automatically to sum to 100 A NUM INS Date Time 10 24 03 10 01AM 4 CAPS Figure 27 Reproductive Rates input section Adult Females Breeding Here you specify the mean percentage of adult females that breed in a given year or stated another way the probability that a given adult female will successfully produce offspring in a given year Data on the interbirth interval or the timespan between successive birth events for a given female can be useful for estimating the percentage of adult females breeding annually A simple example if the average length of time between successive births for adult females is 2 years then 50 of all adult females are expected to br
240. lity Assessment Workshop Report Apple Valley MN Conservation Breeding Specialist Group SSC TUCN Seal U S J D Ballou and C V Padua eds 1990 Leontopithecus Population Viability Analysis Workshop Report Apple Valley MN Captive Breeding Specialist Group SSC TUCN Seal U S and M W Bruford eds 1991 Pink Pigeon Columba Nesoenas mayeri Conservation Viability Assessment Workshop Apple Valley MN Captive Breeding Specialist Group SSC IUCN Seal U S and T Foose eds 1989 Javan Rhinoceros Population Viability Analysis Apple Valley MN Captive Breeding Specialist Group SSC IUCN Seal U S P Garland D Butler A Grant and C O Donnell eds 1993 Population Viability Analysis for the Kea Nestor notabilis and Kaka Nestor meridionalis Apple Valley MN Captive Breeding Specialist Group SSC ATUCN Seal U S and S Hereford eds 1992 Mississippi Sandhill Crane Population and Habitat Viability Assessment Report Apple Valley MN Captive Breeding Specialist Group SSC IUCN Seal U S and R C Lacy eds 1989 Florida Panther Population Viability Analysis Report to the U S Fish and Wildlife Service Apple Valley MN Captive Breeding Specialist Group SSC IUCN Seal U S and R C Lacy 1990 Florida Key Deer Odocoileus virginianus clavium Population Viability Assessment Report to the U S Fish and Wildlife Service Apple Valley MN Captive Breeding Specialist Group SSC TUCN S
241. lity Assessment Reports Apple Valley MN Captive Breeding Specialist Group SSC TUCN Ewins P M de Almeida P Miller and O Byers eds 2000 Population and Habitat Viability Assessment Workshop for the Wolves of Algonquin Park Final Report Apple Valley MN Conservation Breeding Specialist Group SSC IUCN Fisher A E Rominger P Miller and O Byers 1999 Population and Habitat Viability Assessment Workshop for the Desert Bighorn Sheep of New Mexico Ovis canadensis Final Report Apple Valley MN Conservation Breeding Specialist Group SSC IUCN Foose T J R C Lacy R Brett and U S Seal eds 1993 Kenyan Black Rhino Metapopulation Workshop Report Apple Valley MN Captive Breeding Specialist Group SSC IUCN Forys E A and S R Humphrey 1999 Use of population viability analysis to evaluate management options for the endangered Lower Keys marsh rabbit Journal of Wildlife Management 63 1 251 260 Galimberti F S Sanvito L Boitani and A Fabiani A 2001 Viability of the southern elephant seal population of the Falkland Islands Animal Conservation 4 1 81 88 Gonzalez L M B Heredia A Araujo I Robinson J Worms P S Miller and U S Seal eds 2002 Population and Habitat Viability Assessment for the Mediterranean Monk Seal Monachus monachus in the Eastern Atlantic Apple Valley MN Conservation Breeding Specialist Group SSC TUCN Gonzalez S M Merino M Gimenez Dixon S Ellis and
242. ll population will remove all sampling error in estimation of current parameter val ues but it will not necessarily provide sufficiently precise values for predicting future trends The entire existing population is still only a sample of the universe of all possi ble populations that could have resulted from the same processes Given that highly detailed models employing accurate estimates for a large number of parameters might be needed to project the dynamics of small populations well should PVA models be used to help guide conserva tion actions The alternative to using incomplete models with poorly estimated parameters that may overestimate population viability is to use even more general models that will omit many threatening processes and often more seriously underestimate risks or to rely on intuitive assess ments of complex probabilistic phenomena something that people are innately poor at doing Piattelli Palmarini 1994 Margolis 1996 When planning conservation ac tions for species that have already declined to near extinc tion we should use the best tools available but also recog Northern White Rhinoceros Observed Population Model Predictions e 0 d Number in Garamba Nationai Park 10 1985 1986 1987 1988 1989 1990 1991 48 ae 1992 1993 1994 1995 1996 Fig 5 Observed numbet solid line of northern white rhinoc oo one le
243. llowing material is adapted from Lacy 1993a and Lacy 1993 4 The Dynamics of Small Populations Many wildlife populations that were once widespread numerous and occupying contiguous habitat have been reduced to one or more small isolated populations The primary causes of the decline of many species are obvious and deterministic Populations are over harvested natural habitat is converted and lost to the species often involving the replacement of diverse ecological communities with monocultures environments are polluted with the dumping of toxins into the air water and soil local and now even global climates are modified by the actions of humans and numerous exotic competitors predators parasites and diseases are introduced into communities that have never evolved defenses to the new invaders The primary causes of species decline are usually easy to understand and often easy to study and model but usually though not always difficult to reverse Even if the original causes of decline are removed a small isolated population is vulnerable to additional forces intrinsic to the dynamics of small populations which may drive the population to extinction Shaffer 1981 Soul 1987 Clark and Seebeck 1990 Of particular impact on small populations are stochastic or random or probabilistic processes Indeed the final extinction of most populations often occurs not so much because of a continuation of the pressures that led to the initi
244. low fecundity and only slow population growth under optimal conditions Finally it may be difficult to know when a population is so small that additional stochastic factors must be included in a PVA to obtain an accurate projection of its dynamics Therefore it is often useful to test several models to deter ECOLOGICAL BULLETINS 48 2000 mine if added complexity substantially alters PVA predic tions and provides a better fit to observed population trends A good example of this type of exploration is pro vided by the ongoing work of Lindenmayer and his col leagues on the fauna of fragmented forests in Australia Lindenmayer et al 1999 2000 PVA models should be no more complex than necessary but to be useful for con servation they must also be detailed enough to model the real population dynamics accurately Starfield and Bleloch 1986 Starfield 1997 Ak akaya and Sj gren Gulve 2000 Lacy and Miller 2001 Acknowledgements I thank the editors for their many construc tive comments References Ak akaya H R 2000 Population viability analyses with demo graphically and spatially structured models Ecol Bull 48 23 38 Ak akaya H R and Ferson S 1992 RAMAS Space Spatially structured population models for conservation biology Appl Biomath New York Ak akaya H R and Sj gren Gulve P 2000 Population viabili ty analyses in conservation planning an overview Ecol Bull 48 9 21 A
245. lpin 1991 Metapopulation dynamics A brief history and conceptual domain Biological Journal of the Linnean Society 42 3 16 Hanski I A and M E Gilpin eds 1997 Metapopulation Biology Ecology Genetics and Evolution London Academic Press Hedrick P W 1994 Purging inbreeding depression and the probability of extinction full sib mating Heredity 73 363 372 Herrero S P S Miller and U S Seal eds 2000 Population and Habitat Viability Assessment Workshop for the Grizzly Bear of the Central Rockies Ecosystem Ursus arctos horribilis Apple Valley MN Conservation Breeding Specialist Group SSC IUCN Hobbs N T and D M Swift 1985 Estimates of habitat carrying capacity incorporating explicit nutritional constraints Journal of Wildlife Management 49 814 822 Holling C S ed 1978 Adaptive Environmental Assessment and Management International Series on Applied Systems Analysis 3 International Institute for applied systems analysis Toronto John Wiley and Sons Hosack D A 1998 Population Viability Analysis Workshop for the Endangered Sonoran Pronghorn Antilocapra americana sonoriensis in the United States Washington DC Defenders of Wildlife Ims R A and N G Yoccoz 1997 Studying transfer processes in metapopulations Emigration migration and colonization Pages 247 265 in Hanski I A and M E Gilpin eds Metapopulation Biology Ecology Genetics and Evolution London Academic Press IU
246. ls are produced by matings between genetic relatives Inbreeding depression seems to affect most perhaps even all species of sexually reproducing organisms and can cause reduction in survival of infants juveniles and adults mate acquisition fertility fecundity number of progeny per litter or brood and a variety of physiological measures related to fitness such as growth rate disease resistance stress resistance metabolic efficiency sensory acuity and behavioral dominance see Lacy 1997 and references therein Although inbreeding depression can affect many components of fitness often the overall effect can be reasonably well summarized by or combined into an effect on infant survival For example if inbreeding causes a 10 reduction in litter size and then a 10 reduction in survival of those individuals born the cumulative effect would be the same as a 19 reduction in infant survival resulting in 81 of the yearlings which would have been produced if no inbreeding had occurred Also most of the published literature on inbreeding depression in wild species of animals deals only with effects on juvenile survival Ralls et al 1988 Lacy et al 1993 Therefore the primary way in which inbreeding depression is incorporated into Vortex is through a reduction in first year survival of inbred individuals If desired inbreeding effects on later survival reproduction carrying capacity and even dispersal can be modeled using functions
247. ls et al 1988 Barrett and Kohn 1991 Lacy et al 1996 The rate of adaptive evolution of any population is ex pected to be proportional to its additive genetic variation and heritability for the traits under selection Fisher 1958 and the limited evolutionary potential of domesti cated animals with depleted genetic variation has been shown repeatedly It would be difficult to know whether limited response to selection in rapidly changing habitats is a contributing threat to the persistence of natural popula tions Some populations have persisted at small numbers for many generations e g the Javan rhinoceros Rhinoceros sondaicus and until 1986 the black footed ferret Mustela nigripes but other populations have rapidly gone extinct when an unusual stress appeared in the environment e g the golden toad Bufo periglenes Pounds and Crump 1994 and the black footed ferret in 1986 Clark 1989 Given the current situation of unprecedented environ mental change and an accelerating extinction rate perhaps more PVA models should consider the maintenance of suf ficient genetic variability to ensure ecological and evolu tionary flexibility rather than solely immediate fitness ef fects and short term population persistence One way to accommodate long term viability into conservation plan ning would be to use the potential for rapid recovery as the primary measure of population viability rather than mere population persistence at s
248. ly the proportion of females breeding would decrease as the population size becomes large In addition it is possible to model an Allee effect a decrease in the proportion of females breeding at low densities due for example to difficulty in finding mates The equation that VORTEX uses to model density dependence is PN PO PO PERIL DA Chapter 3 45 The Data Input Process VORTEX Version 9 User s Manual in which P N is the percent of females the breed when the population size is N P K is the percent that breed when the population is at carrying capacity K to be entered later and P 0 is the percent of females breeding when the population is close to zero in the absence of any Allee effect The exponent B can be any positive number and determines the shape of the curve relating the percent breeding to population size as the population becomes large If B 1 the percent breeding changes linearly with population size If B 2 P N is a quadratic function of N Figure 24A shows representative density dependence curves for different values of B in the absence of an Allee effect The term A in the density dependence equation defines the magnitude of the Allee effect One can think of A as the population size at which the percent of females breeding falls to 50 of its value in the absence of the effect Ak akaya 1997 Figure 24B shows several density dependence curves for different values of A with a steep decrease in breeding a
249. ly be paired with a single female each year Males are paired only with those females which have already been selected for breeding that year Thus males will not be the limiting sex unless there are insufficient males to pair with the successfully breeding females If the breeding system is polygynous then a male may be selected as the mate for several females The degree of polygyny is determined by the proportion of males in the pool of potential breeders each year The size of the litter produced by that pair is determined by comparing the probabilities of each potential litter size including litter size of 0 no breeding to a randomly drawn number The offspring are produced and assigned a sex by comparison of a random number to the specified birth sex ratio Offspring are assigned at random one allele at the hypothetical genetic locus from each parent 16 The genetic kinship of each new offspring to each other living animal in the population is determined The kinship between new animal A and another existing animal B is fap 0 5 fue fpg in which fy is the kinship between animals 7 and j M is the mother of A and P is the father of A The inbreeding coefficient of each animal is equal to the kinship between its parents F fup and the kinship of an animal to itself is f4 0 5 1 F See Ballou 1983 for a detailed description of this method for calculating inbreeding coefficients 17 The survival of each animal is de
250. ly insert your Input Notes into a report of your work Input Notes are always saved when you save a Project Chapter 3 25 The Data Input Process VORTEX Version 9 User s Manual Creating a Scenario Input of model parameters into VORTEX is accomplished in 13 sections each containing questions pertaining to a category of model parameters You move among the input sections by clicking on their labels in the list on the left hand side of the Simulation Input screen You can move among the sections to enter data in any order although the list provides a logical sequence for data input After you have visited an input section within a VORTEX session the label for that section will be in italics This may help you to quickly check whether you have completed data entry for every section If you jump around among input sections you risk forgetting to visit a section and then running EF models that are missing some parameters or that have values from scenarios used as templates In addition VORTEX uses answers on some early screens to complete intermediate calculations such as the stable age distribution that are useful when you reach later input sections Scenario Settings The first data input screen you encounter when creating a Scenario asks for some basic Scenario Settings Figure 18 above Subsequently you will need to step through 12 more input screens to complete the process of specifying the values for all of the input parameters nee
251. mall numbers It is also possible to use models that include both the effects of inbreeding on demographic rates and the effects of reduced genetic variability on vulnerability to environmental variation and ability to survive catastrophes The individual based mod el VORTEX Lacy 2000 can accommodate such depend encies on inbreeding and similar effects could be built into population based matrix models as in INMAT by Mills and Smouse 1994 Parameterization of models with ge netic demographic interactions is difficult but data are in creasingly available on the effects of inbreeding on demo graphic rates Ralls et al 1988 Brewer et al 1990 Saccheri et al 1998 persistence through environmental stress Miller 1994 Keller et al 1994 and population extinc tion Frankham 1995b Saccheri et al 1998 Interactions among threatening processes Although each process described above can individually threaten the viability of small populations synergistic in teractions exacerbate the impacts of many of the processes and are at the center of extinction vortices Gilpin and Soul 1986 Interactions among threats are sufficiently 45 complex that they are often omitted from analytical PVA models and from the functions driving demographic pro jections in simulation models Most analytical models are constructed by deriving the impact that a factor would have when acting in isolation from other threatening proc esses Below are a
252. marins In Young A and Clarke G eds Genetics demography and population viability Cambridge Univ Press in press Ellis S et al 1992 Alala akohekohe and palila population and habitat viability assessment reports IUCN SSC Captive Breeding Specialist Group Apple Valley Minnesota Fahrig L and Merriam G 1985 Habitat patch connectivity and population survival Ecology 66 1762 1768 Fahrig L and Merriam G 1994 Conservation of fragmented populations Conserv Biol 8 50 59 Fisher R A 1958 The genetical theory of natural selection Dover New York Foley P 1994 Predicting extinction times from environmental stochasticity and carrying capacity Conserv Biol 8 124 137 Forman L et al 1986 Genetic variation within and among lion tamarins Am J Phys Anthropol 71 1 11 Frankel O H and Soul M E 1981 Conservation and evolu tion Cambridge Univ Press Frankham R 1995a Conservation genetics Annu Rev Genet 29 305 327 Frankham R 1995b Inbreeding and extinction a threshold ef fect Conserv Biol 9 792 799 Franklin I R 1980 Evolutionary change in small populations In Soul M E and Wilcox B A eds Conservation biol ogy An evolutionary ecological perspective Sinauer pp 135 149 Gilpin M E and Soul M E 1986 Minimum viable popula tions the processes of species extinction In Soul M E ed Conserv
253. mmalian and avian populations but its capabilities have improved so that it can now be used for modeling some reptiles and amphibians and perhaps could be used for fish invertebrates or even plants if they have relatively low fecundity or could be modeled as if they do The purpose of this manual is to provide you with complete instructions on how to install and use VORTEX It is not intended as a primer on population biology you must be conversant with this discipline to use the program appropriately and effectively In addition you must know something about the biology of the species that you intend to model You should gather as much information as possible in order for VORTEX simulations to be meaningful The old computer adage of garbage in garbage out is aptly applied to population viability analysis and PVA using VORTEX is certainly no exception Having said this it is important to recognize that many of the questions VORTEX asks as you construct your population model cannot be answered simply because the data do not exist The only recourse that you will have is to enter your best guess Oftentimes your best guess is not yours alone most if not all population viability analyses have succeeded through the efforts of many Two or more heads are usually better than one when you find yourself faced with a VORTEX question with no known answer Further information about VORTEX and the structure of the model is provided in publications re
254. monstrate that the simple models are sufficient to provide guidance for conservation A third method of conducting a PVA is the use of computer simulation modeling to project the probability distribution of possible fates of a population Simulation models can incorporate a very large number of threatening processes and their interactions if the processes can be described in terms of quantitative algorithms and parameterized Although many processes affecting small populations are intrinsically indeterminate the average long term fate of a population and the variance around the expectation can be studied with computer simulation models The focus is on detailed and explicit modeling of the forces impinging on a given population place and time of interest rather than on delineation of rules which may not exist that apply generally to most wildlife populations Modeling and Population Viability Analysis A model is any simplified representation of a real system We use models in all aspects of our lives in order to 1 extract the important trends from complex processes 2 permit comparison among systems 3 facilitate analysis of causes of processes acting on the system and 4 make predictions about the future A complete description of a natural system if it were possible would often decrease our understanding relative to that provided by a good model because there is noise in the system that is extraneous to the processes we wish to un
255. mulation models can be well suited for the complex task of evaluating risks of extinction Simulation models can include as many factors that influence population dynamics as the modeler and the user of the model want to assess Interactions between processes can be modeled if the nature of those interactions can be specified Probabilistic events can be easily simulated by computer programs providing output that gives both the mean expected result and the range or distribution of possible outcomes In theory simulation programs can be used to build models of population dynamics that include all the knowledge of the system which is available to experts In practice the models will be simpler because some factors are judged unlikely to be important and because the persons who developed the model did not have access to the full array of expert knowledge Although computer simulation models can be complex and confusing they are precisely defined and all the assumptions and algorithms can be examined Therefore the models are objective testable and open to challenge and improvement PVA models allow use of all available data on the biology of the taxon facilitate testing of the effects of unknown or uncertain data and expedite the comparison of the likely results of various possible management options PVA models also have weaknesses and limitations A model of the population dynamics does not define the goals for conservation planning Goals in te
256. mulation of the Extinction Process File Edt Yortex Window Help Dem see SG jos i EAZPG D WORTEXS ZPG ZPG vpi 15 x Project Settings Simulation Input Text Output Graphs and Tables Project Report Add Scenario Delete Scenario lt zp gt Reorder ZPE ZPG2 cenario Settings pecies Description abels and State Vars Reproductive System Catastrophe 1 Catastrophe 2 Reproductive Rates ortality Rates Population 1 atastrophes Global Local ate Monopolization Frequency 1 nitial Population Size anying Capacity Severity proportion of normal values Population 1 Reproduction 5 Survival 75 Catastrophes Copy input values from Population 1 This Section to subsequent populations Copy Inputs Vortex 9 21 Enter a percent to define the annual probability of this catastrophe CAPS NUM INS Date Time 10 24 03 9164M Figure 7 Catastrophes input section Because it was specified in the Species Description that the model should contain two types of catastrophes the Catastrophes section has buttons to toggle between these two types Hit the button to go to input for Catastrophe 2 In this particular Scenario the two types of catastrophes have the same input values so it is not obvious that you are moving between the two types but you are When you are done looking through all the input sections click on the Run icon the green triangle on the ico
257. n Using a fairly simple method known as normalizing a distribution we can calculate that 68 3 of all observations in a normally distributed population fall within the range of w o 95 5 fall within 2c and 99 7 fall within u 3c This kind of information is helpful when estimating standard deviations in demographic rates caused by environmental variation when only a range of observations are available see Box E for additional details It is also noteworthy that the binomial distribution becomes quite close to a normal distribution when the number of observation per sample n is large say when n gt 20 Observe that even when n is as small as 5 the distributions shown in Figure C 1 look like approximate bell curves However one important distinction between the binomial and normal distributions is the binomial distributions are always bounded at 0 and n while normal distributions have tails that are infinitely long but rapidly diminishing For more information on the theory and applications of these and many other concepts relevant to an understanding of population dynamics and risk projections see Caughley 1977 Sokal and Rohlf 1994 and Zar 1996 Case Study IT Correlating environmental variation for reproduction and survival North America s whooping crane Grus americana shows a classic migratory pattern typical of many bird species The last remaining substantial population breeds in Alberta s Wood Buffalo Na
258. n to yield precise Lambda Set r p log Lambda Set Generation Time p log RO r p FOR each age x Determine stable age distribution Set StableAgeClassSize p x 1 SexRatio Lix I Lambda x ECOLOGICAL BULLETINS 48 2000 Add StableAgeClassSize p x to SumStableAgeClassSize p END LOOP Repeat age distribution calculations for males but use female based Mx and Lambda FOR each age x Set male survival P x 1 MaleMortality p x FOR each type of catastrophe c Adjust P x for catastrophes Multiply P x by CatastropheFrequency p c CatastropheSurvivalSeverity p c Q CatastopheFrequency p c END catastrophe LOOP Multiply cumulative survivorship L x by P x END LOOP FOR each age x Determine stable age distribution Set StableAgeClassSize p x SexRatio L x I Lambda x Add StableAgeClassSize p x to SumStableAgeClassSize p END LOOP FOR each age x and sex 5 Divide StableAgeClassSize p s x by SumStableAgeClassSize p END LOOP END FUNCTION CALC_DETERMINISTIC_GROWTH BEGIN FUNCTION GLOBAL_EV_RANDS O FOR each type of catastrophe Set GlobalCatastropheRand RAND Select random number to determine if global catastro phe occur See Note 5 END catastrophe LOOP Set GlobalBreedEVRand RAND Select random number for specifying EV in breeding for that year Set GlobalBreedEVNRand NRAND Select random normal deviate for
259. n bar to open up the Run Simulation dialog box shown in Figure 8 Check the box to select Scenario ZPG1 and then click Run 14 Chapter 2 Getting Started with VORTEX VORTEX Version 9 User s Manual Run Simulation Select the scenarios that you want to be included in the simulation run I Select All Run Cancel Figure 8 Run Simulation window Now sit back and watch the simulation work The lines on the screen Figure 9 show the changing population size over 100 years for 100 different iterations for the ZPG1 Scenario When the simulation is complete which should take only a few seconds with this small population the VORTEX Simulation display window will show a few summary statistics along the top When you are done viewing this graphical display of the simulations click on its close icon x in the upper right corner x Final statistics r 0 010 SD r 0 237 PE 0 80 N 10 H 49 50 45 40 35 30 N 2y ira N W LN 20 AN Mh Mir Bi hi i i NSA UN 4 ANO hy N Veit iN 5 0 Project ZPG Scenario ZPG1 Iteration 100 Figure 9 VORTEX Simulation display window Chapter 2 15 Getting Started with VORTEX VORTEX Version 9 User s Manual The VORTEX Simulation window cannot be resized and toggling to another window during the EF VORTEX simulations may leave you with a blank VORTEX Simulation window when you return to it It is best not to move off of this window while the simulations are runn
260. n sustain controlled harvest Can it sustain poaching Would a corridor connecting fragmented habitats improve long term viability Could the same effect be achieved by translocating a few individuals What will happen to population viability if mortality increases for individuals dispersing between habitat patches What will happen to the wildlife population if trends in human populations and human impacts on the environment continue unabated The VorTex Population Viability Analysis Model The VORTEX computer program is a simulation of the effects of deterministic forces as well as demographic environmental and genetic stochastic events on wildlife populations It is an attempt to model many of the extinction vortices that can threaten persistence of small populations hence its name VORTEX models population dynamics as discrete sequential events that occur according to probabilities that are random variables following user specified distributions VORTEX simulates a population by stepping through a series of events that describe an annual cycle of a typical sexually reproducing diploid organism mate selection reproduction mortality increment of age by one year migration among populations removals supplementation and then truncation if necessary to the carrying capacity Although VORTEX simulates life events on an annual cycle a user could model years that are other than 12 months duration The simulation of the population is itera
261. n value is simply that statistic calculated for the observed sample For some other statistics such as the variance and standard deviation the statistic calculated on the sample is a biased measure of the value for the whole population so that correction factors must be applied to get a better estimate of the population statistic Below we somewhat loosely follow a common convention of using Greek letters to symbolize the true but often unknown population statistic Roman letters for sample statistics and letters with hats for example A to symbolize estimated values Measures of Central Tendency and Variability When a biologist studies a particular demographic characteristic in a wildlife population over some period of time one generally notes an abundance of values clustered near the middle of a range of annual observations In the language of statistics the description of this concentration near the midpoint is a measure of central tendency The most common measure of central tendency is the arithmetic mean or more simply the mean The mean of a sample of observations is calculated as which says that the sample mean equals the sum of all measurements in the sample divided by the number of measurements in that sample Another common measure of central tendency is the median which is the value at which 50 of the observations fall below and the remainder fall above that value For a symmetrical distribution the median will approxim
262. n which the Project files will be stored but it usually is reasonable to accept the default which is a subdirectory with the same name as the Project Click OK to continue New Yortex Project Basic Project Data Project Name Project Main User s Name Directory C Wortex9 Project1 Figure 16 Dialog box for entering a new project name 4 Vortex Stochastic Simulation of the Extinction Process Oj x File Edit Vortex Window Help Osais aa S lafi f4Project1 not previously saved Simulation Input Text Output Graphs and Tables Project Report Project Name Project Send all to Report User Nomos UserName Add User Name Remove User Name Special options Project Notes Vortex 9 0 7 CAPS NUM INS Date Time 5 2 2003 7 33PM 4 Figure 17 The Project Settings window 22 Chapter 3 The Data Input Process VORTEX Version 9 User s Manual In the Project Settings windows Figure 17 you have the option of listing the names of the user team that is developing the project this documentation may be especially helpful in workshop or classroom settings and add any notes that you wish We strongly encourage you to take the time to add notes to your Project at this screen during EF specification of input parameters and in your Project Report The extra few minutes you spend documenting your work may save you and others many hours of work later when you try to remember wha
263. nal Windows Settings Although we cannot guarantee that VORTEX will work correctly with all possible configurations of MS Windows we believe that it will adapt appropriately to most Regional Settings of date time and numeric formats Throughout this manual screen displays are shown from a system configured with the American English regional settings For example the is used as the decimal delimiter so that the number three would be shown as 3 0 If your operating system is configured to use the as the decimal delimiter then you would use that format throughout VORTEX for input and output so that the number three would be shown as 3 0 Do not use any delimiter between thousands e g thirty thousand would be 30000 not 30 000 nor 30 000 nor 30 000 VORTEX will try to automatically convert input and output files to the data format specified by your Windows Regional Settings VORTEX Technical Support If you are having trouble using VORTEX and want additional information there are a number of resources available to you Be advised however that CBSG is unable to provide the kind of technical support you have come to expect but rarely receive from large software companies In this context the phrase you get what you pay for is particularly appropriate VORTEX is provided on the Internet free of charge because of our commitment to promoting the use of science in the service of biodiversity conservation Significant r
264. nd Lindenmayer 1995 can be analyzed and monitored Although not yet common monitoring of population health could also utilize measures of developmental stability Clarke 1995 physiological parameters Appendix I 105 An Overview of Population Viability Analysis Using VORTEX VORTEX Version 9 User s Manual such as body condition Altmann et al 1993 or levels of the hormones related to stress and reproduction Sapolsky 1982 1986 or the stability of behavior and the social structure of the population Samuels and Altmann 1991 The interactions and synergism among threatening processes will often cause numerical distributional physiologic behavioral and genetic responses to concordantly reflect species decline and vulnerability It remains important however to understand and target the primary causal factors in species vulnerability The recent proposal to base IUCN categories of threat on quantified criteria of probability of extinction or changes in such indicators as species range numbers and trends Mace and Lande 1991 Mace et al 1992 Mace and Stuart 1994 IUCN Species Survival Commission 1994 reflects the increased understanding of the extinction process that has accompanied the development of PVA and simultaneously demands that much more progress be made in developing predictive models gathering relevant data on status and threats and applying the PVA techniques Population and Habitat Viability Analysis PHVA Popula
265. ndard deviation closest to the desired EV is determined by solving the equation for the binomial vari ance V p 1 p n for the parameter n when given the mean p and variance V SD The parameter n is then rounded to the nearest whole number If n lt 26 the bino mial distribution with parameters p and 7 is used for EV Because of the rounding step necessary to produce the dis crete binomial distribution this distribution will often have a slightly different variance than that entered by the user If 7 gt 25 the normal distribution with mean p and variance V will be used to model EV In such cases the normal distribution very closely approximates the bino mial distribution The binomial distribution is restricted to the interval 0 to 1 and it fits well the distribution of demographic rates across years observed in some natural populations e g Lacy 1993 The PVA program INMAT Mills and Smouse 1994 uses the related beta distribution for this purpose and it too is restricted to the biologically mean ingful 0 to 1 interval In contrast the normal distribution extends infinitely in both directions although the tails be yond 0 and 1 are typically very small in those cases for which VORTEX uses a normal distribution to model EV For example if p 0 5 and SD 0 1 so that the binomial parameter 7 25 the limiting case for VORTEX to use the normal approximation then the area of the normal distribution outside of the
266. nfant mortality was set at 16 and the frequency of non sterile females in the population was estimated at 91 Given these data a corrected interbirth interval can be calculated as 0 84 5 0 16 2 0 91 Based on this estimate of the interbirth interval the percentage of adult females producing an offspring in a given year is 4 97 20 1 Bl corr 4 97 Box E A Quick and Easy Way to Estimate a Standard Deviation from Scant Data Ideally to estimate the standard deviation of a demographic rate across years we would want to have many years perhaps 10 or more of field data However we often have information on just a few years and often only the best and worst years in recent times Fortunately the expected range observed in a sample of n values from a normal distribution can be specified see below and Rohlf and Sokal 1981 To estimate the standard deviation of a distribution the observed range best worst years can be divided by the expected range For example across 15 years of observations on Sonoran pronghorn antelope Hosack 1998 the mortality rate of fawns was 85 in the worst year and 55 in the best year Dividing the observed range 30 by the expected range for a normal distribution 3 47 SD units provides us with an estimate of the SD of 30 3 47 8 64 Table E 1 Mean ranges in SD units for samples of a normal distribution from Table 26 in Rohlf and Sokal 1981 Number of observations Rang
267. ng Population Viability csscsssecsessesseeseeseeneneens 109 Modeling and Population Viability Analysis c c0ssessesseeseeseeseeneeeees 110 Contents iii VORTEX Version 9 User s Manual Dealing with uncertainty c ee 112 Questions that can be explored with PVA models cscssessesesseeseaeees 113 The VorTex Population Viability Analysis Model ssscssessessesseeseeaes 114 Demographic StochastiCity ccsssecssseessseeeeeseeeeseeeeeseeneseessesonseeaeaeeneaseeneneess 115 Environmental VariatiOn ccccccssscscscccccccccccceceeeeeeeeeeeegeeeeagsssssssssssssssssssssseeees 115 Catastrophes vsssisissccdecisivievscessacasdsieiedaccsearwcieccusssdseasecusvecareceessteaedecens 115 Genetic processes cassecssssccsssecenseconnecaseeonneeeoseeonnseeaneeoseeonaseesnseesnasseaeseeanas 116 Deterministic PrOC SSES 1ccccceseceeeseesseeeesseeneeeeoeaeeeeeneeeseeaeseesoeseeseaeeenaseeeneess 117 Migration among populations ccessee eee 117 Output eae vaa eva evan uvauuvanavanavanvangvangvanvangeauvanavenueanueanuvenueenuvenueanueans 118 Sequence Of program flOW cssscccsssceeseeseeeeeeeseeeeseeeeeseeeeseeensneenseeaeaeesnaseeaeaeeneas 118 Appendix IT Literature Cited cscs 123 Appendix III Vortex Bibliography ssccscsesscsseseseeseeneeeeeeaseeeas 129 Appendix IV Reprints ee 139 Lacy R C 2000 Structure of the VORTEX simulation model for population viability analysis Ec
268. ng observed and Variables which summary variable is being tabulated These three dimensions need to be assigned to the columns rows 76 Chapter 4 Viewing Model Results VORTEX Version 9 User s Manual and cell values of the table you create For example a common table would be to display some Variable such as the mean population size as the cell contents in a grid with a series of Years such as 0 10 20 as the column headings and Populations such as Population1 Population2 and Metapopulation as the row headings See Figure 44 for an example of a table specification similar to this However you could instead want the Years to be arrayed down the side of the table as the rows with the Populations across the top as the columns To do this you would select Populations from the dropdown list for Columns and Years from the dropdown list for Rows You could instead tabulate multiple Variables such as PE N SD N and MedianTE as columns with Populations as rows or Variables as rows with Populations as columns In the specification of the remaining dimension Years you then give from which Year of the simulation you want the value of these Variables displayed Usually but not always you would select the final year Figure 45 shows an example of a table of this type ed Vortex Stochastic Simulation of the Extinction Process File Edt Vortex Window Help Jose sBealS los 4ZPG D WORTEXS ZPG ZPG Ypi Pro
269. normal population behavior Case Study V Estimating age of first breeding in males and females The babirusa Babyrousa babyrussa is one of the more interesting endemic mammals on the Indonesian island of Sulawesi Individuals in captivity can reach sexual maturity as early as 5 months of age However most captive animals approach the age of one year before reaching sexual maturity Even at this age the animals are quite small and it is considered unlikely that they will reproduce until they are older than one year of age Taking into account the gestation length of about 5 months usually 155 158 days it is likely that female babirusa in the wild will have their first litter at the age of 2 years On the other hand males of this age will have to deal with strong competetion for mates among older and stronger males Consequently Manansang et al 1996 developed Vortex models for this species in which the age of first breeding among males was estimated to be delayed until 4 years Maximum Age of Reproduction VORTEX assumes that individuals can breed at a rate typical for that species throughout their adult lifespan If your species does not reproduce throughout its entire adult life do not enter the species maximum life expectancy For example humans typically reach reproductive senescence before they die In this case if the typical life expectancy is 70 years but they cease reproduction at 50 years then enter 50 as the maximum bree
270. ns that each request values for a section of input parameters Scenario Settings Species Description etc Clicking on one of the section labels in the list on the left side of the screen takes you to that section of input Within a section it does not matter what order you enter values and the input sections can be accessed in any order you wish However it makes sense to enter values in the order they appear in the program so that you don t forget to specify some critical value In addition some input sections will use values already entered from prior sections to compute useful values such as the stable age distribution during input Notice that one section label Dispersal Rates is greyed out and disabled That is because the current Scenario has only one population so there can be no dispersal among populations Similarly some other sections and individual input boxes will become disabled if values you have specified would make that section meaningless Take a quick look at the data input boxes on the Scenario Settings screen As you click on any box a message will be displayed at the bottom of your screen with hints about what you need to enter into that box Now click on the Species Description label on the left to take you to that input section Figure 6 Note again that some input boxes are disabled because they pertain only to metapopulation models 4 Vortex Stochastic Simulation of the Extinction Process
271. nt to capture for inclusion in project reports of any sort It is always easy later to edit or delete sections of your Project Report but it may be difficult to later resurrect information that you neglected to send to the report Chapter 4 81 Viewing Model Results VORTEX Version 9 User s Manual The Project Report gives you tools for standard format changes including fonts colors italics bold alignment and bullets You also have the option to Save Open or Print reports VORTEX automatically saves your Report with the Project and re loads it when you open the Project again You only need to explicitly Save a Report if you wish to save it under a new filename When you save a report it is saved in Rich Text Format an rtf file Such files can be imported directly into MS Word and most other word processors where you can use their more powerful editing capabilities to further refine your report Access to Other Stored Output The results made available to you in the Text Output and Tables and Graphs sections of VORTEX are all stored in text files with extensions inp det out dat sum run and rtf placed into your Project directory You can access these files directly if you wish to view the data within other word processing spreadsheet database or graphical software However if you wish to edit these files in any way you should first make a copy of the files and then edit only the copy If you change the files that were
272. o oie eros in the Garamba National Park Congo formerly Zaire the entire range of the only re maining population of the tax on and the number projected dashed line from the 1985 population Error bars show the standard deviation across simulations of the projected population size each year Adapted from Lacy 1996 ECOLOGICAL BULLETINS 48 2000 nize that our assessments may be crude Because all PVA models include only a subset of potentially threatening processes it is possible that many PVAs overestimate via bility Lacy 1993 1994 and that our error will tend to be greatest in the smallest populations i e those which are most critically in need of effective conservation action Ac cordingly margins for error and ongoing monitoring of results should always be part of implementation see also Ak akaya 2000 Although the dynamics of small populations can be complex and subjected to many stochastic processes exist ing PVA models can provide good representations of dy namics of many such populations PVA models have pre dicted well the dynamics of some critically rare species such as the whooping crane Brook et al 1999 and the northern white rhinoceros Ceratotherium simum cottoni see Fig 5 Brook et al 2000 found that PVA models that are sufficiently detailed and for which there are ade quate data for estimating parameters can provide unbiased and reasonably accurate predictions for a number of spe
273. o show minimal susceptibility to environ mental variation Observed variation in the numbers of hatchlings from 1976 to 1991 was approximately that which would be expected due solely to the demographic varjation that would result from a random annual sam pling of breeders from the pool of adult birds each with a constant probability of reproductive success Mirande et al 1991 Variation across years in first year survival was more than three fold greater than what would be expected due to demographic sampling indicating that the proba bility of chick mortality fluctuates across years due to envi ronmental variation Adult mortality however seemed to fall into two classes in some years mortality was signifi cantly greater than mortality in other years and deviated significantly further from the mean than can be expected from random demographic stochasticity The cause of Estimated Number Fig 4 Estimated numbers of palila with 90 confidence in tervals from field surveys Adapted from Ellis et al 1992 1980 ECOLOGICAL BULLETINS 48 2000 9000 8000 7000 6000 5000 4000 3000 2000 1000 0 Whooping Cranes 1938 1995 1950 1960 1970 1980 1990 these years of poor survival is not known as census counts were made only once a year during those years However they would appear to be examples of natural catastrophes If these catastrophe years are excluded from the data as spe cial cases the annual variation in a
274. o specify up to two numbers for use as state variables describing some characteristic of the population These state variables must be numeric values that are entered on the same line as the population label State variables may describe characteristics such as measures of habitat quality or habitat suitability for the population elevation or some other descriptor of the habitat or perhaps an identifying code for the subspecies or local population This option of entering population state variables is provided so that demographic rates such as fecundity mortality and carrying capacity can be specified to be functions of these state variables See Chapter 5 for a description of the use of functions for demographic rates In such functions the state variables are symbolized in order as B and C Symbol A is used for age Functions characterizing the demographic rates for each population could always be entered in earlier versions of VORTEX even without using state variables but the use of state variables can allow for a more consistent representation of demographic rates across populations and easier testing of the effects of varying habitat or population characteristics These capabilities will be explained in much greater detail in Chapter 5 38 Chapter 3 The Data Input Process VORTEX Version 9 User s Manual 4 Vortex Stochastic Simulation of the Extinction Process File Edt Vortex Window Help DSH seal S les
275. odel such as one of the packages in the RAMAS family of software these are produced and distributed by Applied Biomathematics Setauket NY or to use analytical methods e g life table analysis that exclude most or all stochastic factors entirely Box A Is Vortex the Best PVA Model for Your Analysis Different PVA models have different strengths and weaknesses with respect to what kinds of life histories they can model what range of processes can be examined what aspects of population dynamics are modeled well and how easy they are to use for different analyses Below is a list of some considerations for evaluating whether Vortex is more or less appropriate for your analysis While they are certainly not hard and fast rules they should help you make informed decisions about how to best conduct your analysis VoRTEX may be less appropriate or VORTEX is more appropriate may not be needed and may be necessary a YH rrr High fecundity Low fecundity Short lifespan Long lifespan Polyploid Diploid Genetic effects of little interest Changes in genetic variation of interest Local population N gt 500 Local population N lt 500 gt 20 populations modeled lt 20 populations modeled Demographic rates not estimable Age specific fecundity and survival rates estimable only population growth trajectories known Stage or size dependent demography Age dependent fecundity and survival rates Demographic rate fluctuations not estimabl
276. of adult females breeding and survival The fecundity and survival rates for years in which a catastrophe occurs are obtained by multiplying those rates in a normal non catastrophe year by the specified factor These severity factors range from 0 0 to 1 0 Entering 0 0 indicates a total loss of reproduction or survival for the population and 1 0 means that the catastrophe when it occurs will have no effect For example entering 0 75 for the severity factor with respect to reproduction means that if 50 of adult females breed in a normal year then only 50 0 75 37 5 breed in a year with a catastrophe EF Catastrophe severity factors greater than 1 0 can be used in your model This would result in catastrophes having beneficial effects on reproduction and or survival Mate Monopolization You are now asked to specify the male breeding characteristics of your population This information is important for those species that may have an established social structure and consequently exclude some adult males from the pool of available breeders The look of this screen Figure 30 will depend on whether you specified Monogamous or Polygamous breeding back in the Reproductive System section If you previously specified that the breeding system in your population was polygynous you must specify how many of the males are breeders To describe the degree of polygyny you will need to provide an value in one of the following three lines
277. of inbreeding to specify demographic rates see Chapter 5 for more information While inbreeding depression is widely known and has been for centuries understanding the various possible underlying mechanisms the ways of quantifying it and the consequences for population survival and viability is not at all simple Inbreeding depression may result from recessive deleterious alleles which are exposed more frequently in homozygous inbred individuals or from a general disadvantage of homozygotes relative to heterozygotes or from other genetic mechanisms see Charlesworth and Charlesworth 1987 Lacy 1993b In studies of Drosophila flies it has been observed that about half of the effect of inbreeding depression on survival is due to recessive lethal alleles Simmons and Crow 1977 The relationship between survival and inbreeding caused by the presence of recessive lethal alleles is described by an exponential decline S Sge F in which Sg is the survival of non inbred individuals F is the inbreeding coefficient b is the average number of lethal alleles per haploid genome half the number per diploid individual and S is the resultant survival rate Morton et al 1956 Figure B 1 gives the expected relationship between the extent of inbreeding and juvenile survival for a series of hypothetical scenarios differing in the total number of lethal equivalents Even if the overall inbreeding depression is due only partly to recessive lethal al
278. of its binomial distribution as was the number used to specify reproductive rate Otherwise a new random number is drawn to specify the deviation of age and sex specific mortality rates from their means Environmental variation across years in mortality rates is always forced to be correlated among age and sex classes The carrying capacity K for the year is determined by first increasing or decreasing the carrying capacity at year 1 by an amount specified by the user to account for changes over time Appendix I 119 An Overview of Population Viability Analysis Using VORTEX VORTEX Version 9 User s Manual Environmental variation in K is then imposed by drawing a random number from a normal distribution with the specified values for mean and standard deviation 13 Birth rates and survival rates for the year are adjusted to model any catastrophes determined to have occurred in that year 14 Breeding males are selected for the year A male of breeding age is placed into the pool of potential breeders for that year if a random number drawn for that male is less than the proportion of adult males specified to be breeding Breeding males are selected independently each year there is no long term tenure of breeding males and no long term pair bonds 15 For each female of breeding age a mate is drawn at random from the pool of breeding males for that year If the user specifies that the breeding system is monogamous then each male can on
279. of the IUCN SSC Primate Specialist Group and was sponsored by the World Bank The involvement of many agencies and interested parties is critical to endangered species recovery An early requirement or prerequisite of a PHVA workshop is to determine the conservation problem to be addressed and to state the goals of the management plan Many endangered species programs have not clearly identified their goals For example at a PHVA and Conservation Assessment and Management Plan workshop on the forest birds of the Hawaiian islands Ellis et al 1992a 1992b it became apparent that the agencies responsible for the conservation of Hawaii s bird fauna had not determined whether their goal was to prevent species extinctions prevent taxa species or subspecies from becoming extirpated on any of the islands they presently inhabit preserve species in sufficient numbers and distribution to allow them to continue to fill ecological roles in the biological communities or the restoration of taxa to most or all parts of the original ranges The management actions required to achieve these various levels of conservation are quite different In contrast a PHVA on the Grizzly Bear in the Central Rockies of Canada Herrero and Seal 2000 clearly identified that provincial policy called for maintenance of stable or growing populations of the species Thus the criterion against which alternative management scenarios were judged was whether the PVA projections indica
280. of the grid a Males in Breeding Pool b Males Successfully Siring Offspring producing at least one offspring in the average breeding cycle or year c Mean of Mates Successful Sire the mean number of litters sired by successful males in each year Whichever one of the three parameters you specify VORTEX will calculate the other two values based on the assumption that some males are excluded from the breeding pool and breeding success among males in the pool of available breeders is described by a Poisson distribution Only the top number is actually used in the simulation model the other two are provided as alternative ways to enter the degree of polygyny If you earlier specified that the species has a monogamous breeding system you are asked specify only the percentage of the total adult male population that makes up the pool of available breeders and each male can breed with only one female each year Remember that not all males within this pool may breed in a given year depending on the number of adult females that are successful breeders 56 Chapter 3 The Data Input Process VORTEX Version 9 User s Manual 4 Vortex Stochastic Simulation of the Extinction Process File Edt Vortex Window Help JOSH seal SG les gt pages D WORTEXS ZPG ZPG vp Project Settings Simulation Input Text Output Graphs and Tables Project Report Add Scenario Delete Scenario lt zpa2 gt Reorder 2ZPG1 ZPG
281. ological Bulletins AS19120 3 ccdsiscnvicddunnenscndnsinavecatsicidatauadneiuenrnceessta 139 Lacy R C 2000 Considering threats to the viability of small populations using individual based models Ecological Bulletins 48 39 51 csscsssssssesssseesesssees 139 iv Contents VORTEX Version 9 User s Manual Chapter 1 Introduction VORTEX is an individual based simulation model for population viability analysis PVA This program will help you understand the effects of deterministic forces as well as demographic environmental and genetic stochastic or random events on the dynamics of wildlife populations VORTEX models population dynamics as discrete sequential events e g births deaths catastrophes etc that occur according to defined probabilities The probabilities of events are modeled as constants or as random variables that follow specified distributions Since the growth or decline of a simulated population is strongly influenced by these random events separate model iterations or runs using the exact same input parameters will produce different results Consequently the model is repeated many times to reveal the distribution of fates that the population might experience under a given set of input conditions VORTEX simulates a population by stepping through a series of events that describe the typical life cycle of sexually reproducing diploid organisms The program was written originally to model ma
282. on Population 1 Population 2 Copy input values from Females Age 1 Population 1 z Females Age 2 Females Age 3 This Section Females Age 4 to subsequent Females Age 5 populations Females Age 6 Copy Input Values Females Age 7 Vortex 9 21 The stable age distribution is calculated from the mortality schedule Us NUM INS Date Time 10 24 03 10 18AM 4 CAPS Figure 31 Initial Population Size input section Carrying Capacity see Figure 32 Carrying Capacity K The carrying capacity describes the upper limit for the size of your simulated population within a given habitat and must be specified by the user in this next section of input see Box F for a more in depth discussion of this parameter If the population size N exceeds K at the end of a particular time cycle additional mortality is imposed across all age and sex classes in order to reduce the population back to this upper limit The probability of any animal dying during this truncation process is set to N K N so that the expected population size after the additional mortality is K SD in K Due to EV If you think that the habitat carrying capacity varies over time due to environmental variation EV you can enter a standard deviation SD here to account for this variability For example the habitat might support different population sizes in different years due to changing conditions such as rainfall or food resources The standard devia
283. on the order of weeks or months such as mice or shrews for example true calendar years would be an inappropriate time scale to use for modeling population dynamics In this case a year for this type of species may actually represent only one or a few months When calculating your demographic inputs it is vitally important that you make this adjustment consistent throughout your calculations see Case Study I for more information Case Study I Calculating input parameters when the time cycle is less than one year Consider a hypothetical rodent population where the average generation time is 180 days In order to model this population most effectively in VoRTEx the user must adjust the time cycle to account for this shortened generation time In this case we will define a VorTex year as 90 days Consequently events whose occurrences are typically described on an annual or per generation basis must be redefined in terms of the new definition of year For example consider a major catastrophic flood that is thought to occur on average once every 100 years The annual probability of occurrence then is 0 01 Because of the altered definition of year the rodent model must define the probability that this flood will occur in any given 90 day interval The number of 90 day time cycles in a calendar year is T 365 90 4 06 Therefore Pr flood 365 0 010 T 4 06 Pr flood g9 0 0025 The same consi
284. onservation policy With reference to Australia Environmental Management 17 745 758 Lindenmayer D B and R C Lacy 1995a Metapopulation viability of Leadbeater s possum Gymnobelideus leadbeateri in fragmented old growth forests Ecological Applications 5 164 182 Lindenmayer D B and R C Lacy 1995b Metapopulation viability of arboreal marsupials in fragmented old growth forests comparison among species Ecological Applications 5 183 199 Lindenmayer D B and R C Lacy 1995c A simulation study of the impacts of population subdivision on the mountain brushtail possum Trichosurus caninus Ogilby Phalangeridae Marsupialia in south eastern Australia I Demographic stability and population persistence Biological Conservation 73 119 129 Lindenmayer D B and R C Lacy 2002 Small mammals habitat patches and PVA models A field test of model predictive ability Biological Conservation 103 3 247 265 Lindenmayer D B R C Lacy and M L Pope 2000 Testing a simulation model for population viability analysis Ecological Applications 10 580 597 Appendix III 133 VorTEX Bibliography VORTEX Version 9 User s Manual Lindenmayer D B R C Lacy V C Thomas and T W Clark 1993 Predictions of the impacts of changes in population size and environmental variability on Leadbeater s Possum Gymnobelideus leadbeateri McCoy Marsupialia Petauridae using Population Viability Analysis An application of the computer program VORTE
285. oriinae Conservancy Apenheul Zoo Arbeitskreis Natur u Artenschutz in den Bighorn Institute Brandywine Zoo Darmstadt Zoo Elaine Douglas Folsom Children s Zoo Jardin aux Oiseaux Jean P LeDanff Kew Royal Botanic Gardens Lisbon Zoo Miller Park Zoo National Birds of Prey Centre Nigel Hewston Steven J Olson Palm Beach Zoo at Dreher Park Parc Zoologique de Thoiry Prudence P Perry Safari Parc de Peaugres Teruko Shimizu Steinhart Aquarium Tautphaus Park Zoo Touro Parc France Supporters 15 Oglebay s Good Children s Zoo Judy Steenberg Thank You August 2003 VORTEX Version 9 User s Manual Contents Chapter 1 Introduction s sssssssss12 0 5 1 What s New in VORTEX Version 9 sssssssnsnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnna 1 How to Use This Manual ssssssssssnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn nnna 2 A Note about Regional Windows Settings sssssssunnnnnnnnnnnnnnnnnnnnnnnnnnnnnn 3 VORTEX Technical SUppOrt s ssssssssnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn na 3 Chapter 2 Getting Started with VorteX 1ccsescscssesnseeesenseeesenseeeees 5 System Requirements sssssssnnsnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn nnna 5 Installation sassssssnonnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn nnna 5 R nning VORTEX swisiiicecscsnsedisvecuswsuunbenschwasice deandcdentecswestienadunvteniindde
286. ortEV into the compo nent that is common to all populations GlobalMontEV and the component that is specific to each population LocalMortEV END age LOOP END sex LOOP 194 Set GlobalKEV p KEV p EVConcordanceAmongPopulations Set LocalKEV p SQRT KEV p 2 GlobalKEV p 2 I Partition EV in carrying capacity KEV into the com ponent that is common to all populations GlobalKEV and the component that is specific to each population LocalKEV END population LOOP FOR each iteration FOR each population Create initial individuals assigning population sex age alive dead status inbreeding coefficient and kinships initially 0 and alleles at six loci FOR each of five non neutral loci FOR each founder allele a I The probability that a given founder allele is a lethal is NumberLethals 10 because there are 10 alleles across the five diploid loci IF RAND lt NumberLethals 10 Set Lethalfl a TRUE Allele a of locus 4 is a recessive lethal ELSE Set Lethalfl a FALSE END IF ELSE END founder allele LOOP END locus LOOP Display initial population sizes on screen and write to output files END population LOOP FOR each year IF NumberPopulations gt 1 GLOBAL_EV_RANDS I Generate random numbers for specifying environmen tal variation concordant across populations for the year END NumberPopulations IF FOR each population p LOCAL_EV_RANDS CATAS
287. ou access to tools to customize your graph The Data Specification area can be confusing but it gives you considerable flexibility in what you put into your tables and graphs To understand how the Data Specification works you should first realize that the results from your analyses can be considered to be a series of data points in a three dimensional space ed Vortex Stochastic Simulation of the Extinction Process File Edt Vortex Window Help Dentre f EZPG D AWWORTEXS ZPG ZPG Ypi Project Settings Simulation Input Text Output Graphs and Tables Project Report Data Specification Data Graphs Columns years Year 0 Year 5 Year 10 Year 15 Year 20 Rows Populations u 1a Population 1 10 00 2 43 4 48 3 05 13 60 Boat M Year 0 Year 5 Year 10 Year 15 Year 20 Population 1 10 00 2 48 4 39 9 40 14 84 want the Mean z of Population 2 10 00 2 74 4 47 9 63 14 39 5 Metapopulatior 20 00 5 22 8 86 19 03 29 23 variable N all Print Table Sendto Report Export Table Scenar Columns M 2PG1 0 5 10 15 20 J ZPG2 0 5 10 15 20 N A Z N A Z Vortex 9 21 CAPS NUM INS Date Time 10 24 03 1 29PM 4 Figure 44 Data Specification and Table screen of the Graphs and Tables for output The three dimensions of the data are Years the year of the simulation at which the data point was taken Populations Scenarios which Population from which Scenario is bei
288. ou save as a file name other than what you originally specified for the Project VORTEX will prompt you to find out if you wish to change the Project name to match the file name It makes sense to keep the file name and the project name the same although you do not have to do so To run your simulation click on the Run icon the green triangle on the toolbar or select Run Simulation from the VORTEX menu The Run Simulation box Figure 35 will then appear Check the boxes to indicate which scenario s you wish to run and then hit the Run command Run Simulation Select the scenarios that you want to be included in the simulation run Scenarios Select All unl Cancel Figure 35 Run Simulation selection window During the simulation a graph of the changing population size will be displayed Figure 36 If the simulation runs slowly as it will if you have a very large population size you can hit buttons to Stop Pause or Clear Lines Stopping will terminate the simulation without completing all of the iterations Pausing will temporarily stop the simulation as you might want to do while describing the model to others and then will Resume when you hit that button which appears after you hit Pause Clear Lines just gives you a way to erase all prior lines if the screen is getting cluttered and unreadable VORTEX uses a very fast method to write all of the lines to the screen If they are slow that is because the simulation i
289. own in Fig 2 for monoga mous species that would be expected due to sex ratio fluc tuations Many population models ignore sex ratio and breeding system entirely projecting numbers of females l Effect of random fluctuations in sex ratio on reproduction in monogamous species 1 0 1 0 E Q os 0 9 o F ke 2 5 08 08 o g T 5 o7 07 F 0 6 06 0 5 0 5 0 100 200 300 400 500 Size of breeding population Fig 2 Mean proportion of monogamous pairs that could be formed relative to the case of a constant 50 50 sex ratio as a con sequence of random fluctuations in the sex ratio in breeding pop ulations of varying size under the assumption that there are always males available for mating Individual based models are well suited for cas es in which sex ratio biases can disrupt breeding because they automatically generate stochastic variation in the sex ratio Rules defining the breeding system can then be built into the model Thus if there is not promiscuous breeding random fluctuations in the sex ratio can depress population growth in even moderate sized populations Similarly random de mographic stochasticity in the numbers of births and deaths per year can depress mean population growth be cause of variation in the age distribution and other disrup tions of optimal breeding For example managers of zoo populations are often distressed to find that reproduction is kept well below optimal levels because of tempora
290. p SSC IUCN Allendorf F and N Ryman 2002 The role of genetics in population viability analysis Pages 50 85 in Beissinger S R and D R McCullough eds Population Viability Analysis Chicago IL University of Chicago Press Araya B D Garland G Espinoza A Sanhuesa A Simeone A Teare C Zavalaga R Lacy and S Ellis eds 2000 Population and Habitat Viability Assessment for the Humboldt Penguin Spheniscus humboldti Final Report Apple Valley MN Conservation Breeding Specialist Group SSCAUCN Armbruster P P Fernando and R Lande 1999 Time frames for population viability analysis of species with long generations An example with Asian elephants Animal Conservation 2 1 69 73 Armstrong D P and J G Ewen 2002 Dynamics and viability of a New Zealand robin population reintroduced to regenerating fragmented habitat Conservation Biology 16 4 1074 1085 Armstrong D P Perrott J K and Castro I 1997 The effect of food supply on the viability of hihi populations An experimental study on Mokoia Report to WWF NZ Wellington New Zealand 130pp Arteaga A I Canizales G Hernandez M Cruz Lamas A De Luca M Mufioz A Ochoa A Seijas J Thorbjarnarson A Velasco S Ellis and U Seal eds 1997 Taller de An lisis de la Viabilidad Poblacional y del Habitat del Caiman del Orinoco Crocodylus intermedius Apple Valley MN Conservation Breeding Specialist Group SSC IUCN Ashraf N V K
291. performing the analyses that are in tended and so that PVA practitioners in general can see an example of the structure of an individual based PVA mod el The VORTEX program is available at http www2 netcom com rlacy vortex html The pseudo code presented below is an English language outline of the program flow and primary algo rithms used by VORTEX which is written in the C pro gramming language This pseudo code omits coding for 1 input routines for reading parameters from files and or keyboard 2 output routines for writing results to files 3 specification of default parameter values 4 checks for ille gal values error handling 5 memory management and initialization of memory 6 details of C coding to achieve algorithms 7 routines for on line help 8 routines for graphical display of functions specifying demographic rates population sizes during simulations simulation re 192 sults 9 routines for evaluating equations that specify de mographic rates e g breeding mortality as functions of population and individual variables e g population size gene diversity year age sex inbreeding see note 3 be low 10 tallies of mean within population statistics and metapopulation summaries 11 algorithms for calculating basic statistics such as means standard deviations stand ard errors and medians across years and across iterations Variables for storing input intermediate calculations and output
292. populations regardless of the stability of the environment As a binomial sampling proc ess it is highly dependent on the population size Environ mental variation results from variation in habitat quality over time and is unrelated to population density The var iance in demographic rates caused by environmental varia tion would be additive with variation due to demographic stochasticity Goodman 1987 Environmental variation is not usually affected by the local size of the wildlife population except in those cases such as predator prey interactions in which the organisms have large effects on their local environment However the threat to population viability caused by a given level of en vironmental variation would be more severe in smaller populations because smaller populations are closer to ex tinction Moreover the amount of environmental varia tion would be highly dependent on the total area of habitat occupied by a population Many environmental stresses are localized so a population exploiting a large area would benefit from the averaging of any environmental fluctua tions that are not synchronous over the entire range Indi viduals might use spatial variation in environmental condi tions to allow escape from temporal variation in the envi ronment Kindvall 1996 Even if individuals do not move away from areas with temporarily poor conditions tempo rary population declines in some areas would be offset by growth el
293. printed as appendices to this manual What s New in VoRTEX Version 9 The biggest change from prior versions of VORTEX is that the program is now a Windows application Although the user interface is now totally new experienced VORTEX users will quickly recognize that the content of the program the input variables the information output etc is still very much like that of the old MS DOS versions of VORTEX In fact unless you invoke one of the few new features of the overall model results generated by the Windows version should match except for stochastic uncertainty the results produced by the earlier DOS versions Chapter 1 1 Introduction VORTEX Version 9 User s Manual You cannot directly import input files from prior DOS versions of VORTEX into version 9 However for an experienced VORTEX user it usually takes only a few minutes to re enter the input values from a prior analysis Attempts will be made to make future updated versions of VORTEX capable of importing projects from all previous Windows versions of the program version 9 0 and higher The user interface for entering input values running simulations seeing tabular and graphical representations of output and obtaining help are clearly very different in the Windows VORTEX than in the earlier DOS versions The easiest way to get a feel for these differences is to open the program and explore it A Quick Tour of the new program is provided in Chapter 2 and ne
294. pulation variability and instability is being ignored in your analysis Another difficulty with these approaches which may add a significant bias if sample sizes are small is that some of the year to year variation observed in reproductive and mortality rates is actually due to the expected demographic stochasticity resulting from random sampling of individuals even if environmental factors do not cause fluctuations in the annual probabilities of birth and death Refer to Box D for methods of removing this source of variation as a means of estimating EV alone In order of ease of use easiest to most difficult and precision least precise to most precise your options for estimating environmental variation EV in population demographic rates are EF guess at the typical fluctuations in your species reproduction and mortality rates calculate the variation across years in these rates from long term field data adjust the observed variation by subtracting the variance due to demographic stochasticity random sampling even if the probabilities of birth and death remain constant through time Use Normal distribution approximation Specify exact distribution Previously you defined the maximum number of offspring produced annually per female you are must now specify the percentage of litters clutches broods produced by the breeding adult females that are of a given size You have two options for specifying the distribution of numbers of pro
295. r programs The deterministic calculations are performed by VORTEX as soon as you enter the input values for your model Therefore you can view these results and also the Input Summary text even before you run your simulations It is often helpful and always recommended to look at the deterministic projections before proceeding with stochastic simulations so that you will know whether the rates of reproduction and survival are at least minimally adequate to allow for population growth in the absence of random fluctations and other destabilizing processes such as inbreeding and harvest Chapter 4 71 Viewing Model Results VORTEX Version 9 User s Manual Box G Deterministic Calculations in VORTEX Before the actual stochastic simulation begins VorTex performs a standard life table analysis to calculate the deterministic mean population growth rate r the exponential growth rate or 4 lambda the annual multiplicative growth rate the mean generation time for males and females and the stable age distribution used optionally to initialize the starting population These calculations will provide accurate long term averages if stochastic variation due to demographic stochasticity environmental variation catastrophes and inbreeding effects is minimal Life table analyses implicitly assume that age specific birth and death rates are constant through time they yield over estimates of long term population growth if there is any
296. rSize n 1 Set LitterSize n BREAK from Litter Size LOOP END IF END LOOP ELSE I MaximumLitterSize 0 is a code for using normal distri bution of litter sizes Set LitterSize MeanLitterSize p SDLitterSize p NRAND Set LitterSize max 0 LitterSize Set LitterSize min 2 MeanLitterSize p LitterSize Truncates symmetrically to avoid creating bias Set IntegerLitter Largest integer less than LitterSize Set Remainder LitterSize IntegerLitter IF RAND lt Remainder Round off litter size probabilistically Set LitterSize IntegerLitter 1 ELSE Set LitterSize IntegerLitter END IF ELSE END IF ELSE Create the offspring Set Inbreeding Kinship between Sire and Dam FOR Offspring from 1 to LitterSize Assign ID age 0 population alive TRUE FOR each of six loci First locus is neutral others can have lethals Pick at random an allele from Dam Pick at random an allele from Sire END LOOP IF not hermaphroditic AND RAND lt SexRatio Assign sex as male ELSE Assign sex as female ECOLOGICAL BULLETINS 48 2000 END IF ELSE Does offspring live Offspring mortality is placed here in the code rather than in the MORTALITY function for better speed and lower memory requirements FOR each non neutral locus IF homozygous AND allele is a lethal Offspring dies END IF END LOOP IF not yet dead GETDEATHRATE Set SurvivalRate 1 DeathRa
297. ram just click on the Close button marked by an x in the top right corner of the program window before closing the program will always prompt you to determine if you wish to save any open projects Size Limitations on VorTEX Analyses VORTEX allocates computer memory as it needs it depending on the characteristics of the population or metapopulation you are modeling VORTEX will make optimal use of all available memory to carry out the simulations but the available RAM on your computer may limit the size of analysis you can complete However there are also some absolute limits to how large or complex a simulation can be These limits are listed below gt Number of iterations 10000 gt Duration of simulation 2000 years gt Number of populations 50 gt Types of catastrophes 25 gt Maximum age 250 years gt Maximum litter size 50 gt Initial population size 30000 individuals gt Carrying capacity 60000 individuals Only if specifying an exact distribution see page 44 for an alternative method to increase maximum litter size Some combinations of parameters can require large amounts of memory For example if you are including inbreeding depression in your simulation and have chosen to model it as only partially due to the presence of lethal alleles more than 50 megabytes of memory may be required to analyze a population that reaches 5000 living animals In these cases it is possible that VORTEX will abort an analysis if
298. rd errors of the mean are reported for population size and the measures of genetic variation Under the assumption that extinction of independently replicated populations is a binomial process the standard error of the probability of extinction is reported by VORTEX as in which the frequency of extinction was p over n simulated populations Demographic and genetic statistics are calculated and reported for each subpopulation and for the metapopulation Sequence of program flow 1 The seed for the random number generator is initialized with the number of seconds elapsed since the beginning of the 20 century 2 The user is prompted for an output file name duration of the simulation number of iterations the size below which a population is considered extinct and a large number of population parameters 3 The maximum allowable population size necessary for preventing memory overflow is calculated as Kmax K 3s 1 L in which K is the maximum carrying capacity carrying capacity can be specified to change during a simulation so the maximum carrying capacity can be greater than the initial carrying capacity s is the annual environmental variation in the carrying capacity expressed as a standard deviation and L is the specified maximum litter size 4 Memory is allocated for data arrays If insufficient memory is available for data arrays then Nmax iS adjusted downward to the size that can be accommodated within the available m
299. re severe in a stressful environment Zoo Biol 13 195 208 Mills L S and Smouse P E 1994 Demographic consequences of inbreeding in remnant populations Am Nat 114 412 431 Mills L S et al 1996 Factors leading to different viability pre dictions for a grizzly bear data set Conserv Biol 10 863 873 Mirande C Lacy R and Seal U 1991 Whooping crane Grus americana conservation viability assessment workshop re port IUCN SSC Captive Breeding Specialist Group Ap ple Valley Minnesota Pettersson B 1985 Extinction of an isolated population of the middle spotted woodpecker Dendrocopos medius L in Swe den and its relation to general theories on extinction Biol Conserv 32 335 353 Piattelli Palmarini M 1994 Inevitable illusions How mistakes of reason rule our minds Wiley Pounds J A and Crump M L 1994 Amphibian declines and climate disturbance the case of the golden toad and the har lequin frog Conserv Biol 8 72 85 Rabenold K N 1990 Campylorhynchus wrens the ecology of delayed dispersal and cooperation in the Venezuelan savan na In Stacey P B and Koenig W D eds Cooperative breeding in birds Cambridge Univ Press pp 159 196 Rabenold P P et al 1991 Density dependent dispersal in social wrens genetic analysis using novel matriline markers Anim Behav 42 144 146 Ralls K Ballou J D and Templeton A 1988 Estimates of l
300. recessive lethal alleles vs other genetic effects such as overdominance Recessive lethal alleles are modeled such that the death of animals homozygous for lethal alleles will reduce the frequency of the lethals and thereby reduce the average effects of future inbreeding The proportion of inbreeding depression not due to lethal alleles is modeled as an impact on fitness that follows a negative exponential equation Morton et al 1956 and is not reduced during generations of inbreeding Note 3 For rates which can be specified as functions of age sex inbreeding population size gene diversity year and population the rate to be used is determined by evalu ating the function specified by the user If the user enters a fixed constant for the rate as is usually the case then the function simply returns that constant However the user can specify a mathematical formula that defines a demo graphic rate as being density dependent or a function of other population parameters For example fecundity could be specified to decline in older age classes adult mortality could be specified to increase with inbreeding or habitat carrying capacity could be specified to decrease over time The algorithms for parsing and evaluating user defined rate functions e g the first step of functions GETBREEDRATE and GETDEATHRATE are not given in the pseudo code Note 4 The proportion of males in the breeding pool can be entered directly
301. refined analyses could be conducted With the PVA model projections of the most likely fate and distribution of possible fates of the population under the specified assumptions are made Because so much of a PVA the data the model and even the interpretation of output is uncertain a PVA that provides an estimate of the probability of extinction under a single scenario is of very limited usefulness An essential component of the PHVA process therefore is sensitivity testing Ranges of plausible values for uncertain parameters should be tested to determine what effects those uncertainties might have on the results In addition several different PVA models might be examined at a PHVA workshop or the same general model tested under different structural assumptions Different participants in the process should assess and interpret the results Such sensitivity testing reveals which components of the data model and interpretation have the largest impact on the population projections This will indicate which aspects of the biology of the population and its situation contribute most to its vulnerability and therefore which aspects might be most effectively targeted for management In addition uncertain parameters that have a strong impact on results are those which might be the focus of future research efforts to better specify the dynamics of the population Close monitoring of such parameters might also be important for testing the assumpt
302. rentheses to produce the order of operations that you desired After you have confirmed that you have the function that you want you can cut and paste it into an input box or if you triggered the Function Editor by typing an into an input box just hit OK to transfer your function over to the input box you had left Chapter 5 85 Using Functions in VORTEX VORTEX Version 9 User s Manual Table 1 Valid Function Variables Population descriptors Population size Carrying capacity Year Population identifier Run simulation iteration Number of adult males in the population Number adult females Number of juveniles age 0 1 Number of subadults age gt 1 lt breeding age Number of females all ages Number of males all ages Percentage of initial gene diversity expected heterozygosity remaining in the population and C population state variables entered with population labels Dispersal rate from the matrix entered used only in functions modifying dispersal N K Y P R M F J U X w G B D BB p CC p etc the parameter above B C etc for population p Individual descriptors Age Individual ID an arbitrary integer assigned to each individual Sex 0 or F for female 1 or M for male Inbreeding coefficient must be expressed as a percentage Number of mates 0 or 1 for females and monogamous males possibly more for polygamous males Paternal allele identifier
303. requencies of all founder alleles in each population averaged across all iterations can be outputed to a file if that option is selected within Special Options of Project Settings The allele frequencies are placed into a file with extension gen Examples of Rate Functions The easiest way to demonstrate the formats in which functions can be entered into VORTEX is with a series of examples The examples shown below include a plot of the function where appropriate as well as the actual expression 1 Continuous linear decline over time RATE 50 O 2 Y This function specifies a starting rate 50 0 perhaps for adult female breeding success or 45 0 for carrying capacity equal to 50 in year 0 g 40 07 with a decline of 0 2 per year resulting in a e 35 0 rate equal to 30 after 100 years fey S00 Q 25 0 3 20 0 asol a 10 0 f 5 0 0 0 10 20 30 40 50 60 70 80 90 100 Year of Simulation 90 Chapter 5 Using Functions in VORTEX 2 Linear decline limited to a period of years RATE 50 0 2 MIN Y 1 50 In this case the decline occurs only through the first 50 years of the simulation Note that the decline is specified to start in year 2 so that year 1 still has a rate of 50 This is the form of the function used by VORTEX if the user specifies a linear trend in carrying capacity 3 Linear decrease during intervals of years RATE The rate starts at 45 in year 1 declines to 25 by year 5 and a
304. ression Lethal Equivalents Bi ortality Rates Percent Due to Recessive Lethals 50 ZEE V EV Concordance of Reproduction amp Survival ate Honopolization nitial Population Size EY Correlation Among Populations fi 5 anying Capacity Number of Types of Catastrophes R T ra sic a a4 GIG ESE z z e ES Ts amp ls 3 upplementation Copy input values from Population 1 This Section to subsequert populations Copy Input valles Don t forget to enter your notes about input values here Vortex 9 21 Check this if you want to model inbreeding depression as an increase in 1st year mortality A CAPS NUM INS Date Time 10 24 03 3 34AM Figure 20 Species Description section of Input Inbreeding depression Check this box if you want to include inbreeding depression in your model as a reduction in first year survival among inbred individuals See Box B for more information Although most diploid species that have been studied show depressed fitness when inbred you may sometimes want to leave inbreeding depression out of your model so that you can compare results with and without inbreeding depression thereby allowing you to document what impacts inbreeding depression could have on population viability 28 Chapter 3 The Data Input Process VORTEX Version 9 User s Manual Box B Quantification of Inbreeding Depression Inbreeding depression is the reduction in fitness commonly observed when individua
305. rios that systematically vary in one or more parameters The new Scenarios you create will initially be named as Scenariol Copy 1 Scenariol Copy 2 etc in which Scenario1 is the name of whatever Scenario you chose to use as the template After you create new Scenarios you can toggle among the Scenarios in any of three ways 1 you can use the drop down list to select the Scenario you wish to work on 2 you can click on the small lt and gt buttons alongside the dropdown list to move backwards and forwards through the list of Scenarios and 3 you can click on the buttons to the right with the Scenario names See Figure 38 4 Vortex Stochastic Simulation of the Extinction Process File Edt Vortex Window Help OSH amp B Be SB lls gt EJZPG D AWORTEXS ZPG ZPG Ypi Project Settings Simulation Input Text Output Graphs and Tables Project Report Add Scenario Delete Scenario lt zp Copy 1 gt Reorder ZPG1 ZPG2 ZPG1 Copy 1 cenario Settings pecies Description abelis and State Vars Reproductive System Scenario Name ZPG1 Copy 1 Reproductive Rates ortality Rates Number of Iterations fi oo atastrophes Number of Years ate Monopolization as in 100 initial Population Size Extinction Definition Only 1 Sex Remains g Capacity Total N lt Critical Size Number of Populations fi Scenarto Settings uppiementation Copy input values from
306. rms of population growth probability of persistence number of extant populations genetic diversity or other measures of population performance must be defined by the management authorities before the results of population modeling can be used Because the models incorporate many factors the number of possibilities to test can seem endless and it can be difficult to determine which of the factors that were analyzed are most important to the population dynamics PVA models are necessarily incomplete We can model only those factors which we understand and for which we can specify the parameters Therefore it is important to realize that the models probably underestimate the threats facing the population Finally the models are used to predict the long term effects of the processes presently acting on the population Many aspects of the situation could change radically within the time span that is modeled Therefore it is important to reassess the data and model results periodically with changes made to the conservation programs as needed Dealing with uncertainty It is important to recognize that uncertainty regarding the biological parameters of a population and its consequent fate occurs at several levels and for independent reasons Uncertainty can occur because the parameters have never been measured on the population Uncertainty can occur because limited field data have yielded estimates with potentially large sampling error Uncertainty can o
307. rom sto chastic or random processes In any sampling process the predictability of an outcome decreases as the sample size is reduced Many aspects of population dynamics are inher 39 ently sampling processes rather than completely deter mined events including mate acquisition breeding suc cess sex determination transmission of genetic alleles sur vival and dispersal The uncertainty in such processes can lead to instability in population dynamics Moreover fluc tuations in demographic and genetic processes cause de pression in long term rates because the geometric means and other appropriate compound measures of population performance are less than the arithmetic means Finally reductions in growth rates and fluctuations in rates can in teract synergistically causing increasing instability and more rapid decline until the ultimate stability is reached when the population becomes extinct These processes were termed extinction vortices by Gilpin and Soul 1986 and their examination constitutes the core of most population viability analyses PVA Soul 1987 Boyce 1992 Lacy 1993 1994 Caughley 1994 argued that there is a dichotomy in conservation biology between those who follow a declin ing population paradigm examining deterministic causes of population decline and those who follow a small pop ulation paradigm examining the processes that further imperil populations after they have become
308. ronto Zoo Conservators 15 000 19 999 Columbus Zoological Gardens Saint Louis Zoo Walt Disney s Animal Kingdom Wildlife Conservation Society NYZS World Association of Zoos amp Aquariums WAZA Zoological Society of London Guardians 7 000 14 999 Cleveland Zoological Society Nan Schaffer Toledo Zoological Society White Oak Conservation Center Zoological Society of San Diego Protectors 1 000 6 999 African Safari Wildlife Park Albuquerque Biological Park Allwetter Zoo Munster ARAZPA Audubon Zoological Gardens Bristol Zoo Caldwell Zoo Calgary Zoo Chester Zoo Cincinnati Zoo Colchester Zoo Copenhagen Zoo Denver Zoological Gardens Detroit Zoological Park Durrell Wildlife Conservation Trust Everland Zoo Federation of Zoological Gardens of Great Britain amp Ireland Fort Wayne Zoological Society Fort Worth Zoo Fossil Rim Wildlife Center Gladys Porter Zoo Great Plains Zoo Greater Los Angeles Zoo Association Japanese Association of Zoological Parks amp Aquariums JAZGA Robert Lacy Leisure amp Cultural Services Department of Hong Kong Lincoln Park Zoo Living Desert Loro Parque Marwell Zoological Park Memphis Zoo Milwaukee County Zoo North Carolina Zoological Park Oklahoma City Zoo Paignton Zool amp Botanical Gardens Parco Natura Viva Garda Zool Park Philadelphia Zoological Garden Phoenix Zoo Pittsburgh Zoo Rotterdam Zoo Royal Zoological Society of
309. ropriate Figure 46 Specify Years E T Ordering saan 9 i 2 3 2 5 E 32 Order Selections a you would 4M a EEGA TE Year 0 like touse 19 v Year 5 in your sah va _ 30 v v Year 20 40 v v Year 25 50 lv v Year 30 Select All anl 5 5 Year 35 Unselect All 5 Year 40 _ 0 Year 45 z 80 v v 90 g a 7 a pa r Sort Ascending Sort Descending Ok Cancel Figure 46 Year Specification window for creating tables and graphs Specification of the Years in this window can be confusing but it is also very fast once you learn how to use it You can quickly Select All years by clicking on the command if you want every year shown in your table and graph You can also Deselect All if you want to remove a prior selection To specify that only some years should be selected you can check on those years in the grid The boxes in the grid are arrayed across rows for each decade That is the check boxes in the first row of the grid are years 0 1 2 9 the check boxes in the second row of the grid are years 10 11 12 19 etc If you want to select all of the years in one column such as years 0 10 20 you can click on the column heading Similarly to select all of the years in one decade e g 20 21 22 29 you can click on the row label Th
310. rs the mortality rate will be set at 100 and the population will EF immediately go extinct For example if all age specific mortality rates are 50 and the standard deviations are set at 25 then in about 1 in 40 years the mortality rate after adjustment for EV will be 100 since the rate will exceed the mean by 2 standard deviations about 2 5 of the time A substantial literature exists on the many methods by which one can estimate age sex specific mortality rates in wild populations Caughley 1977 is a good text from which to start an exploration of this body of information Case Study IX Estimating mortality rates from sightings of banded Whooping Cranes As of 1991 the last remaining population of the whooping crane Grus americana could be tracked and censused from its breeding grounds in Wood Buffalo National Park Alberta Canada to its wintering grounds along the Texas Gulf Coast at Aransas National Wildlife Refuge During a Conservation Viability Assessment for this population Mirande et al 1991 estimated mortality rates for the population based on recorded sightings of banded birds From 1976 through 1989 about 234 5 cranes were observed to hatch at Wood Buffalo NP taking the midpoint of the possible range in those few years in which counts were imprecise of which 172 arrived in Aransas the following winter This yields an estimated juvenile survival rate of 73 3 During the 14 years of close monitoring of the Wood Buffalo
311. ry im balances in the sex ratio or the age distribution Following the advice of conservation biologists zoo managers have assumed that a population of 50 or more is safe from the threat of demographic stochasticity but random fluctua tions are causing problems for maintaining stable popula tions of rhinoceroses spectacled bears lions and other species for which there is limited flexibility to accommo date changes in numbers Environmental variation Environmental variation or stochasticity is the variation in demographic rates or probabilities that results from fluc tuations in the environment Shaffer 1981 Thus local environmental variation causes temporal clustering of births and deaths which would increase uncertainty and variability in population size and thereby make a small population more vulnerable to extinction The kinds of perturbations of the environment which cause variation in birth and death rates include disease sporadic predation 42 irregular food availability and variable weather Natural catastrophes are the extreme of environmental variation in which droughts floods fires disease epidemics and other local disasters can decimate a population Although both demographic stochasticity and environ mental variation cause fluctuations in the number of births and deaths in a population the processes are conceptually distinct and statistically independent Demographic sto chasticity is intrinsic to all
312. s Inbreeding depression the reduction in fitness of in bred individuals frequently occurs when normally out crossing organisms mate with close relatives It is common ly believed that it is a problem only for captive populations which can be substantially buffered from many other risks facing small populations and for a very few and very small natural populations or perhaps only as a transient prob lem that would diminish as selection removes deleterious alleles during repeated generations of inbreeding Yet in creasing numbers of studies are showing that inbreeding depression can impact population viability to a greater ex tent more quickly and less reversibly than previously sup posed Frankham 1995b Lacy 1997 Jim nez et al ECOLOGICAL BULLETINS 48 2000 1994 found that inbreeding caused much lower survival of white footed mice Peromyscus leucopus that had been re leased into a natural habitat than would have been predict ed from laboratory measures of inbreeding depression A population of the greater prairie chicken Tympanuchus cu pido pinnatus which had suffered a demographic decline from ca 25 000 birds to lt 50 birds over 60 yr consequently lost substantial genetic variability and suffered reduced fer tility and egg viability from inbreeding depression Weste meier et al 1998 In Sweden inbreeding depression of fertility may have been the cause of the rapid decline to extinction of a population of 15
313. s Read in First YearSupplementation p Last YearSupplementation p SupplementationInterval p FOR each age x up to FemaleBreedingAge Read in NumberFemales ToBeSupplemented p x END LOOP FOR each age x up to MaleBreedingAge Read in NumberMatles ToBeSupplemented p x END LOOP END IF END FUNCTION READ_POPULATION_PARAMETERS BEGIN FUNCTION CALC_DETERMINISTIC_GROWTH for popula tion p Use standard life table analysis solve the Euler equation to find the deterministic growth rate Set fecundity M MeanLitterSize p 1 SexRatio I SexRatio is proportion males at birth FOR each type of catastrophe c I Adjust M for catastrophes Multiply M by CatastropheFrequency p c CatastropheBreedSeverity p c 1 CatastopheFrequency p c END catastrophe LOOP FOR each age x Set female survival P x 1 FemaleMortality p x FOR each type of catastrophe I Adjust P x for catastrophes Multiply P x by CatastropheFrequency p c CatastropheSurvivalSeverity p c 1 CatastopheFrequency p c END catastrophe LOOP Multiply cumulative survivorship L x by P x IF x gt FemaleBreedingAge Add L x M to SumLxMx Add x Lix M to SumAgeLxMx END IF END age LOOP Set RO SumLxMx Set Generation Time p SumAgeLxMx SumLxMx Preliminary estimate Set Lambda RO 1 Generation Time Preliminary estimate Solve Euler equation by iterative approximatio
314. s In addition the expected mortality changes from year to year due to environmental variation with each annual curve again reflecting the sampling variance demographic stochasticity expected for that year s value Note that these curves become tighter the standard deviation resulting from demographic stochasticity decreases as the means deviate from near 50 In addition notice that the mortality rate in year 7 is particularly high perhaps a catastrophic event occurred in that year to produce such high mortality With annual rate data in hand we can actually calculate the relative contributions that demographic stochasticity DS and environmental variability EV make to the total observed variance Consider the example presented in Figure D 1 The mean mortality rate calculated from these annual data is 0 387 with a standard deviation combining effects of DS and EV of 0 148 Note however that the catastrophe shown as the outlier in the dataset was not included in this calculation if it were the mean and standard deviation would change to 0 435 and 0 204 respectively If we consider the data with the outlier absent we can calculate the standard deviation due to EV es ee CEV yPEV yO ToT IDs where Eror is the total variance across the data and he is the mean sampling binomial variance across the individual rates see Box B for how to calculate a binomial variance In the example above the mean binomial variance turns out to
315. s of parts of an overall system For example an epidemiological modeling program OUTBREAK can model the dynamics of an infectious disease in the population VORTEX and OUTBREAK can be run at the same time on the same simulated population with VORTEX simulating demographic and genetic changes and constantly informing OUTBREAK of the current census of the population while OUTBREAK models the changes of disease state susceptible latent infected infectious recovered and constantly informs VORTEX which individuals are in each state The disease states can then be used to modify reproduction survival dispersal or other demographic rates for individuals in the meta model More information about OUTBREAK will be made available at http www vortex9 org outbreak html At this time OUTBREAK is the only other model that is provided for linking with Vortex In the future we plan to provide also built in links to GIS models of landscape change models of animal movements on the landscape and perhaps other models However VORTEX already provides the capability for a user to Chapter 3 39 The Data Input Process VORTEX Version 9 User s Manual create or otherwise obtain his or her own model and link it to VORTEX as a dynamic multi component meta model This capability of VORTEX to link with other models is still being developed and tested Full explanation of the proper use of meta models is beyond the scope of this manual and users are stron
316. s between the model and reality will not cause substantial differences in long term population dynamics and risk EF Although definitive confirmation of this assumption may require testing a more complex and complete model to see if the refinements do matter In many cases VORTEX does provide the capability to create models that are more complex sometimes much more complex than the standard VORTEX model These more complex population models are built by using functions rather than constants for input values Using such functions provides considerable flexibility but you should use them cautiously if you are not yet fully familiar with the VORTEX model When you are finished with entering Species Description parameters click on the heading for Labels and State Variables on the left hand list Labels and State Variables In this Input section you can enter optional labels for your populations as well as define parameters that describe characteristics or states of your populations and individuals Population Labels and State Variables VORTEX allows the user to enter a label for each population being modeled Figure 21 The labels can be any text up to 20 characters long These population labels will be used as headers for entry of population specific demographic rates on subsequent data entry screens and as labels in the output files One population label is entered per line When entering a population label the user may als
317. sRSG 1996 Report of a meeting of the IUCN SSC Asian Rhi no Specialist Group AsRSG Sandakan Malaysia 29 Nov 1 Dec 1995 Ballou J D 1997 Ancestral inbreeding only minimally affects inbreeding depression in mammalian populations J He redity 88 169 178 Ballou J D et al 1998 Leontopithecus H The second popula tion and habitat viability assessment for lion tamarins Leon topithecus Conservation Breeding Specialist Group SSC IUCN Apple Valley Minnesota Barrett S C H and Kohn J R 1991 Genetic and evolutionary consequences of small population size in plants implications for conservation In Falk D A and Holsinger K E eds Genetics and conservation of rare plants Oxford Univ Press pp 3 30 Barton N H and Whitlock M C 1997 The evolution of metapopulations In Hanski I A and Gilpin M E eds Metapopulation biology Academic Press pp 183 210 Belovsky G E 1987 Extinction models and mammalian per sistence In Soul M E ed Viable populations for con servation Cambridge Univ Press pp 35 57 Boecklen W J 1986 Optimal reserve design of nature reserves consequences of genetic drift Biol Conserv 38 323 338 Boyce M S 1992 Population viability analysis Annu Rev Ecol Syst 23 481 506 Brewer B A et al 1990 Inbreeding depression in insular and central populations of Peromyscus mice J Heredity 81 257 266 Brook
318. safely stored under names that you specify and will not be overwritten if you run the simulation again Click now on the Graphs and Tables tab Figure 11 The program may display a warning message stating that it could not find the data from one or more Scenarios that have not yet been run That is OK for now as long as you don t need yet to see the results from these other Scenarios The Graphs and Tables section has two subsections Data Specification and Data Graphs Data Specification is where you will identify which results you wish to put into your table and graph fea Vortex Stochastic Simulation of the Extinction Process File Edt Vortex Window Help DEH 42 e SB osi o Se Page D WORTEXS ZPG ZPG Ypi Project Settings Simulation Input Text Output Graphs and Tables l Project Report Data Specification Data Graphs Columns ysars Table 1 Rows Populations I want the Mean z of variable P survive Print Table Sendto Report Export Table Scenar Columns Rows Vortex 9 21 CAPS NUM INS Date Time 10 24 03 9 20AM Figure 11 The Graphs and Tables window Chapter 2 17 Getting Started with VORTEX VORTEX Version 9 User s Manual In the lower left list of Scenarios make sure that ZPG1 is checked and then double click on the box under Columns This will bring up a window that lets you specify which years you want to show as the columns of your table and t
319. scecsu 6 Size Limitations on VORTEX Analyses sssssssnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnna 6 Getting Around in VORTEX ssssssssssssssnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn nn 8 A Quick Tour of VORTEX bicssscsisscdiacatennvessensiaisedinenss deveuswsiinsadduuncunadwdendcedones 9 Chapter 3 Creating a Project Data Input sccscsssseseesseeeeeeaseeeees 21 Creating a Projecto is cctideceecces de cicacnases ceeeedddsceaassacanewswasucasensedaceiesdsdaens 21 Documenting Your Input with Notes sssssssssnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn 25 Creating a Scenario sssssssssnsnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn nnn 26 Scenario Settings savsestes settee eee 26 Species Description ssccssseccsssecssseceseneeeeseeeeeeenseeneseeeeaseeneseeoeaneeneseeaeaneseeneessaeas 28 Contents i VORTEX Version 9 User s Manual Labels and State Variables 0 cees see 38 Dispersal RateS sisdssiectesdicsedecessnccnedcotasadeuasccddcasssaucaescucusaedusssccausenasincsestonns 41 Reproductive Syste ccccsssecssseeeneseessseeeenseeeeceeeeeeeeaseenseeanaseeneneeneaeesoeseeneaeenoas 43 Reproductive Rates icsescccsssecssseesssseeeseesssseeeeseeeseeoeaseenseeeneaeeneaseeneseeaeaeeseneeseas 48 Mortality vannnaneenuseeneaeeennseeneneeeeaneeoeneeanaseeaseeneaeennaseeneaeeonaeesneseeseaeenoas 52 Catastrophes _aeasecenaneeneseeeeeeeneseeaeaeeeeeseeaeaeeeoeseoseeanasesneseeaeaeesseneeaeaeenane 53 Ma
320. scription of the simulated population s behavior it is not excessive to enter 500 or even 1000 iterations in this field Note that commas are not used when specifying larger numbers during the input process even if your computer is set to use American data formats Number of years How far into the future do you wish to project your population The usual answer to this question is 100 to 200 years although a shorter duration can be entered so that you can assess the validity of your input parameters or to examine the short term viability of a population If you simulate your population for just a few decades however you should be aware that processes controlling population dynamics might be leading the population toward extinction but especially for long lived species the final extinction may not occur until a later time By the time that the factors influencing extinction are apparent the process may be so far along as to be almost irreversible One of the major advantages of PVA modeling is that it can reveal the instability of a population long before it would be apparent through field observations 26 Chapter 3 The Data Input Process VORTEX Version 9 User s Manual An important point to keep in mind is that VORTEX does not necessarily require years to be defined as calendar years Rather the program operates more broadly in terms of time cycles If the species you are modeling has a short generation time and life span
321. sed as a variance that is global in scope i e common to all populations 34 Chapter 3 The Data Input Process VORTEX Version 9 User s Manual Box D The Statistics of Demographic Stochasticity and Environmental Variability Now that you have reviewed some of the general definitions of central tendency and variability see Box C as well as some characteristics of the binomial and normal distributions we can discuss the statistical nature of demographic and environmental stochasticity Demographic stochasticity is the random fluctuation in observed birth rate death rate and sex ratio of a population resulting from stochastic sampling processes even if the probabilities of birth and death remain constant over time In such cases the annual variation in numbers of individuals that are born that die and that are of a given sex can be specified from statistical theory and would be expected to follow binomial distributions Environmental variability is the annual fluctuation in probabilities of birth and death arising from random fluctuations in the environment e g weather abundance of prey or predators prevalence of nest sites etc Annual fluctuations in the probabilities of reproduction and mortality are modeled in Vortex as binomial distributions while environmental variation in carrying capacity see Box F for more on this topic is modeled as a normal distribution Note that the distinction between demographic stochasticity
322. ser Most of the material in Chapters 1 5 of the manual is available through the Help menu of the program Selecting Contents on the Help menu will take you to a Table of Contents which provides links to each section of the Help manual Click on a section heading in the Table of Contents to jump to that topic in the manual Selecting Context sensitive help from the menu or clicking on the icon on the toolbar will open the Help file and jump right to the place in the file that describes the current program screen 24 Chapter 3 The Data Input Process VORTEX Version 9 User s Manual Documenting Your Input with Notes Whether you are using VORTEX as a researcher a wildlife manager or a student it is highly likely that you will need to document for others and even for yourself when you return to a Project that had been set aside for a period of time why you used the input values you did to create your Scenarios When you are eager to get a Project running it is very tempting to skip over the task of documenting the sources and reasons for your input values However you may save yourself later hassles if you take the time at the outset to record why program options and parameter values were chosen VORTEX provides a utility to attach a note with each piece of data requested as input You can access the Input Notes by any of three methods clicking on the Notes icon at the lower right corner of the Simulation Input screen
323. servation 92 2 163 173 Portales G L P Reyes H Rangel A Velazquez P S Miller S Ellis and A T Smith eds 1997 Taller Internacional para la Conservacion de los Lagomorfos Mexicanos en Peligro de Extincion Reporte del Taller Apple Valley MN Conservation Breeding Specialist Group SSC IUCN Pucek Z I Udina U S Seal and P S Miller eds 1996 Population and Habitat Viability Assessment for the European Bison Bison bonasus Apple Valley MN Conservation Breeding Specialist Group SSC IUCN Rao R J D Basu S M Hasan S Molur and S Walker eds 1995 Indian Gharial Population and Habitat Viability Assessment Report Apple Valley MN Conservation Breeding Specialist Group SSC IUCN Appendix III 135 VorTEX Bibliography VORTEX Version 9 User s Manual Reed D H J J O Grady B W Brook J D Ballou and R Frankham 2003 Estimates of minimum viable population sizes for vertebrates and factors influencing those estimates Biological Conservation 113 23 34 Rodriguez J P and F Rojas Suarez 1994 Population viability analysis of three populations of insular psitacids of Venezuela Pages 97 113 in Morales G I Novo D Bigio A Luy and F Rojas Suarez eds Biologia y Conservacion de los Psitacidos de Venezuela Caracas SCAV EBAFY Econatura SCAPNHP and Provita Rodriguez Luna E L Cort s Ortiz P S Miller and S Ellis eds 1996 Population and Habitat Viability Assessment for
324. sewhere In PVA models consideration should be given to whether the amount of environmental variation in the sys tem should change with range contraction and expansion Unfortunately data on variation in demographic rates are woefully inadequate for almost all species Usually we have no more than crude guesses as to the magnitude of envi ronmental variation for use in population viability analy ses There would be considerable value in a compilation of data across species which would allow generalizations con cerning the typical magnitude of fluctuations in demo graphic rates for species with various life histories trophic guilds and habitat types Figures 3 and 4 show two examples of fluctuations in natural populations that contrast markedly in the extent to which they are impacted by environmental variation The population trend for whooping cranes during recovery from a near extinction shows the reduced relative fluctua tions in numbers as the population increased in size Cranes form long term monogamous pair bonds they re turn to nesting sites for a number of years they have low fecundity and they are very long lived Hence they would ECOLOGICAL BULLETINS 48 2000 Fig 3 Number of whooping cranes arriving each winter at the Aransas National Wildlife g 160 Refuge Texas Data from Mi z rande et al 1991 e 1991 S140 D 120 2 i 100 is 80 D 2 60 w 5 40 E 2 zZ 1940 be expected t
325. specifying EV in breeding for year Whether EVRand or EVNRand will be used depends on the magnitude of EV See Note 6 Set GlobalBreedEVNRand to same sign as GlobalBreedEVRand IF EVCorrelation Between ReproductionAndSurvival No Set GlobalMortE VRand RANDO Select random 0 1 number for specifying EV mortality for that year Set GlobalMortEVNRand NRANDO Select random normal deviate for specifying EV in mor tality for that year Whether EVRand or EVNRand will be used depends on the magnitude of EV Set GlobalMortEVNRand to same sign as GlobalMortE VRand Set GlobalKEVNRand NRAND Q 197 I Select random normal deviate for specifying EV in K for year ELSE EV in breeding is correlated with EV in mortality Set GlobalMortEVRand GlobalBreedEVRand Set GlobalMortEVNRand GlobalBreedEVNRand Set GlobalKEVNRand GlobalBreedEVNRand END EV correlation IF ELSE END FUNCTION GLOBAL_EV_RANDS BEGIN FUNCTION LOCAL_EV_RANDS Set LocalBreedEVRand RANDO I Select random number for specifying EV in breeding for year Set LocalBreedEVNRand NRAND Select a random normal deviate for specifying EV in breeding Set LocalBreedEVNRand to same sign as LocalBreedEVRand IF EV Correlation BetweenReproductionAndSurvival FALSE Set LocalMortEVRand RAND Select random number for specifying EV in mortality Set LocalMortEVNRand NRAND O Select random normal deviate for specifying EV in mor tality Set
326. ss iterations The mean observed heterozygosity equal to 1 mean inbreeding coefficient remaining in the extant populations with standard error and standard deviation across iterations The mean number of alleles remaining AlleIN within extant populations from an original number equal to twice the number of founder individuals with standard error and standard deviation and if the inbreeding depression option is included in the simulation gt The number of lethal alleles remaining per diploid individual with standard error and standard deviation determined by the nature and extent of the genetic load identified in the input process and the intensity of inbreeding the population undergoes Following these yearly reports the output file presents a series of final summary information that includes gt The final probability of population extinction and the converse the probability of population persistence gt Ifat least 50 of the iterations went extinct the median time to extinction gt Of those iterations that suffer extinctions the mean time to first population extinction with SE and SD across iterations gt The mean times to re colonization and re extinction of those simulations that went extinct gt The mean final population size with SE and SD across iterations for all populations including those that went extinct e g had a final size of 0 gt The mean final population size for those it
327. status meets certain conditions You enter this as a function see Chapter 5 For example if you enter N K gt 0 8 then harvests will only occur if the ratio of the population size to the varying capacity is at least 0 8 and if it is a harvest year as defined above Leave the grid cell entry as 1if you do not want to provide any harvest threshold criteria Female Male Ages being Harvested Enter the number of females and or males that you will harvest at each time interval defined for each age class through adults Enter O for no individuals to be harvested in a given age class VORTEX will conduct the harvest immediately prior to calculating the year s breeding pairs so the youngest individual that can be harvested is one year old If the program attempts to harvest individuals from an age class and finds an insufficient number of individuals the simulation will continue without the harvest of those individuals determined not to exist VORTEX will then report at the end of the simulation that some of the attempted harvests could not be carried out Supplementation You also have the option of adding any number of juvenile or adult male or female individuals to each population Figure 34 This option can simulate supplementation through for example a translocation or releases from a captive breeding program As with the harvest option supplemental individuals can be added at any time and interval within the specified time frame for t
328. stems In a monogamous system a relative scarcity of breeding males may limit reproduction by females In polygamous or monogamous models the user can specify the proportion of the adult males in the breeding pool Males are randomly reassigned to the breeding pool each year of the simulation and all males in the breeding pool have an equal chance of siring offspring Deterministic processes VORTEX can incorporate several deterministic processes in addition to mean age specific birth and death rates Density dependence in mortality is modeled by specifying a carrying capacity of the habitat When the population size exceeds the carrying capacity additional morality is imposed across all age classes to bring the population back down to the carrying capacity Each animal in the population has an equal probability of being removed by this truncation The carrying capacity can be specified to change over time to model losses or gains in the amount or quality of habitat Density dependence in reproduction is modeled by specifying the proportion of adult females breeding each year as a function of the population size The default functional relationship between breeding and density allows entry of Allee effects reduction in breeding at low density and or reduced breeding at high densities Populations can be supplemented or harvested for any number of years in each simulation Harvest may be culling or removal of animals for translocation to another
329. structure and prey dynamics on extinction risk in gray wolves Conserv Biol 11 957 965 Westemeier R L et al 1998 Tracking the long term decline and recovery of an isolated population Science 282 1695 1698 51
330. t a population of 100 breeders would all be males is essentially zero so it might be assumed that ran dom fluctuations in sex ratio are unimportant in popula tions approaching such a size However fluctuations in sex ratio can depress population growth significantly even in such cases In a population of 100 breeders we expect ca 50 females and 50 males But due just to demographic sto chasticity the number of females will deviate by 5 or more one standard deviation from this expectation in about one third of the years In monogamous species such as most birds this means that typically lt 50 pairs could be formed The mean depression in reproduction relative to a population with a constant equal sex ratio can be calculat ed from the mean absolute deviation of the binomial dis tribution Due solely to the random fluctuations in sex ra tio reproduction in a monogamous population with 100 adults would be depressed by ca 8 This level of reduced population productivity is enough to cause low fecundity species to switch from positive population growth to long term population decline and eventual extinction Brook et ECOLOGICAL BULLETINS 48 2000 al 1999 found that interaction of the breeding system with fluctuations in the sex ratio strongly influenced pro jections for population growth of whooping cranes Figure 2 shows the mean depression in breeding caused by random variation in the sex ratio for monogamous pop ulations of
331. t can shift species from long term average population growth to population decline include the well known threats of over harvest habitat destruction pollution or other degradation of environmental quality and the introduction of exotic predators competitors and diseases Singly or combined these forces have driven many wildlife populations to low numbers and for some to extinction Once a population becomes small and isolated from conspecific populations that might serve as sources for immigrants that could stabilize demographics and genetics its dynamics and fate can become dominated by a number of random or stochastic processes as outlined above and by Shaffer 1981 Thus even if the original deterministic causes of decline are stopped or reversed the instability caused by the action of stochastic processes acting on small populations can cause the extinction of a population In nature most threatening processes have both deterministic and stochastic features For example a high level of poaching might be seen as a deterministic factor driving a wildlife population toward extinction but whether an individual animal is killed might be largely a matter of chance In a PVA poaching might be modeled as a deterministic process by killing a determined proportion of the animals or it might be modeled as a stochastic process by giving each animal that probability of being killed but allowing the exact numbers killed to vary over time If the popu
332. t high densities B 8 Figure 24C gives the same curves as in Figure 24A but with the addition of an Allee effect 4 1 By inspecting the density dependence equation one can see that when the population is at carrying capacity P N P K When the population is very small N is near 0 then P N P 0 if there is no Allee effect It is also apparent that the Allee effect term N N A will have a strong impact on the value of P N when N is small When N is much larger than A the Allee term will have very little effect on the value of P N Fowler 1981 provides a review of density dependence functions and presents some density curves for large mammals We have chosen to model density dependence using the equation given above because it provides the user with considerable flexibility despite its relatively simple 100 90 Adult Females Breeding per Year P N P 0 80 P K 40 K 100 A 0 P 0 80 P K 40 K 100 B 8 50 60 70 80 90 100 Population Size N Figure 24 Plots of the default density dependence relationship as used by VORTEX in the absence of an Allee effect A 0 panel A in the presence of a steep decrease in breeding success at high population densities B 8 panel B and both a steep decrease in breeding success at high population densities and an Allee effect A 1 and B 8 panel C Adult Females Breeding per Year P N P 0 80 P K 40 K 10
333. t information and logic was used to create the project Unfortunately many PVAs are irreproducible because the authors did not fully document their work The Project Settings screen also has a button to send all of the settings to your Project Report this is always a good idea so that your settings are documented in any printed reports that you create and another button that takes you to a screen for specifying Special Options The Special Options will not be needed by most users They include options to e change the way population sizes are graphed during the simulations e use the last population as a holding site for individuals that are harvested from one population and then supplemented into others if this option is chosen then you specify also what percent of the individuals die during this translocation among populations e omit the last population from metapopulation tallies this is useful if the last population is considered an outside source for immigration into a metapopulation e prevent individuals from dispersing into populations that are at their carrying capacity where the immigrant or some individual would therefore die because of the population exceeding capacity e define extinction as any reduction in population size this is useful when the management goal is to prevent further population declines e produce files with more detailed results e include more neutral loci in the genetic model useful for examinin
334. tards Chlamydotis undulata macqueenii Animal Conservation 4 2 133 141 Conservation Breeding Specialist Group SSC TUCN 1996 Population and Habitat Viability Assessment for the Striped Legless Lizard Delma impar Mosman NSW Australasian Regional Association of Zoological Parks and Aquaria Conservation Breeding Specialist Group SSC IUCN 2000 Conservation Assessment and Management Plan for Arabian Carnivores and Population and Habitat Viability Assessment for the Arabian Leopard and Tahr Apple Valley MN Conservation Breeding Specialist Group SSC IUCN Conservation Breeding Specialist Group SSC IUCN 2002 Evaluation et Plans de Gestion pour la Conservation CAMP de la Faune de Madagascar Lemuriens Autres Mammiferes Reptiles et Amphibiens Poissons d eau douce et Evaluation de la Viabilite des Populations et des Habitats de Hypogeomys antimena Vositse Apple Valley MN Conservation Breeding Specialist Group SSC TUCN Edroma E L N Rosen and P S Miller eds 1997 Conserving the Chimpanzees of Uganda Population and Habitat Viability Assessment for Pan troglodytes schweinfurthii Apple Valley MN Conservation Breeding Specialist Group SSC IUCN Ellis S and U S Seal 1995 Tools of the trade to aid decision making for species survival Biodiversity and Conservation 4 553 572 Ellis S K Hughes C Kuehler R C Lacy and U S Seal eds 1992 Alala Akohekohe and Palila Population and Habitat Viabi
335. te IF Inbreeding gt 0 Set SurvivalRate exp 0 50 LethalEquivalents Inbreeding ENDIF IF RAND gt SurvivalRate Offspring dies END IF END IF IF not dead Calculate kinship to every living animal I See Ballou 1983 for the method of calculating inbreed ing and kinship coefficients END IF END offspring LOOP END breeding females LOOP END FUNCTION BREED BEGIN FUNCTION GETBREEDRATE Obtain BreedRate by evaluating fecundity function for population and individual parameters I Most often the fecundity function will simply return ProportionFemalesBreeding entered by the user VORTEX provides the option however of making breeding a func tion of PopulationSize GeneDiversity Inbreeding and other variables See Note 3 ADJUSTRATE BreedRate LocalBreedEV p LocalBreedEVRand LocalBreedEVNRand Adjust rate for local EV ADJUSTRATE BreedRate GlobalBreedEV p GlobalBreedEVRand GlobalBreedEVNRana Adjust rate for global EV FOR each type of catastrophe c IF CatastropheFlag c TRUE Multiply BreedRate by CatastropheBreedSeverity p c END IF END LOOP END FUNCTION GETBREEDRATE BEGIN FUNCTION MORTALITY for population p FOR each living animal in the population IF age gt 0 Infant mortality occurs within the BREED function not here 199 IF at maximum age Animal dies ELSE GETDEATHRATE IF RANDO lt DeathRate Animal dies END IF E
336. te MOnOpoliZation ccsssecssseecssseeseseeeeseeeeeseeeseeaaeeeeaseeneseeseaseeneneeasaeesnenenenes 56 Initial Population SiZe ccccssseessseeeesseeseseeeeseeeneeeeaeeeeeaseeneseeoeaeeseaseeneneeaeaeennenee 57 Carrying Capacity gt ccscccssssccssseccssseecsseeesseeenaseenseeeeseeensseenesseneaseeneseeanasesneneeseaeas 58 Harvest 2 2 eyuva tuts nts n sons nnn 61 Supplementation srasaccensccnesecceseeeeeeeeeseeeeeeeeeeaeeeeeseeaeaeaeaseeoeseeseaeeseneeaeaeesanes 62 Saving your Input and Running the Simulation csscssssssessssesseeessees OF Adding and Deleting Scenarios sssssssnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn OB Adding Scenarios to Your Project ccceceeesseeteee ee 66 Deleting Scenarios from Your Project se eee 68 Reordering SCenariOS 0 c ee 68 Chapter 4 Viewing Model Results Text Tabular and Graphical Text Output sidewidddubidadsGumtidsiaweseuawewsl dueuedidaaseaaarcccdseutesasewionuannnedtonen OO Input Summary ___haaeett eee 69 Deterministic Calculations ssssssssnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnnn nnmnnn 70 Output SumMary nse se eee 73 Other Output eaasecensseeneseeeeseeeeeseeeeaeeeneneeaeaeeeeseeneseeaeaseeoeseeaeaeeseneeasaeensene 74 ii Contents VORTEX Version 9 User s Manual Graphs and Tables ies ccisasaccactacecseaiessaseccstdancecddiadscacedieddbasiesaieucteneuecdiads 76 Data Graphs 0 wisiasaecesdsiucdiveeavicesitiasiadeossiec
337. te of 50 at age 5 but 50 0 f then declines by 2 each year thereafter 45 0 40 0 35 0 30 0 25 0 20 0 15 0 10 0 5 0 L 0 0 Demographic Rate O 10 20 30 40 50 60 70 80 90 100 Age Years 7 Age dependent fecundity with a symmetrical peak at age 15 RATE A gt 5 50 ABS A 15 2 50 0 45 0 40 0 35 0 30 0 25 0 f 20 0 15 0 10 0 5 0 0 0 Demographic Rate O 10 20 30 40 50 60 70 80 90 100 Age Years 92 Chapter 5 Using Functions in VORTEX VORTEX Version 9 User s Manual 8 Age dependent fecundity with an asymmetrical peak at age 10 10 RATE Different trends are specified for age intervals 0 4 5 9 and 10 Note the use of parentheses brackets and braces to improve readability Increase in mortality with inbreeding RATE 100 50 ExP 1 57 1I 100 The survival rate declines exponentially described by the portion within the outermost parentheses while the percent mortality is set at 100 survival This is the equation used by VORTEX to model increased juvenile mortality if there are 3 14 lethal equivalents and no recessive lethal alleles contributing to inbreeding depression Stepwise increase RATE The rate increases from 50 to 80 at 10 year intervals An alternative way to express the same function would be RATE 50 10 MIN 3 FLOORC Y 1 10 Demographic Rate Demographic Rate Demographic Rate A gt 5
338. ted above more proc esses threaten the viability of small populations than are commonly addressed in PVA models Analytical models and simple population projection models can therefore overestimate population growth underestimate popula tion fluctuations and seriously underestimate probabili ties of extinction More accurate PVA of small populations may often require individual based models that simulate interactions among threatening processes rather than rely ing on theoretical equations derived under assumptions of simplified population processes acting in isolation Lindenmayer et al 2000 found that PVA model predic tions matched the observed dynamics of populations of three species of marsupials in a highly fragmented land scape only when the models incorporated distance dependent and density dependent dispersal high mortal ity during dispersal and spatial variation in habitat quality Knowledge of times since isolation of each habitat frag ment was also critical as the metapopulations were pro jected to lose more component subpopulations before reaching extinction recolonization equilibria In an alter native approach Sj gren Gulve 1994 Sj gren Gulve and Ray 1996 used a logistic regression model to incorporate similarly detailed information about the habitat character istics spatial arrangement and surrounding forestry prac tices on the extinction recolonization dynamics of pool 47 frog Rana lessonae met
339. ted many times to generate the distribution of fates that the population might experience VORTEX is an individual based model That is it creates a representation of each animal in its memory and follows the fate of the animal through each year of its lifetime VORTEX keeps track of the sex age and parentage of each animal Demographic events birth sex determination mating dispersal and death are modeled by determining for each animal in each year of the simulation whether any of the events occur See figure below VORTEX Simulation Model Timeline Breed Immigrate Supplement Su N T Age 1 Year A Death Emigrate Harvest Carrying Capacity Truncation Census Events listed above the timeline increase N while events listed below the timeline decrease N VORTEX requires a lot of population specific data For example the user must specify the amount of annual variation in each demographic rate caused by fluctuations in the environment In addition the frequency of each type of catastrophe drought flood epidemic disease and the effects of the 114 Appendix I An Overview of Population Viability Analysis Using VORTEX VORTEX Version 9 User s Manual catastrophes on survival and reproduction must be specified Rates of migration dispersal between each pair of local populations must be specified Because VORTEX requires specification of many biological parameters it is not necessarily a good model for the examination o
340. ted that the populations would not decline 106 Appendix I An Overview of Population Viability Analysis Using VORTEX VORTEX Version 9 User s Manual PHVA workshops facilitate the assembly of all available data Often important information is found in the field notes of researchers or managers in the heads of those who have worked with and thought about the problems of the species and in unpublished agency reports as well as in the published scientific literature A pending PHVA can be the impetus that encourages the collection of data in anticipation of presentation review and analysis at the workshop For example a Sumatran Tiger PHVA helped stimulate the systematic collection of data on sightings and signs of tigers in protected areas throughout the island of Sumatra and collation and integration with a Geographic Information System GIS map of habitats and human pressures on those habitats The PHVA on the Grizzly Bear in the Central Canadian Rockies Ecosystem provided the opportunity for detailed habitat mapping data to be integrated with population biology data on the bears resulting in the development of models which would allow projection of the impacts of habitat changes on the bear populations It is important to specify the assumptions that underlay a PHVA and any consequent management recommendation For example the Hawaiian bird conservation efforts are constrained by a belief that no birds bred outside of the islands should
341. termined by comparing a random number to the survival probability for that animal In the absence of inbreeding depression the survival probability is given by the age and sex specific survival rate for that year If a newborn individual is homozygous for a lethal allele it is killed Otherwise the survival probability for individuals in their first year is multiplied by e b 1 Pr Lethals F in which b is the number of lethal equivalents per haploid genome and Pr Lethals is the proportion of this inbreeding effect due to lethal alleles 18 The age of each animal is incremented by 1 19 If more than one population is being modeled migration among populations occurs stochastically with specified probabilities 120 Appendix I An Overview of Population Viability Analysis Using VORTEX VORTEX Version 9 User s Manual 20 If population harvest is to occur that year the number of harvested individuals of each age and sex class are chosen at random from those available and removed If the number to be removed do not exist for an age sex class VORTEX continues but reports that harvest was incomplete 21 Dead animals are removed from the computer memory to make space for future generations 22 If population supplementation is to occur in a particular year new individuals of the specified age class are created Each immigrant is assumed to be genetically unrelated to all other individuals in the population and it carries the numb
342. the function against the N parameter Depending on the shape of the density dependence curve you have specified and the mortality EF rates you will enter later your population may never be able to reach the carrying capacity K also to be specified later The combination of density dependence in both reproduction and survival will determine over what range of sizes the population is expected to experience average net growth and over what range it would be expected to decline since deaths outnumber births f42PG C Yortex9 2PG 2PG vpj Project Settings Simulation Input Text Output Graphs and Tables Project Report Add Scenario Delete Scenario lt zpa2 x ae ZPG1 Il ZPG2 cenario Settings Long Term Monogamy Long Term Polygamy pecies Description Age of First Reproduction for Femal abels and State Vars ge of First Reproduction for Females 2 ae ro To 100 HE ml ispersal Rates Age of First Reproduction for Males Maximum Age of Reproduction fio ortality Rates Maximum Number of Progeny per Year 2 atastrophes Sex Ratio at Birth in Males 50 ate Monopolization nitial Population Size anying Capacity Population 1 Popula Density Dependent Reproduction Breeding at Low Density P 0 75 Supplementation Breeding at Carrying Capacity PIK 50 Allee Parameter amp 1 Steepness Parameter B 2 Harvest Supplementation Copy input values from Population 1 7 This Section
343. the migration rate is then calculated to be 1 8175 19 044 0 0000954 Finally the authors assumed a symmetrical pattern of migration so that the estimate of the rate of migratin from Middle to West Anacapa equivalent to that from West to Middle Anacapa is 0 5 0 0000954 0 0000477 42 Chapter 3 The Data Input Process VORTEX Version 9 User s Manual Reproductive System Monogamous Polygamous Long term Monogamy or Long term Polygamy VORTEX models breeding systems as monogamous vs polygamous and short term vs long term With monogamous breeding there must be a male for every breeding female males may therefore become a limiting factor restricting breeding In polygamous models there only needs to be at least one male for all females to have an opportunity to breed However in a later section Mate Monopolization you can specify that only a subset of males have opportunities to breed For example you can create a polygynous system in which some males control harems of typically 5 females while the remaining males are excluded from breeding If you do not choose a Long term option then VORTEX will assume that mates are randomly reshuffled each year and that all available individuals have an equal probability of breeding If you do specify one of the Long term models then once pairs are formed those pairs will remain together across years of the simulation until either the male or the female dies or disperses to
344. the population size the size of EV depends on the constancy of the environment Number of Types of Catastrophes Catastrophes can be thought of as extremes of environmental variation that strongly impact reproduction and or survival Types of catastrophes might include sudden habitat destruction floods forest fire epidemic disease outbreaks etc Catastrophes can be significant threats to small isolated populations For example disease decimated the last population of black footed ferrets and a hurricane killed half of remaining wild Puerto Rican parrots It is up to you to determine what types of catastrophe if any may impact your population Later in the data input process you will be given the opportunity to define how each type of catastrophe will impact reproduction and survival You may be able to identify historical catastrophes by examining birth and or death rate data over EF several past years for your species of interest If you find a demographic rate that is significantly different than that described by normal levels of variation for example at least 2 standard deviations from the mean value you may use that as evidence of a catastrophic event Dispersal Among Populations If you are modeling a metapopulation you now need to specify a few parameters that help to define the system of dispersal of individuals among populations In a later section you will define the rates of dispersal of individuals between populations
345. there is insufficient memory available Even if the program does not abort it may run exceedingly slowly as each individual and its pedigree is tracked throughout its lifetime If you have frequent problems with aborted or slow analyses consider taking one or more of the following steps gt Change the mechanism by which inbreeding depression is modeled The program will run noticeably faster if the population s genetic load is due entirely to lethal as opposed to detrimental alleles gt Construct a simpler general model Often a large population or metapopulation may exist but the real concern may be whether smaller fragments are at risk of local extirpation VORTEX will simulate small populations much more rapidly than large populations or constellations of patches within a metapopulation If local patches do not exchange migrants analyze them separately rather than as parts of a larger more complex metapopulation 6 Chapter 2 Getting Started with VORTEX VORTEX Version 9 User s Manual gt Think about using a different PVA software package If VORTEX is running so slowly as to cause you much grief the types of populations you are analyzing are probably so large that the kinds of random forces modeled explicitly by VORTEX demographic and environmental stochasticity inbreeding and genetic drift are likely to be irrelevant to the population growth dynamics In these cases it may be more appropriate to use a population based m
346. threats to the viability of small populations using indi vidual based models Ecol Bull 48 39 51 As wildlife populations become smaller the number of interacting stochastic processes which can destabilize the populations increases genetic effects inbreeding and loss of adaptability and instability of the breeding structure sex ratio imbalances unstable age distribution and disrupted social systems can decrease population growth and stability Recent analyses have shown that some populations can be very sensitive to these sto chastic processes at larger population sizes than had been suggested previously and often in unexpected ways Interactions among processes can reduce population viability much more so than would be assumed from consideration of isolated factors For exam ple in monogamous species random fluctuations in sex ratio will depress the mean number of breeding pairs in populations with as many as 500 adults At low population densities individuals may not be able to find mates or may not encounter individuals sufficiently unrelated to be accepted as suitable mates Inbreeding depression of demo graphic rates can become a significant contributor to population decline in populations with several hundred individuals even if genetic problems are not the primary threat Most models of genetic decay in small and fragmented populations assume demograph ic stability However when the increases in demographic fluctuations of
347. tion and Habitat Viability Analysis is a multi faceted process or framework for assisting conservation planning rather than a singular technique or tool It is often interwoven with other techniques for managing complex systems such as decision analysis Maguire 1986 Maguire et al 1990 Even when viewed as the PHVA workshop all such conservation workshops involved and required substantial pre workshop and post workshop activities Some PHVA workshops have been extended into multiple workshops and less formal smaller collaborative meetings often focused on subsets of the larger problems of species conservation Although PHVAs are diverse and not well defined the PHVA process contains a number of critical components First it is essential to gather an array of experts who have knowledge of the species or problem A PHVA is not required to bring together experts but it often facilitates such sharing of expertise because the collective knowledge of many is essential for a useful PVA in the narrow sense to be completed In addition to a diversity of people a PHVA workshop also requires and therefore facilitates the involvement of a number of agencies and other concerned organizations For example the PVA on the two endemic primates of the Tana River Primate Reserve in Kenya Seal et al 1991 was convened by the Kenya Wildlife Service facilitated by the IUCN SSC Captive Breeding Specialist Group benefited from the expertise contributed by members
348. tion should be entered as a number of animals not as a percentage of K for example if K 2000 with a standard deviation of 10 then enter 200 58 Chapter 3 The Data Input Process VORTEX Version 9 User s Manual 4 Vortex Stochastic Simulation of the Extinction Process File Edt Vortex Window Help OSH SBA S los gt SS Page D WWORTEXS ZPG ZPG Ypi Project Settings Simulation Input Text Output Graphs and Tables Project Report Add Scenario Delete Scenario lt zPa2 gt Reorder ZPG1 ZPG2 cenario Settings ne pecies Description Carry mg Cap ac ty abeis and State Vars Reproductive System Population 1 Population 2 Reproductive Rates Canying Capacity K 50 50 ortality Rates SD in K Due to EY 0 0 atastrophes ate Monopolization nitial Population Size Population1 Population 2 g Capacity Future change in K v v Over how many years annual increase decrease ez a 2 o s i f Copy input values from Population 1 z This Section z to subsequent populations Copy Input values Vortex 9 21 If K is exceeded additional mortality is imposed across all age classes Maximum K is 30000 CAPS NUM INS Date Time 10 24 03 10 20AM 4 Figure 32 Carrying Capacity input section EF Be careful If you enter a standard deviation for the carrying capacity that is greater than K 3 then the
349. tional Park and spends the winter at Aransas National Wildlife Refuge along the Gulf Coast of Texas Because of this movement pattern the environmental conditions affecting chick production are quite different from those impacting mortality during the majority of the year Mirande et al 1991 Consequently we would expect EV affecting these processes to be uncorrelated when constructing a VorRTEX model EV Correlation Among Populations You specify here the correlation of EV among populations applicable of course only when more than one population is modeled If this value is set to 0 0 then EV will be completely independent among populations If this value is set to 1 0 then EV in reproduction and in survival will be completely synchronized among populations As a result good years for reproduction and or survival in one population will lead to similarly good years in all other populations If this degree of correlation is set to an intermediate value then EV will be partly correlated among populations Environmental variation in the metapopulation context can be considered to exist at two levels local population specific and global acting across all populations The total EV when expressed as a variance rather than a standard deviation as entered by the user is simply the sum of the EV existing at these two levels The correlation of EV among populations that you enter then is simply the proportion of the total EV when expres
350. tric among populations enter whatever probability you deem appropriate for each pair of populations Enter O to indicate no exchange of individuals between a pair of populations The values on the diagonal of the grid the percents of individuals that do not disperse each year is automatically calculated by the program so that the rows will sum to 100 4 Vortex Stochastic Simulation of the Extinction Process File Edt Vortex Window Help Dem BBS lees f4ZPG D WORTEX9 ZPG ZPG vpj Iof x Project Settings Simulation Input Text Output Graphs and Tables Project Report Add Scenario Delete Scenario lt zpa2 gt Reorder ZPG1 ZPG2 Soe Dispersal Among Populations abels and State Vars Dispersing classes Age Range Youngest fi Oldest 5 Dispersing Sexfes Males JY Females s ortality Rates Survival of Dispersers fioo atastrophes Dispersal Modifier Function optional D ate Monopolization nitial Population Size anying Capacity Import Rate Matrix Apply Multiplier of Dispersal Rates Export Rate Matrix Fill Matrix with 4 P S Z2 S z 2 2 5 sales a g t eje aja 3 SiE 3 2 3 a a s P BS 5 EE ee A Annual probabilities as percents of dispersal from source Copy input values from populations rows to recipient populations columns Population 1 Population 1 Population 2 Population 1 Population 2 This Section to subsequent pop
351. tself rather than the graphing is taking a long time Consequently the program may not refresh the display if you drag the graph window or toggle out to another Windows application and back Therefore it is best to not try to do anything else on your computer while the simulation is running This also helps by leaving all memory and system resources available to VORTEX If you feel that you must do other work e g using Word or Excel or check email while the VORTEX simulation is working you should specify the Special Option under Project Settings of Do not show graphs during iterations 64 Chapter 3 The Data Input Process VORTEX Version 9 User s Manual When the requested simulations are complete VORTEX displays a few summary statistics at the top of the graph When you are done viewing the graph close it by clicking on the x icon in the upper right corner If you want to print or save this graph of the simulation use the Windows PrntScrn button to copy the image to your Windows clipboard You can then paste it into Word or PowerPoint or any other program that can display images However data for tabulating and graphing summary results have already been saved on your disk as we will see in the next Chapter so there is usually no need to save these rather cluttered displays of all iterations x Stop Pause Clear Lines Population 1 Metapopulation 90 8 60 50
352. two populations of whooping crane was decimated by a hurricane in 1940 and soon after went extinct Doughty 1989 The only remaining population of the black footed ferret Mustela nigripes was being eliminated by an outbreak of distemper when the last 18 ferrets were captured Clark 1989 Genetic drift is the cumulative and non adaptive fluctuation in allele frequencies resulting from the random sampling of genes in each generation This can impede the recovery or accelerate the decline of wildlife populations for several reasons Lacy 1993b Inbreeding not strictly a component of genetic drift but correlated with it in small populations has been documented to cause loss of fitness in a wide variety of species including virtually all sexually reproducing animals in which the effects of inbreeding have been carefully studied Wright 1977 Falconer 1981 O Brien and Evermann 1988 Ralls et al 1988 Lacy et al 1993 Lacy 1997 Even if the immediate loss of fitness of inbred individuals is not large the 102 Appendix I An Overview of Population Viability Analysis Using VORTEX VORTEX Version 9 User s Manual loss of genetic variation that results from genetic drift may reduce the ability of a population to adapt to future changes in the environment Fisher 1958 Robertson 1960 Selander 1983 Thus the effects of genetic drift and consequent loss of genetic variation in individuals and populations negatively impact on demographic rates and in
353. ulation State Variable Dispersal rate unmodified 27182818 Number of Adult Females x nmonor Update Graph V Show this dialog when pressing in data entry Ok Cancel Figure 50 The Function Editor utility 84 Chapter 5 Using Functions in VORTEX VORTEX Version 9 User s Manual When you open the Function Editor Figure 50 you can enter the desired function by typing it into the box at the top of the window or you can use the screen keypads to select numbers operators and functions which will then be pasted into the function box It is probably fastest to just type the function you want but the keypads can help remind you what operators trigonometric functions Boolean operators and other functions are available for use The population and individual variables available for use in functions are listed in a box in the lower part of the Function Editor window see Table 1 The Function Editor also keeps a list of recently used functions and they can be recalled and further edited if desired by clicking of the drop down list in the Function box In specifying a function you should make no assumptions about the order of precedence of operators see Table 2 for list of valid operators For example the function A B C is interpreted as A B C Precedence is left to right so VORTEX interprets A B C in the standard way but it is risky to assume that VORTEX will read a function the way you would read
354. ulations Copy MPU Valles Are you remembering to enter notes here Vortex 9 21 Values on the diagonal for percents not dispersing are calculated automatically CAPS NUM INS Date Time 10 24 03 3 46AM Figure 22 Dipersal Rates input section Chapter 3 41 The Data Input Process VORTEX Version 9 User s Manual It is important to remember that while most input data should be in the form of EF percentages a few others are input as proportions Check the labels and prompts for clarification of the required data format On the Dispersal Rates screen are five commands that can make it easier to enter dispersal rates Import Rate Matrix allows you import the grid values from a semi colon delimited text file This file can be created in Excel or whatever software you choose It must contain values for all cells of the grid including the labels although the labels in the file will be ignored and will not over write what shows on the screen The easiest way to see the format of the rate matrix file is to select Export Rate Matrix and then look at the file that was created With these commands you can create a large matrix in a spreadsheet program and then import it into VORTEX and you can export rate matrices for modification or for re use in other VORTEX projects When you have only a few populations these commands are usually not worth using However if you have for example 40 populations you very well may
355. ur first VORTEX model you are ready to look at your simulation results A display of changing population sizes was displayed perhaps very quickly on your screen as the simulation was running Figure 36 While you may want to capture that image onto your Windows clipboard with a PrntScrn system command the more useful presentations of model results are generally those that provide mean results across iterations perhaps with standard deviations to indicate the variation among iterations or standard errors to indicate the precision with which the means were estimated from the finite number of iterations run In addition there are many measures of population performance and viability other than just the projected population size This chapter describes how to use VORTEX to view text tabular and graphical summaries of your results Text Output Click on the Text Output tab to access simple text descriptions of your Project input or results Figure 40 There are four subsections of Text Output Input Summary The first section provides a summary of the input values you entered for each Scenario It is wise to scroll through this Input Summary in order to be sure that you entered the values as you intended In addition you can cut and paste from this text summary into any reports that you need to create of your work At the top of the Input Summary and similarly at the top of the other three sections of Text Output are three command buttons These
356. ut screens is a tool that allows you to copy input values from any one population to all subsequent populations You can copy only those values in the current Section of input or copy values in all the input Sections Chapter 3 51 The Data Input Process VORTEX Version 9 User s Manual Mortality In this next section of input Figure 28 you enter the age sex specific mortalites In the language of matrix life table analysis e g Caughley 1977 Caswell 2001 VORTEX defines mortality as the mortality rate qx or the percentage of animals alive at age x that die before reaching age x 1 Enter mortality rates as a percent between 0 and 100 for each age sex class Once reproductive age is reached the annual probability of mortality remains constant over the life of the individual and is entered only once but see Chapter 5 for further information on how to relax this assumption Mortality of Females Males as In these tables enter the mean mortality rates for each age class and enter also a standard deviation SD for each mean to describe the environmental variation EV in each rate For information on the calculation and statistical treatment of variance in demographic parameters used in VORTEX see Boxes C and D 4 Vortex Stochastic Simulation of the Extinction Process File Edt Vortex Window Help OSM BMS los i gt EiZPG D WORTEXS ZPG ZPG vpi iol x Project Settings Simulation Input Text Output Graphs
357. variation in demographic rates The deterministic population growth rate ris calculated by solving the Euler equation Y emye 1 in which x and mx are the age specific mortality and fecundity rates respectively for age class x to x 1 and the summation is over all age classes Lambda is related to r by a The stable age distribution or the proportion of the population at each age class cy is given by I el The determination of a stable age distribution for males in a given population becomes a bit more complicated if the mortality schedules are different for the two sexes In this case r is calculated based on female life history tables since females control population growth but the s used in the age distribution equation are those for males Moreover the exact form of the equation is dependent on when the age classes were censused In the above equation co is the proportion of the population aged 0 plus a small increment just after the breeding season but before mortality is imposed In order to build the initial population VorTEx omits age class 0 because the simulations begin just before the breeding season and re scales the age distribution in order to sum to 1 0 The life table calculations assume that there is no limitation of mates i e there are always enough breeding males to mate with all breeding females Other complications arise if there are catastrophes in the simulation model In those cases VorTe
358. various sizes Even with 500 breeding individu als the mean number of pairs in the population is 3 6 below what would be available if the sex ratio were fixed at 50 50 This simple example of a threat to the viability of small populations illustrates several important points First the random deviation in sex ratio does not in itself cause extinction except in the very smallest of populations but it can interact with other factors such as the breeding system to depress population growth in a vulnerable popu lation sufficiently to cause extinction Second it is unlikely that biologists observing the population would recognize that fluctuation in the sex ratio was a contributing cause of lower reproduction and population decline Third it would be possible to incorporate the reduction in breeding as an average effect in a simple life table projection How ever to do so requires that the demographic rates were esti mated from a population of the size of the population be ing currently assessed and that the population remains constant in size This last assumption defeats the purpose of PVA The effect of biased sex ratios depressing repro duction in monogamous population of changing size could be modeled as a density dependent effect on repro duction Stephens and Sutherland 1999 Courchamp et al 1999 However I am not aware of any cases in which an analytical or population based PVA model incorporated the reduction in breeding as sh
359. w users are encouraged to use it to become more familiar with VORTEX version 9 In addition to the switch to a Windows interface there have been a few upgrades to the underlying population biology model available in VORTEX The most significant one and the one that would be most noticeable to users is the availability now of Individual State variables These optional variables allow you to create descriptors of states or characteristics of individuals in the populations These states can be anything you want them to be for example dominance status body condition location on the landscape or territory quality If you specify Individual State variables then you must define how they are initially determined for each individual at the outset of the simulation and when individuals are born and how an individual s state can change across years Once defined these variables can be used as modifiers of any of the demographic rates such as probability of breeding litter size mortality susceptibility to catastrophes and dispersal Using this feature of the VORTEX model you can create very complex and detailed models of population dynamics For example breeding could be function of the dominance status of individuals which could in turn be determined by maternal dominance status and a random component However we will not hide the fact that appropriate and wise use of Individual State variables can be very difficult and we strongly c
360. x adjusts the fecundity and mortality rates to account for the effect of catastrophes averaged across years For more information on the details of life table analysis refer to any number of general ecology or population biology texts such as Pielou 1977 Krebs 1994 or Caughley 1977 It is important to look at the deterministic projections of population growth for any analysis If ris negative the population is in deterministic decline the number of deaths outpace the number of births and will become extinct even in the absence of any stochastic EF fluctuations The difference between the deterministic population growth rate and the growth rate resulting from the simulation can give an indication of the importance of stochastic factors as threats to population persistence 72 Chapter 4 Viewing Model Results VORTEX Version 9 User s Manual Output Summary The third section of Text Output lists the basic status of each population at each year of the simulations 4 Vortex Stochastic Simulation of the Extinction Process File Edt Vortex Window Help JOSH Be SB oF gt Page D WORTEXS ZPG ZPG Ypi Project Settings Simulation Input Text Qutput a and Tables Project Report Input Summary Deterministic Calculations Other Output Send text to Report Print Save s Scenario to view zPat Population to find Population 1 Results from VORTEX 9 21 simulations completed Fri Oct 24 09 1
361. y can be estimated by the observed proportion within that sample p If this sampling procedure were to be repeated a number of times each estimate of p would likely be different The variance of all possible values of p would be pq o4 n in which p is the true probability in the population and q 1 p If p is estimated from the sample however then this variance is biased underestimated replacing n by n 1 results in a better estimate of the variance of p across samples The standard deviation of p is therefore estimated by pq The Normal Distribution In a manner similar to the categorical data described by a binomial distribution continuous variables are generally observed to have an abundance of values nested around the mean with progressively fewer observations near the maximum or minimum values When these observations are viewed graphically the resulting frequency distribution takes on the look of the familiar bell shaped curve particularly when the W386 a 20 fae u Uro tle Ute number of observations n becomes large This x curve is more formally described as a normal Figure C 2 A normal distribution distribution Figure C 2 shows a typical normal distribution Chapter 3 33 The Data Input Process VORTEX Version 9 User s Manual Box C Continued Note in Figure C 2 the relationship between the population mean x and standard deviation o ina normal distributio
362. y Analysis Using VORTEX VORTEX Version 9 User s Manual population and the underlying nature of the genetic load recessive alleles or heterozygote advantage PVAs must make assumptions about the effects of inbreeding on the population being studied If genetic effects are ignored the PVA will overestimate the viability of small populations In some cases it might be considered appropriate to assume that an inadequately studied species would respond to inbreeding in accord with the median 3 14 lethal equivalents per diploid reported in the survey by Ralls et al 1988 In other cases there might be reason to make more optimistic assumptions perhaps the lower quartile 0 90 lethal equivalents or more pessimistic assumptions perhaps the upper quartile 5 62 lethal equivalents In the few species in which inbreeding depression has been studied carefully about half of the effects of inbreeding are due recessive lethal alleles and about half of the effects are due to heterozygote advantage or other genetic mechanisms that are not diminished by natural selection during generations of inbreeding although the proportion of the total inbreeding effect can vary substantially among populations Lacy and Ballou 1998 A full explanation of the genetic mechanisms of inbreeding depression is beyond the scope of this manual and interested readers are encouraged to refer to the references cited above VORTEX can model monogamous or polygamous mating sy
363. y all have gen otypes that otherwise would confer high fitness and indi viduals may not be inbred in fact it is the avoidance of inbreeding that causes the depression of fitness Genetic homogeneity leads to an epiphenomenon with frequency dependent selection causing the inbreeding depression at the population level Some long isolated populations of beach mice such as Peromyscus polionotus leucocephalus have low genetic diversity low frequencies of breeding when mice are paired in captive colonies and the poor breeding is increasingly exacerbated when experimental populations are further inbred Brewer et al 1990 Lacy and Ballou 1998 It is possible that mate choice behavior that evolved to prevent inbreeding is now often preventing breeding as the mice breed readily when paired with mice from other subspecies Lacy unpubl Inbreeding interacts with other threats to population viability For example Keller et al 1994 found thar in bred song sparrows Melospiza melodia were less likely to survive a severe winter and inbred animals have occasion ally been observed to be more vulnerable to other environ mental stresses Miller 1994 Not only does demographic decline increase inbreed ing which can in turn further depress mean demographic rates but smaller populations undergo greater relative de mographic fluctuations The increased fluctuations in numbers depress the genetically effective population size N as in
364. y of Punta San Juan Peru Conservation Biology 16 5 1333 1343 Manansang J S Hedges D Siswomartono P S Miller and U S Seal eds 1996 Population and Habitat Viability Assessment Workshop for the Anoa Bubalus depressicornis and Bubalus quarlesi Apple Valley MN Conservation Breeding Specialist Group SSC IUCN Manansang J A MacDonald D Siswomartono P S Miller and U S Seal eds 1996 Population and Habitat Viability Assessment for the Babirusa Babyrousa babyrussa Apple Valley MN Conservation Breeding Specialist Group SSC IUCN Manansang J P S Miller J W Grier and U S Seal eds 1997 Population and Habitat Viability Assessment for the Javan Hawk Eagle Spizaetus bartelsi Apple Valley MN Conservation Breeding Specialist Group SSC TUCN Manansang J D Siswomartono T Soejarto U S Seal P S Miller and S Ellis eds 1997 Marine Turtles of Indonesia Population Viability and Conservation Assessment and Management Workshop Apple Valley MN Conservation Breeding Specialist Group SSC TUCN Marmontel M S R Humphrey and T J O Shea 1997 Population viability analysis of the Florida manatee Trichechus manatus latirostris 1976 1991 Conservation Biology 11 2 467 481 Marshall K and G Edwards Jones 1998 Reintroducing capercaillie Tetrao urogallus into southern Scotland Identification of minimum viable populations at potential release sites Biodiversity amp Conservation 7

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