POP-III
Contents
1. POP III SYSTEM DOCUMENTATION By John M Bartholow Copyright O 1990 97 by Fossil Creek Software All Rights Reserved IBM PC Version 1 0 Documentation Slightly Revised January 2009 LICENSE AGREEMENT POP III was developed by John Bartholow 5402 Old Mill Rd Fort Collins CO 80528 970 223 6488 Development is without obligation to the principal employer that might restrict the author from freely distributing the program POP III does not contain any material constituting a trade secret nor is it subject to any restrictions except the use of common sense and continued scrutiny to develop better approaches to wildlife management POP III is distributed by Fossil Creek Software from the address given above The program is copyrighted and is available with a non exclusive institution wide license Permission is granted for you to make as many copies of the program and documentation as you feel necessary for any employee in any office on any computer Permission is not granted for any member of your institution to distribute copies of the program or documentation to any other outside individual agency or university From time to time there may be enhancements to the POP III program released by Fossil Creek Software Enhancements will be available at a nominal charge and may be distributed within your institution as outlined above SUGGESTIONS AND BUG REPORTS We would appreciate any suggestions you might have to help improve P2. Bin Frequency 158 193 193 228 228 262 262 297 297 332 332 367 367 401 401 436 Re rR RWNNWWN ensneonstn 158 133 228 262 2o7 332 367 40i 193 228 262 237 332 367 4al 436 Young per 108 Females In this case POP III would choose a cumulative distribution because the skewness is too large skewness gt 0 5 to be a normal distribution A glance at the frequency plot confirms that Remember you are responsible for tying down the ends of the cumulative distribution something that POP III doesn t do regardless of method If it had looked like a normal distribution you could calculate the median from your sorted data to use as the mean and you could use twice the geometric mean deviation as two times the standard deviation You get the idea 4 3 TRIALS SAMPLES AND YEARS HOW MUCH IS ENOUGH So how do we figure out the best number of trials runs and samples to take per trial This will depend on the spread your parameter distributions contain The narrower their spread the fewer trials and samples required POP III forces you to make at least two trials For reliability POP III also forces you to take at least 10 samples per trial to calculate statistics reliably As you add samples the deviations will narrow further but with less and less gained at each increment and more and more time spent It is up to you to experiment with your data to g
3. K usable memory CGA EGA VGA MCGA AT amp T or HERCULES graphics compatibility Software to copy screen graphics to a graphics compatible printer Optional but highly recommended hardware and software e Math Coprocessor 8087 or compatible POP II companion program NOTE that you must have graphics screen printer software if you wish to print the graphs on the screen to your printer MS DOS comes with a graphics printer driver called GRAPHICS COM If you do not have access to this kind of software I am sure you will be able to buy one for a nominal price I have included public domain programs for EGA VGA graphics on your disk See the README file for more information If you are in need of a versatile screen to printer program contact either Grafplus Pizazz Jewell Technology or Application Techniques 206 937 1081 800 433 5201 1 3 WHAT TO EXPECT IN THIS DOCUMENTATION Like any software documentation this document is meant to be all inclusive It s just a matter of figuring out what information is where This introductory section is an overview Section 2 is almost all of the computerese necessary to really get started like how to copy diskettes install POP III and some tidbits on special operating system problems that might come up Section 3 is meant to be a low key tutorial on what you will encounter while running POP III not exactly keypress by keypress but concept by concept Speaking of concepts an understan
4. of distributions and parameter values to use for the three population segments initial population sizes survival rates and reproductive rates Upon completion of the data entry process you should Save your data set just in case 19 3 3 VITAL INFORMATION REGARDLESS OF METHOD No matter which method you have chosen for starting POP III you probably need to know a bit more on how to navigate through POP III As you have seen by now most POP III commands are single keypress functions But knowing what to do at any given time may be somewhat confusing at first When Creating or Editing data you should choose the distribution type by the first letter For example to choose the Uniform distribution type U Valid choices are always shown on a highlighted bar usually at the bottom of the screen See below Then use the arrow keys to move to appropriate parameters to edit After typing in new values move back to highlight the distributions name if you want to see a Plot of what you have created or press the ESC key to choose another model parameter ESC always either backs up in the program or terminates an ongoing process POP III always remembers the values for each distribution of each parameter so switching back and forth between distributions is easy Editing Adult Male Harvest Survival Rate Distribution Chosen NORMAL 49 80 A x Siecl IDE FE 11 90 Uniform Normal Cumulative Plot lt Arrows gt lt Esc gt The Editing
5. Geometric Mean 104 88 Arithmetic Mean Geo Mean Deviation 18 66 Standard Deviation Skewness LL VO Kurtosis The basic rules are If the distribution of historic values is much less peaked than a normal distribution kurtosis lt 2 25 the distribution is first assumed to be uniform But if the historical distribution leans too far to the left or right skewness gt 0 5 then a cumulative distribution is used In the above example note that the kurtosis is above 2 25 so it is too peaked for a uniform distribution However it is too skewed for a normal distribution Therefore POP III will choose a cumulative distribution You may of course override that decision if you choose POP III s skewness and kurtosis thresholds are somewhat arbitrary but based on experience and are meant to give a very good initial estimate You re probably wondering why the geometric mean and geometric mean deviation are calculated There are two reasons The geometric mean is actually the correct statistic to use when analyzing rate values Schoen 1970 Even if it wasn t the geometric mean is a better more robust indicator of central tendency for most biological data that we run into than is the arithmetic mean The pure arithmetic mean is too strongly influenced by outliers Note the 180 rate from the above data set how often do you expect almost every female have twins If you have reason to believe that your distribution is normal but you reall
6. III after POP II POP III offers a convenient way to determine the parameter distributions by running POP II first When you run the POP II program it will store its results in a temporary data file called TEMP SIM POP III can read this file and make intelligent decisions on what kinds of distributions of the various parameters will be the most appropriate and what the parameters should be You are of course free to change these during the Editing process So after running a POP II simulation immediately eXit that program and start POP III Ask to Load POP II Results If the program says that there are no results to be found you probably have changed directories or changed floppy disks or perhaps the TEMP SIM file is on a RAM disk In this case use the Utility DOS Shell option to leave POP III temporarily change the directory type EXIT to return to POP III and continue Assuming that you can Load the previous Results the program will automatically create a POP III data set from the data in the TEMP SIM file and you will be ready to run You should probably Save the newly created data set just in case 3 2 3 Using POP III As A Stand Alone Program If you are not using POP II in conjunction with POP III the process is easy Simply start POP III and either Create a new data set or Load one of the existing data sets from disk When Creating a new data set or Editing an existing one the program will prompt you for information on what types
7. POP III but your version of POP II is too old You have encountered an error I did not anticipate Please report error number to Fossil Creek Software If you get this message I really want to know about it Your simulation produced numbers too big for POP III to handle Please divide your segment sizes by 10 100 or 1000 Under extreme circumstances you may have to scale your population sizes down Your computer will not display this program s graphics If you have a Hercules display have you loaded MSHERC Your computer presumably either has no graphics capability or you neglected to run the driver MSHERC first NOTE Any other warning messages should be self explanatory Let s hope they are 4 6 RECENT CHANGES TO POP III 27 Version 0 93 to Version 1 0 1 Qi od Go tS The menu structure was completely revised to a bounce bar design and to be more like Microsoft Windows in terminology and to be compatible with POP II Version 1 0 should successfully read any POP II version 7 data set Calculation and display of sex ratio information was added You can send the data listing or tables to your screen your printer or a designated disk file Documentation was revised 28 5 0 RESOURCES FOR FURTHER LEARNING POP III is meant to be a stand alone program in the sense that no additional programming or analyses are required However it does not teach you how to use DOS or your computer Please refer to your DOS man
8. POP III uses a binning formula to determine the number of bins and other heuristics to determine the graph s scale As you may have noticed POP III plots the graph with its scale prior to the sampling The number of bins is derived from Bins 2 Vn after Hoaglin et al 1983 Actually they recommend this formula for N lt 50 but I like it regardless In any event if the distribution is too narrowly confined some of the bars may go off the top of the screen during sampling but usually not by much You see there is no way of knowing exactly what s going to happen until it happens in Monte Carlo that s just the way it is 21 4 SELECTED TOPICS After you have played with POP III for a while you should digest the rest of this documentation It will complete the proper perspective one needs to use POP III efficiently and effectively Efficiently means getting the most out of the program with the least effort Effectively means understanding the program s assumptions and limitations to get what you want 4 1 POP III s ANALYSIS OF POP II S SIMULATION RESULTS When reading the results of a previous POP II simulation POP III makes decisions about the most appropriate parameter distributions to use The underlying statistics come from POP II s output and will be shown on the editing screen For example suppose a particular young per hundred females data set looked like this UNDERLYING STATISTICS N a iy Range 88 00 to 180 00 Median
9. normal distribution MDEER RND PROBABILITY DENSITY FUNCTION AFTER 200 SAMPLES ihe Young per 100 Females Figure 7 An example of POP III s cumulative distribution At least one special case needs to be covered the truncated normal distribution We may define this distribution for postharvest survival for example a mean of 15 percent and a POP III type standard deviation of 10 percent This implies that 99 4 of the survival rates fall within the range from 5 to 25 percent Statistically speaking we should also expect that some small percent of the cases fall below zero however we know that the survival rate can never be below zero POP III knows this too and always assures that the rate will not be negative you need do nothing special Note that the flip side is also true the normal curve must be truncated at 100 for cases of survival Figure 8 shows an example of just such a case MDEER RND PROBABILITY DENSITY FUNCTION AFTER 200 SAMPLES 21 Preharvest Adult Female Figure 8 Example of POP III s truncated normal distribution 3 1 3 Analyzing the Results from the Samples So now we have our model we have our distributions we have sampled from them such that each sample results in a single outcome and we have a set of those outcomes We can collect all of these outcomes sort them and calculate various statistics from them We will know for instance what the whole range of answers is as well as the relative chance of
10. section also provides access to controlling the number of trials samples and years of simulation as well as a choice of Fixed or Randomized starting conditions Randomized is the default choosing this option will ensure that every simulation will start with a truly random number of animals etc The Fixed starting will still be a Monte Carlo simulation but the sequence of random numbers generated will always be the same every time you run the simulation You would use this option to test the sensitivity of changing single parameter values to ensure that the differences in results would be completely attributable to that parameter change Note that this will not be true if you change from one type of distribution to another because of the way that POP III uses random numbers in the calculation sequencing If you choose to see a Narrative style during the Run the program will pause after each set of samples to display the distributions and values it used Pressing any key except ESC will proceed to the next set of samples Pressing the ESC key will terminate the detailed display but continue the Simulation Pressing ESC again will terminate the Simulation completely If you terminate the simulation you will not be able to view any results Only by letting the process continue to completion will results be available to print or plot If you choose to plot any individual distribution or a sample of the results you must keep one thing 20 in mind
11. 1994 Importance of scientific uncertainty in decision making Environmental Management 18 2 161 166 Rubinstein R 1981 Simulation and the Monte Carlo Method Wiley New York 278 pp Schoen R 1970 The geometric mean of the age specific death rates as a summary index of mortality Demography 7 3 317 324 Simpson G G A Roe and R Lewontin 1960 revised Quantitative Zoology Harcourt Brace New York 29 Thank You for Using POP III Printed on Recycled Paper 30
12. Edit allows editing of your data set List displays the file to your screen printer or another formatted disk file Run executes the simulation View displays the tabular or graphic results Utility allows you to change directories through a DOS Shell change graphic modes and turn the sound or color on or off Finally eXit does just that Commands may be selected either by using the arrow keys followed by an Enter or by using the hot letters that are bolded on the screen Commands will appear with their hot letter bolded on the screen only if it would be appropriate to execute that command at that point in your sequence of doing business For example you cannot View the results if you have generated none 3 2 1 Typical Program Flow A typical program command sequence might be to Use File to Create a new data set or Load a data set from disk 18 List to find current values Edit to update or correct errors Use File again to Save the data set on the disk to be safe Run the Simulation View the resulting Tables and Graphs Edit to make a change Run the Simulation again Save the data set on disk for later use eXit the program and return to the operating system There is one additional control command that you should know The message Press Any Key To Continue will appear in order to freeze the screen display At this point you may either choose to copy what is on the screen or simply continue with the program 3 2 2 Using POP
13. II there are three distributions to choose from uniform normal and an arbitrary cumulative distribution These should each be understood The uniform distribution is defined solely by its upper and lower bounds for example you might say that you know that subadult survival rates will vary from 50 to 90 with no rate being more likely than another see Figure 2 The uniform distribution is the least information that could be supplied It is also the distribution of choice in the rare case that you wish to use a constant value for a POP III model variable Simply make the lower and upper limit the same The normal Gaussian distribution is so common that it is truly normal though there is no reason to believe that animal population parameters must necessarily assume a normal shape This distribution is defined by a mean and standard deviation around that mean POP III actually uses two times the standard deviations 2 SD from the mean as its standard deviation therefore 99 44 of all the cases should be found within POP IIT s standard deviation from the mean Figure 3 is a typical normal distribution with a mean of 50 and a statistical standard deviation of 15 a POP III 2 standard deviation of 30 Why use two standard deviations instead of one I have found that people typically think in terms of or visualize two SDs when they think about their data That is people think about a bunch of data and say Yeah that s a normal distribution a
14. OP III If you feel that you have discovered a problem in the software or documentation please call us We will make every effort to repair any bugs that are discovered and provide you with a working solution as soon as possible Fossil Creek Software is also interested in your ideas for additional software products that would prove useful to you Let s talk about them Arrangements may be made for the author to come to you or vice versa for presentations or instruction in modeling with or without POP III Contact the author for more information at the number above or at FCS FossilCreekSoft com Also see http p2 fossilcreeksoft com DISCLAIMER Fossil Creek Software and or any of its program authors shall have no liability to customers with respect to any loss or damage caused directly or indirectly by programs distributed by us Sorry but it had to be said Various hardware and software items may be mentioned in this documentation that are trademarked products of other companies TABLE OF CONTENTS INTRODUCTION sia dac a da data a a cdi da la ied a i 1 121 How POP Works asi ice eat he aes ua ada ets oes a t aes eae rr a z 2 12 System RECULEGERE DES osses mt a dl ga pl claca ala sata ala ae e a 4 1 3 What to Expect in This Documentation nenea amana nana en eennaee 4 GETTING STARTED bo it ara g tit aa a al in la aie gi 5 2 1 Backing Up Your Master Diskettes 5 19 ras sata cai 00 aaa da it 0 a 5 2 2 Diskette Conten
15. POP II POP III s harvest survival rate for each population segment should reflect all forms of harvest loss including wounding or crippling loss Step 4 After the harvest the postseason natural mortality is calculated and subtracted from the population just like the preseason mortality Step 5 The next to last step in the biological year is to calculate the reproductive crop The sum of the pregnant females is multiplied by the reproductive rate and split using a fixed 50 50 sex ratio Step 6 The final step in the simulation is to move the previous year s young now yearlings into the appropriate adult segment POP III goes through the above steps multiple times using survival and reproductive rates sampled from user supplied distributions for these parameters After many hundreds of sample runs the results are summarized in tabular and graphic form By the way there is no reason that POP III s biological year could not be reinterpreted if you have a population that does not fit the above description For example if you are working with an unharvested population just set the survival rates for the harvest period to 100 Or simply divide the year into three other times Or just be creative 1 2 SYSTEM REQUIREMENTS POP III requires the following hardware and software An IBM Personal Computer or compatible that runs MS DOS or PC DOS Version 2 11 or later At least one floppy disk two are recommended e 320 kilobytes
16. d turn on your computer b Insert your blank diskette in drive B c Type FORMAT B S You may refer to your operating system manual if you wish more detailed information on the FORMAT command You must use the S parameter of the FORMAT command since it will place the required DOS system files onto your working copy of the POP III disk Formatting will take a couple of minutes d Type COPY GRAPHICS COM B V This will copy the graphics printer driver to your diskette Remove the DOS diskette from your disk drive and replace it with your master POP III diskette f Type COPYPOP3 B This will copy files from the master POP III diskette to the working copy g Remove the master POP III diskette and put it away someplace safe Remove and label the new copy you just made in drive B Insert this new working copy in your A drive and turn your computer off Wait at least 10 seconds and turn on your computer once again POP III should begin all by itself h You should label your working copy of POP III You should not use a write protect tab on your working diskette as you will be storing data sets on it 2 5 SETTING DOS VARIABLES If you are using POP III on a hard disk computer it may be necessary to add one command to your AUTOEXEC BAT file in order to use the UTILITY command to go to DOS Should you find that trying that option does not work or you receive a Bad or Missing Command Interpreter message add the following line in
17. ding of the Monte Carlo technique is really a prerequisite for using this model wisely so a brief explanation is provided Use of the program differs somewhat depending on whether POP III is used as a companion to POP II or being used in a stand alone mode This difference is explained further in Section 3 Section 4 is less about the program and more about the perspective one should develop in reviewing the results of a Monte Carlo analysis It also provides references if you want to learn more about the techniques POP III employs to model populations 2 GETTING STARTED The following is a summary of the technical information necessary to install and run POP III on your IBM compatible microcomputer Before you do anything with POP III please read these instructions Also see the README file on the distribution diskette for any late breaking news Please consult your DOS documentation if you are unfamiliar with any of these instructions 2 1 BACKING UP YOUR MASTER DISKETTES You have been sent a write protected master copy of POP III A working copy of the program must be created on a new diskette before you use it in your everyday work The procedure you need to follow depends on the kind and number of disk drives your computer has Most systems have at least one floppy disk drive some have two or more Some systems may also have a fixed or hard disk drive Procedures have been provided for systems with either setup You should use the procedur
18. e future uncertainties with POP III but we can better understand them Improved understanding gives us a better foundation to accept or reject the risks POP III offers several substantive benefits over traditional approaches to population modeling Among those benefits are TOP LEVEL PERSUASIVENESS POP III helps to lay out defendable management options to administrators and the public MORE ROBUST PREDICTIONS POP III enables establishment of sound harvest season quotas and helps to provide input to federal planning and impact assessment GREATER UNDERSTANDING OF POPULATION DYNAMICS POP III allows you to integrate your understanding of population dynamics with applied population management EXPLICIT ACCOUNTING OF UNCERTAINTY POP III accounts for two kinds of uncertainty uncertainty about what may happen in the future and uncertainty about the nature of the model itself EASE OF USE Historically agencies have not been able to allocate resources to this kind of analysis Now they can POP III makes dealing with probability theory extremely easy 1 1 How POP III WORKS All models may be characterized by their breadth and depth Breadth refers to the span of elements the model encompasses depth refers to the degree of detail embodied in the elements POP III is a compromise between many explicit events that may occur to a population in any given year and a smaller set of those events that has generally proven satisfac
19. e that applies to your computer If you follow the instructions carefully you should be able to create your working copy of POP III in just a few minutes If you consistently have trouble please seek help from a friend or give us a call 2 2 DISKETTE CONTENTS Please see the disk file README for current diskette contents and documentation updates 2 3 INSTALLING POP III ON A HARD DISK SYSTEM If your computer has a fixed disk use the procedure below to make a working copy of the POP III program disk a Turn on your computer and load DOS from the fixed disk b Make a subdirectory for POP III by typing MD POP3 Then change to the new POP III directory by typing CD POP3 NOTE If you plan to use POP III in conjunction with POP II you may wish to change to your POP II directory instead of making a new one for POP III c Put the POP III diskette in drive A and type A COPYPOP3 C You should get a message like xx file s copied d Remove the master POP III diskette and put it away someplace safe 2 4 INSTALLING POP III ON A FLOPPY DISK SYSTEM If your system has two disk drives use the procedure below to make a working copy of the POP III program disk You ll need a copy of MS DOS or PC DOS and one blank diskette to make your working copy This procedure will copy the necessary system files and POP III files from the master diskette you have been sent onto a single diskette a Insert your DOS system diskette in drive A an
20. et a level of precision and speed you are comfortable with The more samples you choose the smoother the histograms of results will be The maximum number of trials allowed is 10 The maximum number of samples per trial is 200 What about the number of years in the simulation For most managed populations I would suggest one or two years to match the planning horizon More years is better for research models and for populations that have only a few individuals and risk collapse Again the specific choice is up to you One year is the obvious minimum 100 years is POP III s maximum 4 4 WHERE DO WE GO FROM HERE The Monte Carlo approach and our basic population model are just fine But we need to more closely examine the way they are linked together In general it is wrong to construct our estimates of parameter distributions independently of one another It might be more reasonable to expect postseason survival rates to be correlated between population segments It also may be the case that reproductive rates would be correlated with previous survival rates These dependencies have not been incorporated into this release of POP III 26 In addition there is good reason to believe that most populations exhibit some form of persistence This persistence actually represents the natural inputs to the system such as rain snowfall hunter pressure or disease and may be related to what we typically call cycles In Monte Carlo terms long strea
21. forced to choose a tighter set use the average standard deviation 1580 in the above table You can calculate approximately what your odds of being right are by looking at the cumulative distribution If forced tighter yet choose the smallest SD 172 below but you are certainly guaranteed to be wrong Comforting isn t it 16 CHANCES OF ACHIEVING VARIOUS POPULATION SIZES AND SEX RATIOS OVER ALL 2000 RUNS FOR MDEER RND 03 07 1994 09 44 46 Sex Ratio Will Exceed Average Pop Size 12061 Standard Deviation 172 Standard Range is from 11889 to 12233 3 of the average Probability of extinction based on all runs 0 Note that the population sizes and sex ratios shown in the above box are not related to one another on the same line That is you have a 10 chance of having a population greater or equal to 14025 animals You also have a 10 chance of having a sex ratio greater than or equal to 45 But the two do not go hand in hand the 14025 animals will not have a sex ratio of 45 They will have their own distribution of sex ratios but that information is not contained in the table It is no surprise that the distributed inputs have yielded a distribution of possible outcomes The traditional best estimate method would have ignored the possibility of extinction although it is zero as shown here A single best answer has been replaced by a range of possible futures that better estimates the uncertainty in your data and the risks tha
22. ion need not be symmetric like a normal distribution as in the example above In fact the 50 percent probability value need not be present at all see Figure 4 12 Can we really get away with using only six points in our cumulative distribution The best answer is that we would probably be fooling ourselves if we tried to be more specific We are better off realizing that we are going to be imprecise and keep things relatively simple 3 1 2 Sampling from the Distributions Now we have distributions of our variables that are quantitative representations of the uncertainties in our population model We can use any of the three distribution types discussed above With these known or hypothesized parameter distributions we can run our model over and over again randomly sampling from the distributions each time This process is repeated several hundreds or thousands of times to ensure that the entire range of possibilities is covered Figures 5 6 and 7 illustrate typical samples for our three distribution types all generated by randomly sampling each one 200 times Note that given a limited number of samples the distributions will only approximate a smooth curve 13 MDEER RND PROBABILITY DENSITY FUNCTION AFTER 200 SAMPLES 36 Adult Female Harvest Figure 5 An example of POP III s uniform distribution MDEER RND PROBABILITY DENSITY FUNCTION AFTER 200 SAMPLES al Adult Female Harvest Figure 6 An example of POP III s
23. ks of good or bad luck are the rule not the exception Perhaps future versions will include these features and others in the works but remember what Murphy said The future is uncertain you can count on it Now you can assess the risks intelligently 4 5 WARNING MESSAGES Most data input errors do not issue error messages Instead the question prompt is repeated or your entry is reset to be within some predefined range Always use the List data set option to display and double check your input data Error messages are There is a problem reading from or writing to your disk Perhaps your disk is full write protected or not ready Could be lots of things Double check your diskette drive door etc Name is an illegal data set name Please re enter File names must be legitimate DOS names entered without an extension There are no RND files in your current directory Please use the UTILITY DOS option to change directories There seem to be no POP III data files with an extension of RND on your local working directory Your printer doesn t seem to be ready Please correct to continue or press ESC Check out your printer There is a problem writing to filename LST Perhaps your disk is full write protected or not ready Could be lots of things Double check your diskette drive door etc You are using the wrong version of POP II Please use Version 7 0 or later You are trying to load POP II results into
24. ll right but they characterize the tails of the distribution by the extremes not one SD from the mean because they think about the extremes the best and the worst that has happened to the population Therefore when POP III says standard deviation the program really means two SDs from a purist s point of view It s rather like thinking of the bounds for a uniform distribution but recognizing that the frequency of events is more like a normal distribution It is interesting to note that constructing a data set with strictly uniform distributions produces results that tend toward a normal distribution actually lognormal perhaps In fact the method of producing a set of normal deviates besides having children is to multiply two uniformly distributed sets together POP III uses a complicated variation on this theme to calculate normally distributed variables The last of the three distributions the arbitrary cumulative distribution is the most flexible but perhaps the most foreign and most difficult to explain Using only up to six coordinate points you can approximately fit both a uniform and a normal distribution as well as any other data set you want In fact it is probably the distribution that is most correct for ecological data What data really has a uniform or normal distribution anyway 10 PURE UNIFORM DISTRIBUTION 35 30 F R as E Q z U E s N C u Y 5 lt O4ZMCOMAT eee p AAL EEEE o
25. now that survival and reproductive rates are not constant from year to year for an animal population If we have extensive data collection or modeling efforts underway we even have some idea what those rates have been in the past Even if we have little in the way of hard data we still probably have some idea about the range of rates likely in a population from reviewing the literature talking to our peers or reviewing data from a neighboring or similar population Shouldn t we just take the most likely value for each parameter and come up with a most likely result In the past choosing the most likely approach was the way to go It was simpler to do and perhaps simpler to understand The apparent certainty was comforting especially if the future looked rosy But choosing the most likely approach would also tend to underestimate the risks and it would be like putting on blinders to the information we already possess For example it shouldn t be too hard for the informed manager to say that a reasonable harvest rate for adult males will be 10 But there is some chance that it could be 7 or 15 and virtually no chance that 25 will be harvested Though uncertain this is valuable information that can help assess future probabilities Why throw it away An expert s estimates of the uncertainties of population dynamics is valuable information So how do we quantify our uncertain information We construct a probability distribution In POP I
26. obtaining any single result We can even assess the probability of a population being completely eliminated You may have wondered why POP III makes multiple trials runs each taking a set of samples Why not one run with all the samples By making several small trials each with the same sample size instead of a single large one we can obtain information on the adequacy of our sample size Since a Monte Carlo approach is like an experiment each experiment can have its own variability as shown in the shaded box that follows 15 STATISTICS FOR 10 TRIALS OF 200 SAMPLES EACH FOR MDEER RND 03 07 1994 09 44 46 Trial Avg Pop Size Std Dev Avg Sex Ratio Std Average Each trial shows a fairly large degree of variability as demonstrated by its standard deviation a real standard deviation not a POP III type SD If we average these ten averages we get a new standard deviation significantly smaller than for any single trial For example the following shaded box shows a typical set of final results It shows a standard deviation of 172 that is a better estimate of the mean than the 1580 above However remember that it is still only a central tendency not the expected value If you are being asked for a single population size value because the game commission just can t handle a range go ahead and pick the mean but first try qualifying it by putting a 20 80 bounds on it This means you ll have a 60 chance of being correct right If
27. s How Much Is Enough 0 eee eeeeeeeeeeseeeeeeenaeenseeeeees 23 4A Where Do We Go From Elere iain tet connec aaa a tatele aha aa Bin iau nai ba pad 23 4 5 Warning Messages orno neiro eii R EE da a 03 aaa ada a dia 24 4 6 Recent Chan ges to POPE nien ensinei Da a i At vi aaa 25 RESOURCES FOR FURTHER LEARNING nenea eee na nana 26 ii 1 INTRODUCTION POP III is a computer program designed to simulate the dynamics of wildlife populations under uncertain futures POP III has been fashioned especially to help wildlife resource analysts make management decisions in risky environments In addition it is used in both research and college level teaching POP III is the offspring of and companion to the POP II program that has its strength in analyzing and simulating the past POP II and similar programs makes the projection of population response to management decisions trivially easy But POP II s projections are misleadingly precise because they discount the risks of variations in the underlying assumptions concerning both the future and the model Taken as a whole the web of uncertainty can in some situations literally multiply into disaster The weakness of previous approaches has little to do with our mathematical ability to model populations Rather each estimate of future mortality and reproductive success is fraught with such a range of possibilities and probabilities that a corresponding range of risks and rewards results For e
28. t e e Arr ArT e eee Pa iai ei 0 0 10 0 20 0 30 0 40 0 SEI El 60 0 70 0 80 0 90 0 100 0 ADULT FEMALE HARVEST SURVIVAL RATE Figure 3 Example of a pure normal distribution 11 Let s see how the cumulative distribution works A typical cumulative distribution might be described as follows and in Figure 4 Young per 100 Females Probability Interpretation 40 1 00 Certain to have more than 40 young 100 females 50 0 30 30 percent chance of getting more than 50 young 100 females 55 0 20 20 percent chance of more than a 55 100 rate 65 0 10 10 percent chance of more than a 65 100 rate 75 0 05 5 percent chance of more than a 75 100 rate 90 0 00 No chance of more than 90 young per 100 females Y 0 U N G P E R 1 1 8 F E M A L E Ss 6 8 6 7 8 6 8 5 6 4 4 3 0 2 PROBABILITY OF EXCEEDENCE Figure 4 Example of Cumulative distribution Please note a few things about this type of distribution First we must always start and end with two certainties 100 percent a probability of 1 00 and zero Also as you can see the values are arranged in a sorted order Using this format you must always estimate values in terms of a greater than or equal to property Therefore we make no specific estimate for achieving any specific reproductive rate this would be too tedious Instead choose up to four inflection points to capture the essence of the distribution Finally note that the distribut
29. t uncertainty entails If you think this is just a crapshoot you re right Monte Carlo analysis gets its name from the seventeenth century study of the casino games of chance However in most games of chance there is a known theoretical value for the outcomes whereas in population analysis there is no such equivalent 3 2 RUNNING POP III There are basically two ways to start using POP III One way depends on the prior use of POP II the other does not If you have been using POP II to simulate a population s past use the method in Section 3 2 1 If you want to use POP III in a stand alone fashion use the second method in Section 17 3 2 2 First the basics that everyone should know To start POP III if you have a floppy system put your POP III working diskette in drive A turn on the printer and computer and the AUTOEXEC BAT file should do the rest If you have a hard disk go to your POP III directory with the CD command and type POP III Should you exit POP III for any reason you may later type just POP III or POP3 to begin again POP III is a menu driven system The menus are arranged hierarchically The main menu commands are shown in the next shaded box POP III MAIN MENU Version 1 00 Copyright 1990 93 PLEASE DO NOT MAKE UNAUTHORIZED COPIES OF THIS PROGRAM Help File Edit List Run View Utility eXit POP III File allows you to retrieve an existing disk file create a new one or save an edited file
30. th certainty but we can gain some insight about the population consequences of the uncertain future we face Monte Carlo analysis is a surprisingly easy way of quantifying the future possibilities It involves four steps 1 formulating the population model 2 assigning parameter distributions to the uncertain variables in the model 3 sampling from those distributions to determine the outcome for a group of samples and 4 analyzing the results of those samples In POP III the first step has been completed The model has been formulated to be nearly the same as POP II That is we have one harvest season two seasons of natural mortality one preharvest and one postharvest and a reproductive event We subtract animals from the population to account for mortality and then add newborns to see what the overall effects are In POP III we have divided the population into three segments young of the year adult males and adult females Unlike POP IL this program uses survival rates instead of mortality rates Expressed mathematically through time t this would look like Segment i Segment i preharvest survival rate harvest survival rate postharvest survival rate That s the easy part In fact compared to the complexity we could have chosen for a population model this is about as simple crude as you can get However it is surprising how well such simple models work 3 1 1 Assigning Parameter Distributions We k
31. that looks like this note the tie for some ranks Original Data Sorted Data Rank Exceedence Value 158 436 1 05 306 381 2 Pet ab 204 333 3 16 204 325 4 21 214 316 5 26 269 306 6 32 316 269 8 42 436 269 8 42 260 260 9 47 165 259 10 53 333 214 11 58 381 204 13 68 325 204 13 68 158 177 14 74 269 169 15 79 177 165 16 84 169 158 18 95 259 158 18 95 The resulting cumulative distribution is shown in Figure 9 23 Creating a Cumulative Distribution 460 440 420 400 B a Original 380 i Constructed 360 340 320 300 280 260 240 220 200 180 160 140 Y o u n 9 P e r 1 8 8 F e m a 1 e s 6 6 6 4 Probability Figure 9 Constructed cumulative frequency distribution 24 Next recommend calculating the following statistics Arithmetic Mean AM gt x N 255 72 Geometric Mean GM x x x 243 85 Standard Deviation Zx N 79 46 Geometric Mean Deviation x GM N 67 63 Skewness x AM N 0 54 Kurtosis x AM f N 2 43 You can plot a frequency distribution to use in addition to the rules POP III uses to decide if you are dealing with a normal or uniform distribution I recommend calculating the number of bins as the closest integer to 2 VN which is 8 for this example Therefore we can tally the number of observations as 25 Constructina a Frequency Distribution
32. tory to model Though not especially detailed POP III captures the essential nature of most populations under uncertain conditions The simulation may be divided into six main steps that occur through the passage of a biological year Figure 1 These six steps are tracked by POP III in a simple bookkeeping fashion animals are subtracted for each different form of mortality and added for natality i Step 1 Determine number of animals Step amp i Step Z Remove preseason natural Begin again mar tality Step 3 Subtract horvest NUMBER OF ANIMALS Step 4 Remove postseason natural mear tality fim Step 5 Coleulate reproductive erop TIME Figure 1 A schematic of POP III s representation of the biological year Step 1 The first thing that needs to be done is to calculate the initial population This is the number of animals in each population segment at the beginning of the biological year immediately after the young are born Step 2 The next step is to remove the animals lost to preseason natural mortality from the beginning of the biological year to the harvest period For example if the biological year starts in June and the harvest season begins in October we need to know how many animals will die before the harvest Natural mortality includes all forms of mortality during this period such as accidents predation disease rutting poaching and so on Step 3 Next the harvest is subtracted NOTE that unlike
33. ts 322 oe dey eee eye seeds ee ace Da a a e i n d i esa Ta 5 2 3 Installing POP III on a Hard Disk System eee eee 5 2 4 Installing POP III on a Floppy Disk System os sseesssessseessessseessseessseesseesseesserssseesssees 6 2 3 Settna DOS Var alles cs seats cea suede saan uta 650 i ateu dai p tal E pi st dei a a aai 6 2 6 Starting POP sana n eva ii da a mari ad aaa a i ata a o a 7 YOUR FIRST POP III SESSION neta ine atat ia a pad Ri aaa a pa c i 8 3 1 A Primer on Monte Carlo Techniques co pate oa n a inta le ai Biata 08 8 3 1 1 Assigning Parameter Distributions ccceeccssscecesccecsscceesscceesscceesscceeseeeeeeceesues 8 3 1 2 Sampling from the Distributions sm apicole 12 3 1 3 Analyzing the Results from the Samples sseeeseseseseesesseessesressessresressessrersresseseessee 13 3 2 Rimming POP score e ina rata lata 80 a i ni ii a ia lg ra la 16 32 1 Typical Program FLO asa da ce ea da sata aaa da d d i aaa dada ia odes aaa 17 32 1 Using POP after POPII ni ana pac va tao aia ip a n O ancanms 17 3 2 2 Using POP III as a Stand Alone Program sesesssessseeeesseessressesseesseeessseessressseese 18 3 3 Vital Information Regardless ase a a 3 at o nui a alina aaa dai ten 18 SELECTED TOPICS n caiet d ia aa n i ta a 8 cin i cad 20 4 1 POP III s Analysis of POP II s Simulation Results eee nana 20 4 2 Constructing Your Own Distributions men nenea nana emana ana eee 21 4 3 Trials Samples and Year
34. ual for operating system questions In addition the ambitious reader is referred to the following for more information on simulation using Monte Carlo and related modeling techniques Box G E P and ME Muller 1958 A Note on the Generation of Random Normal Deviates Annals of Mathematical Statistics 28 610 611 Center for Conservation Biology 1988 A Computer Model of Population Persistence Department of Biological Sciences Stanford University Stanford CA 20 pp Gauch H G Jr and G B Chase 1974 Fitting the Gaussian Curve to Ecological Data Ecology 55 1377 1381 Hertz David B 1979 Risk analysis in capital investment Harvard Business Review Sept Oct 1979 pages 169 181 Hoaglin D C F Mosteller and J W Tukey 1983 Understanding robust and exploratory data analysis John Wiley and Sons Inc New York 447 pp Macaluso Pat 1983 Learning Simulation Techniques on a Microcomputer Tab Books Blue Ridge Summit PA 139 pp Macaluso Pat 1984 A Risky Business An Introduction to Monte Carlo Venture Analysis Byte Magazine March 1984 pages 179 192 Perez Trejo Francisco 1986 User Manual POPDYN Population Simulation Model Department of Range Science Colorado State University 15 pp plus appendices Peters James A 1971 Biostatistical Programs in BASIC Language for Time shared Computers Smithsonian Contributions to Zoology Number 69 Smithsonian Institution Press Washington Reckhow K H
35. xample we can provide an educated guess of the most likely current population sizes preseason and postseason mortality rates harvest rates and reproductive rates This most likely scenario may appear rosy But the future depends on whether our most likely estimates come true If each of five guesstimated independent rates has a 75 chance of being correct there may be only a 0 75 X 0 75 X 0 75 X 0 75 X 0 75 chance that all five estimates will be correct Therefore our most likely estimate actually turns into a paltry 24 likelihood of being right In fact using most likely inputs essentially assures that the answer will be wrong much of the time What can we do to correct this situation We could make more accurate forecasts Huge data collection efforts might provide more accurate estimates of each of our parameters But we don t have the money to do so nor can we expect the future to really be more certain because of our efforts We could always rely on worst case estimates of our parameters Though this would help cover our ass it would not lead to the most productive use of resources in times of scarcity We could look at three estimates the worst case the best case and the most likely This is a good practice in assessing the range of possibilities but poor in providing insight to which possibility truly has the greatest expectation Population modeling with POP III is one answer to these troubling issues We cannot eliminat
36. y don t have enough observations to prove it the geometric mean is a better indicator of the mode than is the arithmetic mean Also note in the above statistics the standard deviation is the deviation about the arithmetic mean and the geo mean deviation is the deviation around the geometric mean 22 4 2 CONSTRUCTING YOUR OWN DISTRIBUTIONS You ve seen how POP III analyzes data to construct distributions but suppose you want to use POP III without following on the heels of POP II You have a bunch of data that you want to construct distributions for but don t know how to get started Certainly there are many good texts on exploratory data analysis but to get going here is one suggested path Let s assume you have several years of representative fecundity data The first steps should be to sort it from high to low and calculate associated exceedence values Exceedence values may be calculated in several ways but the best in this case is to divide the rank by N 1 to determine the probability of equaling or exceeding the observations for a sample of values This leaves the ends zero and 1 unconstrained and left for you to decide By this I mean you are only aware of a limited sample of possible observations you haven t seen everything yet Therefore you must make decisions as to what the minimum and maximum values might be If ties exist the probability value is the same For example suppose you have a bunch of turkey clutch size data
37. your AUTOEXEC BAT file SET COMSPEC C COMMAND COM This should cure any problem of this sort 2 6 STARTING POP III Start POP III simply by typing POP III or POP3 POP III is a batch file that you can customize as necessary POP3 is the name of the self contained executable program NOTE If you have a Hercules monitor you must type MSHERC first The full command line is POP3 filename M where filename is an optional local file to pre load If used must be the first parameter and be the full file gives help M means use monochrome mode regardless of monitor type This may be good for laptops Example POP3 DEERTEST RND M The menu system explained more fully in Section 3 2 1 should take you from there 3 YOUR FIRST POP III SESSION 3 1 A PRIMER ON MONTE CARLO TECHNIQUES There is little sense in running POP III without some knowledge of what the aim is The following discussion will provide enough to get you started As you read you will need to make one choice that depends on whether you are using POP III in conjunction with POP II or in a stand alone mode Then after playing with the program for a while you will be ready to digest the material in Section 4 of this documentation Making management decisions about animal populations is a risky business One never knows what the future will bring How much snowfall will there be How good a reproductive crop will ensue We cannot know these things wi
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