NOREMARK User`s Manual - Warner College of Natural Resources
Contents
1. Before starting a simulation with a large number of replicates i e gt 500 the user should run the simulation with 5 10 replicates to see how much time the large simulation will take For example if a set of input parameters takes 2 minutes to complete 5 replications then 1000 replications will take about 400 minutes or 6 7 hours You may want to reconsider whether you want to tie up your computer for the next 7 hours The time that a simulation will take depends on the size of N larger values take more time capture probability larger values take more time sighting probability larger values take more time and number of occasions more occasions take more time Also each of the 4 estimators require different amounts of computation and thus take differing amounts of time to compute a single replication Generally Bowden s estimator is the fastest The JHE and the IEJHE estimators require numerical optimization to compute the estimate so take longer The Minta Mangel estimator uses a bootstrap procedure so takes even longer although the amount of time required depends on the number of iterations of the bootstrap procedure that are performed for each replication In summary evaluate the amount of time required before starting a big simulation Estimator Selection Each of the 4 estimators provided in Program NOREMARK have slightly different assumptions and thus apply best to certain conditions The joint hypergeometric estimator as2. Estimate Population Size for No Immigration Emigration with JHE LAAA4AAAAA4AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA AA EXIT The ESC key takes you back one menu screen You can get context sensitive help with the F1 key Nine options are presented for the user to select from To select a choice the user can either specify the first letter of the choice or use the arrow keys to move the cursor to the choice After the cursor is positioned on the desired choice the user hits the Enter key to execute the option For computers with a mouse the mouse cursor can be moved to the desired option and double clicked on the option to select the choice The line Estimate Population Size for No Immigration Emigration with JHE provides additional detail about each of the choices and changes as you move the cursor to different selections from the 9 choices The function key F1 is the help function Context sensitive help can be obtained any time the program is waiting for input by hitting the F1 key A window will pop up on the screen displaying information about the program s request To exit this window hit the Esc key which is equivalent to selecting the Exit option from the menu choices In general the Esc key always takes you back one window to a previous menu NOREMARK Reference Manual 6 The first choice is JHE Closed Population Model Estimation and provides the capability to compute the JHE estimator for a set of
3. with the option to edit each block after entry before proceeding to the next set of 5 The first 5 occasions appear on the screen After the first 5 occasions were entered the Lincoln Petersen estimate is computed for each occasion This output is useful in evaluating whether the correct recapture data were entered To proceed to the next set of 5 occasions select the Proceed option as shown in the following output screen If you select the Edit option you would be given the chance to change the data entered When you hit the Enter key on the last occasion shown on the screen the Lincoln Petersen estimates would be recomputed and you could again evaluate the input Selecting Proceed would allow you to go to the next set of 5 occasions NOREMARK Reference Manual 9 02 01 94 ANS SS S 5S 64444444444444444444444444444444444444444444444444444444444444444444444444444447 5 Mark Resi 444444444444444444444444444444444444444 lations 5 gt 4444444444444444444 444444444444444444 lt More data entry or edit screen t 5 Enter a ti Andrea Neal s M Proceed Edit Alpha leve O05 Enter numb B4444A4AA4LA4AAA4AA4AAAAA4AAAAA4AA4AAAAA4AAA4AA4A4AA Marked Marked Unmarked Lin Pet 95 Confidence Available Seen Estimate Interval The ESC key takes you back one menu screen You can get context sensitive help with the F1 key 44444AAAAAA4A4AAAAAAA4A444444ATOp4444BOot4444Help4444PgUp4444PgDn4444Return4444ESC4 5 5 5 5 5 5 3 5
4. 5 5 5 5 5 5 5 5 5 5 8 The minimum number known alive is reported which is the number of marked animals in the population plus the maximum number of unmarked animals sighted on any occasion This value is a lower bound on the estimate i e the JHE estimate of population size can never be less than this value Next the population estimate is shown with the 95 profile likelihood confidence interval At the top of the above screen the program is requesting whether to proceed or to save the output to a file for later printing or to print the output at this time directly from the program If the File option is selected the output can be appended to the current output file so that several screens pertaining to the same data can be collected together in one output file After you have disposed of the output the next screen allows you to save the input file for later retrieval If you select OK you will be asked for a file name in which to store the recapture data Ideally the file name suffix should indicate that the data are hypergeometric format input data to distinguish the file from others you may create with the Minta Mangel and Bowden estimators The file created here would be compatible with the Immigration Emigration estimator as well I suggest the suffix HYP for hypergeometric To retrieve the data you would select one of the hypergeometric estimators and hit the F2 key at the first prompt for input NOREMARK Referen
5. The latter two estimators do not require the assumption that each animal in the population has the same probability of resighting on a particular occasion as the first 2 estimators require Notation T Number of marked telemetered animals in the population at the time of the i survey i 1 k When the number of marked animals is assumed constant across surveys the value is denoted as T M Number of marked animals in the population that are on the area surveyed at the time of the i sighting survey For all M constant define M M n Number of animals seen during the i sighting survey consisting of m marked animals and u unmarked animals so that n m u f Number of times marked animal i was observed during the k surveys sighting frequencies i J T Note that this is not the same use of as in Otis et al 1978 or White et al 1982 m Total number of sightings of marked animals so that m m Y f u Total number of sightings of unmarked animals so that u Y u where i 1 N T f Mean capture frequency of marked animals m T Sp Variance of the sighting frequencies of the marked animals S Estimators Four estimators of population size for marking and sighting surveys are provided in Program NOREMARK First is the joint hypergeometric maximum likelihood estimator JHE Bartmann et al 1987 White and Garrott 1990 Neal 1990 Neal et al 1993 JHE is the value
6. data Equivalent functions are provided with the next 3 options for computing the Immigration Emigration JHE Minta Mangel and Bowden s estimators The fifth option Design Experiment Using Interpolation for Closed Population allows the user to quickly design a survey using the simulation results from Neal 1990 These simulations were summarized in a dBase file and this option allows the user to interpolate the simulations to provide an idea of confidence interval length for a particular set of parameter values The last 4 choices in the main menu allow the user to simulate experiments These options are useful in the design of experiments that require parameter values outside the ranges simulated by Neal 1990 or to compare performance of the 4 estimators In the following sections the application of each of these options will be demonstrated and details of input and output from them discussed JHE Closed Population Model Estimation When this option is selected the following screen appears 04 20 93 Oe ail ssy2 644444444444444444444444444444444444444444444444444444444444444444444444 4g gagg7T 5 Mark Resight Population Estimation for Closed Populations 5 4444444444444444444444444444444444444444444444444444444444444444444444444 444d 5 Enter a title to identify the data Alpha level for confidence interval construction Enter number of sighting occasions Hit F2 to retrieve an input file The ESC key takes you back one menu scr
7. of N which maximizes the following likelihood NOREMARK Reference Manual 3 k 23 WN M n m jy cea 1 i l N C and the terms are defined for all i 1 to k sighting occasions The estimate can be found by iterative numerical methods Confidence intervals are determined with the profile likelihood method Hudson 1971 Venzon and Moolgavkar 1988 This estimator assumes that all the marked animals are on the area surveyed for each survey i e that the population is geographically and demographically closed and thus N is the same for each survey The number of marked animals M is the same for each survey in the above equation although the probability of sighting animals is not assumed to be the same for each survey An extension allowed in Program NOREMARK is to allow additional marked animals to be added to the population between sighting occasions Thus M replaces M in the above equation but the value of N is still assumed constant across occasions Second the JHE has been extended to accommodate immigration and emigration Neal et al 1993 through a binomial process This estimator is labeled IEJHE and does not assume that the population is geographically closed but the population is still assumed to be demographically closed Assume that the total population with any chance of being observed on the study area is N and that at the time of the i sighting survey N animals occur on the study area I am interest
8. the values reported by NOREMARK are the total confidence interval length as a percent of the estimate not just 1 2 of the confidence interval length Confidence interval coverage of the JHE estimator was not found to differ from the expected 1 coverage rate so coverage is reported as being 1 alpha 100 percent Estimator Simulation The final 4 options in the main menu of NOREMARK allow the user to simulate mark resight surveys This capability is useful in designing surveys when the parameters are outside the range of those allowed for the design option or to compare the performance of estimators for the same input As noted above the design option only provides interpolated output for the joint hypergeometric estimator With the 4 simulation options you can simulate each estimator for a particular set of input values NOREMARK Reference Manual 22 The input for the 4 simulation options is basically the same for each estimator Thus I will only present the input for joint hypergeometric estimator in detail and mention differences for the other 3 estimators The input screen for simulation of the joint hypergeometric estimator is shown below 04 07 94 10 30 26 644444444444444444444444444444444444gdgddgggggdggdgggggdgggggdgggggggggggggggaaT 5 Monte Carlo Simulation of Joint Hypergeometric Estimator 5 Aad ddd ddd add gdg ggg ggg agg gdggagdggagdgagggaggggdgagggagdgggggdgggdggdgdgddgagdggaddaddaddadag 5 Enter the expected
9. to a file 54444444444444444444 lt Enterta its Print Output saved to printer 5 5 Andrea Neal s Mo944444444444444444444444444444444444448 Alpha level for Confidence Interval Construction 0 01 0 50 205 Enter number of sighting occasions 14 Total Marked Marked Unmarked Lin Pet 95 Confidence Occ Marked Available Seen Estimate Interval Total Population Minimum Number Known Alive Total Population Estimate 120 95 CI on Total Population Estimate 109 iL 132 28 Daily Population Estimate gemi 95 CI on Daily Population Estimate Bis T TODAS The ESC key takes you back one menu screen You can get context sensitive help with the F1 key 44444444444444444444444444Top4444Bot4444Help4444 Pgup4444Pgdn4444Return4444ESC4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 9 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 8 13 lower bound on the possible estimates of the total number of animals Next the total population size and its 95 profile likelihood confidence interval is shown followed by the average daily population estimate and its 95 profile likelihood confidence interval At the top of the screen the program is requesting how to dispose of this output You can continue and discard the output or store the output in a file or print the output directly to a printer Minta Mangel Model Estimation When this option is selected the screen that appears is NOREMARK Reference Manual 02
10. values of the parameters for the experiment Guesstimate of population size 45 Expected number of sighting occasions 4 Expected proportion of population to be marked 0 30 Expected proportion of population to be seen on each occasions 0 70 Alpha level for Confidence Interval Construction 0 01 0 50 0 05 Number of replicates to simulate 1000 Random number seed to initiate simulations 4422654 The ESC key takes you back one menu screen You can get context sensitive help with the F1 key 44444444444444444444444444Top4444B0t4444He1p4444 Pgup4444Pgdn4444Return4444ESc4 5 KY 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 9 5 5 5 5 5 J 5 5 5 3 5 5 5 s 5 5 3 5 5 8 The input screen is requesting the size of the population number of sighting occasions expected proportion of the population that will be marked and expected proportion of the population that will be resighted on each occasion Next the level to use for confidence interval construction is entered The number of simulations you request determines precision of results reported If only a small number such as 10 is requested the program doesn t take long and a result that will be quite variable will be reported To obtain more precise results you should specify much larger values such as the default of 1000 although time needed to simulate more replications can be substantial The last input field specifies a random number seed to initialize the
11. 01 94 HG SS oe Rees 644444444444444444444 44444 ggdggdgggggggggggggggdggdgggggggggggggggdggdggdgggggg7T 5 Mark Resight Population Estimation for Minta Mangel Estimator 5 144d ddd gd ggg g ggg ggg ggg ggg gg ggg ggg ggggggggggggggggggggggggggggggggggggggggggggag Enter Enter Alpha Enter 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 9 In the above screen a title to identify the output has been entered The number of marked animals was entered as 25 with 615 unmarked animals sighted during the surveys For confidence interval construction has been entered as 0 05 to obtain 95 confidence intervals Finally the Minta Mangel estimator is based on a bootstrap procedure so the number of bootstraps to perform is requested The value 10 000 is adequate as suggested by Minta and Mangel 1989 number of number of level for number of Enter a title to identify the data Andrea Neal s Mountain Sheep Data marked animals 25 unmarked animal sightings confidence interval construction bootstraps to perform Hit F2 to retrieve an input file 10000 615 OF The ESC key takes you back one menu screen You can get context sensitive help with the F1 key 4aaddgdd ddd gddgddagddagddaddTops444pot4444Help4444pqgup4444Pgdn4444Return4444Esc4 for Minta Mangel Estimator 05 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 8 14 When the user hits the Enter key the program request
12. 44444444444 444d gggggdggdgggggggggggggggdggdgggggggggggggggdggdggdgggggg7T 5 Mark Resight Estimation for Populations with Immigration Emigration 5 44444A4AAA4AAA4AAAAAAAAAAAAAA4AAA4AAAAAAAAAAAAAA4AAA4AAAAAAAAAAAAAAAAAAAAAAAAAA4AAAAA lt Enter a title to identify the data Andrea Neal s Mountain Sheep Data Alpha level for Confidence Interval Construction 0 01 0 50 Enter number 444444444444444444444444444444444444444444444 Torani idence Occ Marked Save data to file for later retrieval x x x 2 Cancel x x x x B4444A4AA4AAAAA4AAAAAAA4AAAAA4AAAAA4AAAAA4AA4AAA4AA44A4A4AAA Total Population Minimum Number Known Alive 99 The ESC key takes you back one menu screen You can get context sensitive help with the F1 key 3 5 5 5 3 5 3 5 3 5 3 5 3 5 5 5 5 5 5 5 9 After you have saved your data or chosen not to the program computes the Immigration Emigration estimates The following screen shows this output 44444444444444444444444444TOp4444Bot4444Help4444 Pgup4444PgdDn4444Return4444ESc4 5 5 3 5 5 5 5 5 3 5 3 5 5 5 5 5 5 5 3 5 8 NOREMARK Reference Manual The minimum number of animals known to be alive is computed with this value serving as a 02 01 94 IES B15 6 S17 6444444444444444444446444444444444444d4ggggggggggggdgdgdgdg744444444g4g4g4gggga7 5 Mark Resight Es5 Continue DO not save output 5on Emigration 5 444444444444444444445 File Output saved
13. 5 5 5 5 5 5 5 5 5 5 5 5 9 3 3 5 5 5 5 5 3 5 3 5 3 3 5 5 5 5 5 5 8 After selecting Proceed for the above screen the user would enter the next set of 5 occasions and then the final set of 4 occasions After the user selects Proceed for the last occasion the Joint Hypergeometric Maximum Likelihood Estimator JHE is computed This numerical optimization can take a few seconds so the user should not expect an instant response The following screen shows the output produced NOREMARK Reference Manual 10 02 01 94 LAYS SG 8 Gs 644444444444444444444644444444444444444ddgdgggdggdggdggdggd7444ggggdggdgggggggaT 5 Mark Resig5 Continue Do not save output Sulations 5 444444444444444444445 File Output saved to a file 54444444444444444444 lt by We alione Output saved to printer 5 5 Enter a tit944444444444444444444444444444444444448 Andrea Neal s Mountain Sheep Data Alpha level for confidence interval construction 0 05 Enter number of sighting occasions 14 Marked Marked Unmarked Lin Pet 95 Confidence Available Seen Estimate Interval 1S Si Minimum number known alive is 90 Population Estimate 100 95 Confidence Interval The ESC key takes you back one menu screen You can get context sensitive help with the F 44444444444444444444444444 Top4444Bot4444Help4444 Pgup4444PgdDn4444Return4444ESC4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 9 5 5 5 5 5 5 5 5 5
14. 986 Modeling demographics of bighorn sheep current abilities and missing links North American Wildlife and Natural Resources Conference Transactions 51 62 73 Miller S D E F Becker and W H Ballard 1987 Black and brown bear density estimates using modified capture recapture techniques in Alaska International Conference on Bear Research and Management 7 23 35 Minta S and M Mangel 1989 A simple population estimate based on simulation for capture recapture and capture resight data Ecology 70 1738 1751 Neal A K 1990 Evaluation of mark resight population estimates using simulations and field data from mountain sheep M S Thesis Colorado State Univ Fort Collins 198pp Neal A K G C White R B Gill D F Reed and J H Olterman 1993 Evaluation of mark resight model assumptions for estimating mountain sheep numbers J Wildl Manage 57 436 450 Otis D L K P Burnham G C White and D R Anderson 1978 Statistical inference from capture data on closed animal populations Wildl Monogr 62 1 135 Press W H B P Flannery S A Teukolsky and W T Vetterling 1986 Numerical recipes the art of scientific computing Cambridge Univ Press Cambridge U K 818pp Schnabel Z E 1938 estimation of the size of animal populations by marking experiments U S Fish and Wildlife service Fisheries Bull 69 191 203 Rexstad E and K Burnham 1991 Users guide for interactive program CAPTURE Co
15. January 25 1996 Gary C White Department of Fishery and Wildlife Colorado State University Fort Collins CO 80523 970 49 1 6678 gwhite cnr colostate edu RH NOREMARK Software Reference Manual White Program NOREMARK Software Reference Manual Gary C White Department of Fishery and Wildlife Colorado State University Fort Collins CO 80523 Key words closure Lincoln Petersen mark resight maximum likelihood population estimation sighting surveys Scientific and Technical Information Estimation of population size of a geographically and demographically closed but free ranging population is a common problem encountered by wildlife biologists The earliest approaches to this problem were developed by Petersen 1896 and later Lincoln 1930 where capture recapture techniques were applied Extensions to the simple 2 occasion Lincoln Petersen estimator were developed for multiple occasions Schnabel 1938 Darroch 1958 for removal experiments Zippin 1956 1958 and for heterogeneity of individual animals Burnham and Overton 1978 1979 Chao 1988 For the capture recapture technique Otis et al 1978 and White et al 1982 provided a summary of the available methods and others White et al 1978 Rexstad and Burnham 1991 describe Program CAPTURE for computing these estimators of population size More technologically advanced approaches to the problem of abundance estimation have incorporated animals marked with radio t
16. am then asks if the input should be saved for later use in the Minta Mangel estimator or also the Bowden estimator The following screen shows this request 02 01 94 TOSS TSS 644444444444444444444444444444ddggdgddggdgggggggggggdggdgggggdggggggggdggdggggdaT 5 Mark Resight Population Estimation for Minta Mangel Estimator 5 Adda dd add gad gag ggg ggg ggg ggg ggg ggg ggg gdggdggdggdggddgddggdggddgddgddaddgddaddadag 5 Enter a title to identify the data Andrea Neal s Mountain Sheep Data for Minta Mangel Estimator Enter n 444444444444444444444444444444444444444444444 Enter n 2 Alpha 1 Save data to file for later retrieval 5 Enter Number x Cancel Populat Percent Complete 0 20 40 60 80 100 SSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS S 4 The ESC key takes you back one menu screen You can get context sensitive help with the F1 key 4aadd add gddg add ggg add agdddddTop4444Bpot4444Help4444Pqgup4444Pgdn4444Return4444Esc4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 Robbins 5 5 95 ConB444444A4444A4A4A4AAAA4A4A4AAAAAAAAAAAAAAAA4A4A4444AAAA 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 9 8 Select OK to save the input to a file I suggest you use the suffix MM for the file extension to identify the file as input for the Minta Mangel or Bowden estimators After you answer this question the program returns you to the main menu Bowden Model Estimation When you select this estimator from the
17. as Bowden s estimator although this estimator is derived under the assumption of sampling with replacement However using this estimator for situations where sampling without replacement is not particularly inappropriate because the estimator would not be particularly biased and confidence interval length would be only slightly larger than the estimator derived under the assumption of sampling without replacement I do not recommend the Minta Mangel estimator because of the poor performance of the confidence interval coverage and suggest that users of NOREMARK use Bowden s estimator if heterogeneity of sighting probabilities is serious or sampling is performed with replacement If there is little or no heterogeneity of sighting probabilities the joint hypergeometric estimator should generate slightly smaller confidence interval lengths than Bowden s estimator because stronger assumptions are made Neal et al 1993 showed that confidence interval coverage drops to 80 for an expected 95 interval when reasonable sighting heterogeneity is simulated The choice of Bowden s estimator over the joint hypergeometric estimator will depend on the degree of heterogeneity in sighting probabilities and whether sampling is performed with or without replacement One additional criterion is useful in deciding between the joint hypergeometric estimator and Bowden s estimator Often conduct of the survey does not fall into logical occasions i e animals may be c
18. capabilities to select choices from a list and input fields interactively The design capability of the program is implemented via a dBase III database named INTERP DBF that the code creates if the database is not present The context sensitive help function is also implemented via a dBase III database HELP DBF which includes a memo field existing in HELP DBT If these files are not present in the local directory the program creates them Numerical optimization is performed with FORTRAN codes for the joint hypergeometric and the immigration emigration estimators For the joint hypergeometric estimator the FORTRAN objects are linked directly into the NOREMARK EXE file For the immigration emigration estimator the NOREMARK EXE code creates an input file TE_NRM INP to the TE_NRM EXE file This file is then executed reads IE_NRM INP computes the estimator creates the output file IE_NRM OUT and exits NOREMARK EXE then reads the estimation results from IE_NRM OUT A golden section search in one dimension Press et al 1986 is used to compute the maximum of the joint hypergeometric estimator The maximum is bracketed with routine MNBRAK then the golden section search initiated NPSOL Gill et al 1986 is used to compute the optimum of the immigration emigration estimator NPSOL is a set of FORTRAN subroutines designed to minimize a smooth function subject to constraints which may include simple bounds on the variables linear constraints and smo
19. ce Manual 02 01 94 16 16 46 6444444444444444444444444444444444444444444444444444444444444444444444444444ag7 5 Mark Resight Population Estimation for Closed Populations 5 4444AA4A4AAA4AA4AAAAA4AAAAA4AA4AAAAA4AAAAAAA4AAAAA4AA4AAAAA4AAAAAAA4AAAAA4AA4AAAAA44A4A4444A44 lt 5 Enter a title to identify the data Andrea Neal s Mountain Sheep Data 27444444444444444444444444444444444444444444444 Alpha 1 Enter n Save data to file for later retrieval Marked Availab 20 L3 38 TsO 57 5 9655 BA Ly 40 69 9 S326 B52 Minimum number known alive is 90 Population Estimate 100 95 Confidence Interval 94 108 The ESC key takes you back one menu screen You can get context sensitive help with the F1 key 5 5 5 5 5 5 3 5 5 5 5 5 5 5 5 5 5 5 5 5 944444444444444444444444444T0p4444 Bot4 444 Help4444Pgup4444Pgdn4444Return4444Esc4 5 3 5 5 5 3 5 3 5 6 5 17 B4444444444444444 44444444 4ggggggggggggggggggdda e6 5 3 5 3 5 5 5 5 5 8 Immigration Emigration Model Estimation When this option is selected the screen that appears is similar to the JHE estimator 11 requesting the title level and the number of recapture occasions After these values have been entered the program requests input for the first 5 resighting occasions as shown in the following screen 02 01 94 LOLS OSS 7 64444444444444444444444444444444gddggdggdggdggdggggggggggggggdggdgggggdgdggggggaT 5 Ma
20. ddition an level for computing confidence intervals has been specified as 0 05 giving a 95 confidence interval Finally 14 recapture occasions have been specified Note that additional information is available on any of these input requests by hitting the F1 Help key A description of the input being requested will be poped on the screen for the user to read To return to entering data just hit Esc to exit the help screen NOREMARK Reference Manual 8 02 01 94 AN BIS S C44 ddd dd ddd ddd add gdg ggg add ggg ggg gdgggggggggggggggggggggdggggggggggggggaggggdggggaayT 5 Mark Resight Population Estimation for Closed Populations 5 Aad ddd add add add gddg ggg ggg ggg ggg ggg gdggdgggggdggagdggggagddagdggddaddaddgagddaddaddadag 5 Enter a title to identify the data Andrea Neal s Mountain Sheep Data Alpha level for confidence interval construction 0 05 Enter number of sighting occasions 14 Hit F2 to retrieve an input file The ESC key takes you back one menu screen You can get context sensitive help with the F1 key 4aaddddd ddd add add gddgddaddTops444pot4444Help4444Ppgup4444Pgdn4444Return4444Esc4 5 5 5 5 5 5 3 5 5 5 5 5 3 5 5 5 5 5 5 5 9 5 5 5 5 5 3 5 3 5 5 5 3 5 3 5 5 5 5 5 8 After the user hits Enter a screen requesting data input appears The user is requested to enter resighting data for each of the 14 occasions specified above The data are requested in sets of 5 occasions
21. ed in estimating the mean number of animals on the study area N and possibly N At the time of the i sighting occasion a known number of the marked animals M are on the study area of the possible T animals with transmitters The probability that an individual is on the study area on the i occasion can be estimated as M T or in terms of the parameters of interest as N N Then the likelihood function for the model that includes temporary immigration and emigration from the study area is a product of the binomial distribution for the probability that a marked animal is on the study area times the joint hypergeometric likelihood of Eq 1 M kIT N N E i m BON N 1 Ty M mend T l gt 1 i i 1 M N N N Nn m N 2 n The parameters N and N for i 1 to k can be estimated by numerical iteration to maximize this likelihood with the constraints that N gt M u and N gt N for i 1 to k Profile confidence intervals can be obtained for the k 1 parameters I was not interested in the k population estimates for each sighting occasion but rather desired the mean of the N estimates Therefore I re parameterized the likelihood to estimate the total population and mean population size on the NOREMARK Reference Manual 4 study area directly and their profile likelihood confidence intervals In the re parameterized likelihood I used N N where a 0 Third Minta and Mange
22. een You can get context sensitive help with the F1 key 4aaddadd add add gddg add gddagddTopadddpot44addddddddddddddagdddddddddTop4444Bot44444 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 9 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 8 This screen is requesting the user to enter a title or other identifying information about the population estimate that is to be computed In addition the level for confidence interval construction and the number of occasions are being asked for The note at the bottom of the screen tells the user to hit the F2 function key if a previously prepared input file should be used for estimation instead of entering data manually At this point we will assume that no data have been previously entered and proceed with the data entry process To enter identifying information type the text in the title entry block which will be highlighted on the screen Left and right arrow keys can be used to move within the entry block NOREMARK Reference Manual 7 the backspace key erases the previous character and the delete key deletes the current character The Insert key can be used to insert text into previously entered text Once the title is correct you move the cursor to the next data entry field by hitting the Enter key which in this case moves you to the alpha level field The default value is 0 05 which you probably do not want to change However should you desire a 90 confidence in
23. ight Population Estimation for Bowden s Minta Mangel Estimator 5 Adda dada dada ggg ggg ggg gg gg gg gg gg gg gg ggggggggggggggggggggggggggggggggggggggggggag Enter a title to identify the Andrea Neal s Mountain Sheep Data Enter n 4444444444444444444444 Enter n x Populat x 5 5 5 5 5 5 5 5 5 5 5 5 B4444444444444444444444 5 5 5 5 5 5 5 5 9 Design Option The fifth option of the main menu of Program NOREMARK allows the user to design a data for Minta Mangel Estimator 44444444444444444444444 aO Enter n Save data to file for later retrieval si Alpha 1 Number 50 x x x x 444444ggggggdgdgdgdgdgdaan The ESC key takes you back one menu screen You can get context sensitive help with the F1 key 4aaddgdd add add add add agdddddTop4444pot4444Help4444Ppqgup4444Pgdn4444Return4444Esc4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 8 20 mark resight survey This design procedure uses simulation data generated by Neal 1990 based on the joint hypergeometric estimator The user provides values of population size number of sighting occasions the expected proportion of the population that will be marked capture probability and the expected sighting probability An example of the input screen follows 04 07 94 5 Expected Results for a Proposed 10 00 39 644444444444 dg ggg ggg ggg ggg ggg gggggggggggggggggggggggggggggggggggggggggggggggggg7 Design Using Interpolat
24. ion 5 Aad dda ada d ggg g ggg gg ggg gg gg gg ggg ggg ggg ggg ggggggggggggggggggggggggggggggggggggagy Enter the expected values of for the Press ESC to exit bac Guesstimate of population size Expected number of sighting occasions Expected proportion of population to Expected proportion of population to parameters of the experiment k to main menu 450 8 be marked 0 15 be seen on each occasions 0 65 The ESC key takes you back one menu screen 5 NOREMARK Reference Manual The range of the input parameters is limited because results are determined by interpolating a 21 database from Neal 1990 Population size must be in the range 50 500 number of occasions 5 20 capture probability 0 1 0 5 and sighting probability 0 1 0 7 Output consists of the estimated bias of the resulting estimate and the confidence interval coverage and confidence interval length for 0 01 0 05 0 10 and 0 20 The following screen shows output from the above input 04 07 94 Expected R5 Continue 444444444444444444445 File 5 Print Do not save output 5 rpolation 10 00 39 6444444444444444444A4AG44A4A4A444A4A4AA4A4A44A4A4A44A4A4A4A44A44AT444A44A44444A4A4444AAT 5 Output saved to a file 54444444444444444444 lt Output saved to printer 5 Enter the expect944444444444444444444444444444444444448 experiment Press ESC to Guesstimate of population si Expected number of sighting Expected propo
25. l 1989 suggested a bootstrap estimator MM of population size based on the sighting frequencies of the marked animals f For unmarked animals sighting frequencies are drawn at random from the observed sighting frequencies of the marked animals until the total number of captures equals u The number of animals sampled is then an estimate of the number of unmarked animals in the population so that M plus the number sampled is an estimator for N Only bootstrap samples where the number of sightings was exactly equal to u were used i e cases where the cumulative sightings exceeded u were rejected Minta and Mangel 1989 accepted the first value where the cumulative sightings equalled or exceeded u The stopping rule I used results in less bias than the rule used by Minta and Mangel 1989 Minta and Mangel 1989 suggested the mode of the bootstrap replicates as the population estimate Confidence intervals were computed as probability intervals with the 2 5 and 97 5 percentiles from the bootstrapped sample of estimates White 1993 demonstrated that the MM estimator is basically unbiased but that the confidence interval coverage was not at the expected 95 for a 0 05 He suggested a modified procedure but coverage still was not satisfactory Fourth Bowden 1993 suggested an estimator for the Minta Mangel model where the confidence intervals on the estimate were computed based on the variance of the resighting frequencies of the marked a
26. lo Coop Fish and Wildl Res Unit Colo State Univ Fort Collins 29pp Rice W R and J D Harder 1977 Application of multiple aerial sampling to a mark recapture census of white tailed deer J Wildl Manage 41 197 206 Venzon D J and Moolgavkar S H 1988 A method for computing profile likelihood based confidence intervals Appl Stat 37 87 94 NOREMARK Reference Manual 30 White G C 1993 Evaluation of radio tagging marking and sighting estimators of population size using Monte Carlo simulations Pages 91 103 in J D Lebreton and P M North eds Marked Individuals in the Study of Bird Population Birkhauser Verlag Basel Switzerland White G C K P Burnham D L Otis and D R Anderson 1978 User s manual for program CAPTURE Utah State Univ Press Logan UT 40pp White G C D R Anderson K P Burnham and D L Otis 1982 Capture recapture and removal methods for sampling closed populations Los Alamos National Laboratory LA 8787 NERP Los Alamos N M 235pp White G C and R A Garrott 1990 Analysis of wildlife radio tracking data Academic Press New York N Y 383pp Zippin C 1956 An evaluation of the removal method of estimating animal populations Biometrics 12 163 169 Zippin C 1958 The removal method of population estimation J Wildl Manage 22 82 90
27. lowing screen 02 01 94 LOSST 6 SS 644444444444444444444 6444444 4d 4ggggggggggggggggggggggggdgdg744g4g4g4g4gggggggga7 5 Mark Resight5 Continue Do not save output 5 Estimator 5 444444444444444444445 File Output saved to a file 54444444444444444444 lt SEPINE Output saved to printer 5 5 Enter a tit944444444444444444444444444444444444448 Andrea Neal s Mountain Sheep Data for Minta Mangel Estimator Enter number of marked animals 25 Enter number of unmarked animal sightings 615 Alpha level for confidence interval construction 0 05 Enter bootstraps to perform 10000 Number of marked animal sightings 162 Population Estimate 119 95 Confidence Interval 112 128 Percent Complete 0 20 40 60 80 100 SSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS S The ESC key takes you back one menu screen You can get context sensitive help with the F1 key 4aadddgdd add ddd add add agddaddTops444Bpot4444Help4444Ppqgup4444Pgdn4444Return4444Esc4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 Robbins Monro Procedure Buckland and Garthwaite 1990 5 5 95 Confidence Interval 107 60 130 97 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 9 8 NOREMARK Reference Manual 17 The previous screen is asking how to dispose of the output Select Continue to discard the output File to save the output to a file and Print to print the output on a printer connected to your computer After you have disposed of the output the progr
28. main menu the following screen appears NOREMARK Reference Manual 18 02 01 94 7247216 64444444444444444444 444444 4ggggggggggggggggggggggggggggggdgdgdgdgdgggggggggggga7 5 Mark Resight Population Estimation for Bowden s Minta Mangel Estimator 5 444444A44AA4A4AA4AAA4AAA4AAAAA4AAA4AAA4AAA4AAA4AAA4AA4AA4AAA4AAA4AAA4AAA4AAA4AA4AAA4AAA4A4AA44A44A4A 4 lt 5 Enter a title to identify the data Andrea Neal s Mountain Sheep Data for Minta Mangel Estimator Enter number of marked animals 25 Enter number of marked but unidentified animals 0 Enter number of unmarked animal sightings 615 Alpha level for confidence interval construction 0 050 Hit F2 to retrieve an input file The ESC key takes you back one menu screen You can get context sensitive help with the F1 key 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 944444444444444444444444444T0p4444 Bot4444 Help4444Pgup4444Pgdn4444Return4444Esc4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 8 The user has specified a title to identify the output and that 25 marked animals are to be used for the analysis The number of marked but unidentified animals are the number of sightings where a marked animal was noted but its unique identification was not ascertained For Neal s study no marked animals were not identified Next is the number of unmarked animals counted 615 Finally the level for use in confidence interval construction is specified When the user hi
29. mals The ESC key takes you back one menu screen You can get context sensitive help with the F1 key 44444444444444444444444444Top4444B0t4444He1p44 44 Pgup4444Pgdn4444Return4444ESc4 5stimator 5 54444444444444444444 lt 5 Print Output saved to printer 5 5 Enter the expect944444444444444444444444444444444444448criment 45 4 0 30 1000 4422654 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 8 23 The program reports the estimaed bias of the estimate the expected confidence interval length as a percent of the estimate and as the number of animals total length see the discussion of these values in the design section and the expected coverage based on the replicate simulations For the immigration emigration estimator one additional input value is requested i e the proportion of the population on the study area at the time of each sighting survey For the Minta Mangel estimator the number of bootstraps to perform for each estimate is requested For Bowden s estimator the expected proportion of the marked animals that are identified is requested allowing the user to evaluate the loss in precision of the estimator as a smaller and smaller proportion of the marked animals are individually identified Output for all the estimators is the same except that for the immigration emigration estimator the bias confidence interval length and confidence interval coverage are reported for both total popula
30. nimals He approached the problem from a sampling framework where each animal in the population has the attribute f of the number of times it was resighted The values of f are known for the marked animals and the sum of the f s u are known for the unmarked animals Then an unbiased estimator of the population size is 2 S u m PA with variance TF Confidence intervals for N are computed from a log transformation as N ex Fann thas ever and N x ex lay ever ay me NOREMARK Reference Manual 5 where CV N is Var N N and ae ae is a distribution with T 1 degrees of freedom User s Guide and Demonstration Runs Program NOREMARK executed with the command NOREMARK typed at the DOS prompt The following menu appears 01 05 94 Memory Available 141 10 47 57 O44 adda dada dada dd dda gaa ddd gad g gd ad gga adda gad g ggg dg gggdgdgddgggddddggggggddgg7 5 DESIGN AND ANALYSIS OF MARK RESIGHT EXPERI MENTS 5 c LAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA A lt 5 odel Estimation ion Model Estimation sti mation JHE Closed Populat mmi gration Emi gra Mi nta Mangel Model Bowden s Model Estimation odel Simu ation n Model Simulation Si mulation lation JHE Closed Populat Immi gration Emi gratio Mi nta Mangel Esti mato Bowden s Estimator Si 0 i E m Design Experiment Using Interpolation for Closed Population 0 i t S
31. oth nonlinear constraints NPSOL uses a sequential quadratic programming algorithm in which the search direction is the solution of a quadratic programming subproblem The algorithm treats bounds linear constraints and nonlinear constraints separately The NOREMARK code is not portable to other operating systems at this time because the CA Clipper compiler is available only for DOS Program Files The following is a list of files distributed with the program as an archive created with PKZIP The archive can be unzipped with PKUNZIP Directory of C NOREMARK README 1S7 262 01 05 94 10 29a ANDREA HYP 369 06 20 92 8 3la ANDREA MM 250 06 20 92 9 54a ANDREA OUT 3 692 04 27 94 4 07p NOREMARK EXE 611 328 02 25 95 9 30a NOREMARK Reference Manual 27 INTERP DBF 29 186 06 20 92 8 14a HELP DBF 1 116 02 02 94 6 38a HELP DBT 13 989 02 02 94 6 38a ITE_NRM EXE 350 720 04 07 94 6 49p DOSXMSF EXE 374 950 01 30 93 12 00a BADGER MM 169 06 22 92 10 0la BISON76 MM 170 06 22 92 10 33a BISON77 MM 160 06 22 92 12 47p PORCUPIN MM 109 06 22 92 1 41p KUFELD MM 250 11 15 93 8 43a NOODLES HYP 224 06 17 93 12 37p NOODLES MM 371 06 17 93 12 36p USERMAN WP 291 342 02 25 95 9 46a The file ANDREA OUT is output for checking the program using as input the files ANDREA HYP JHE and immigration emigration estimators and ANDREA MM Minta Mangel and Bowden s estimator
32. ounted multiple times during one occasion Examples are photographing bears at bait sites with motion sensing cameras where the same bear may visit the same bait site multiple times in a few hours time Besides the fact that this type of survey probably has heterogeneity of sighting probabilities structure of the survey basically precludes use of the joint hypergeometric estimator Such surveys should be considered as sampling with replacement Program Testing User s can verify their copy of the program by duplicating results in the previous sections Input files supplied with the program can be retrieved with the F2 function key and the output verified against the output shown in the above screen reproductions The input file ANDREA HYP provides input for the JHE and immigration emigration estimator ANDREA MM provides input for the Minta Mangel and Bowden s estimators Verification of the code has been performed by checking the numerical optimization results against independent codes However the strongest evidence that the code is correct is NOREMARK Reference Manual 26 that simulation results for data simulated under the correct model generates correct results That is estimators are unbiased and confidence interval coverage is the expected 1 level for reasonable inputs Programming Logic NOREMARK user interface is implemented using the CA Clipper compiler This language is a superset of the dBase III language and provides the
33. random number generator The default value will change for each run because the default value is computed from the current date and time set in the computer To generate identical data for 2 different estimators and hence achieve a better comparison of their performance specify the same random number seed for each estimator After you hit the Enter key on the last input field or hit PgDn the program displays a horizontal bar showing the percent of the simulations that have been completed This display gives you a good idea of how long before the simulations will be completed The following screen shows the output for the above input NOREMARK Reference Manual 04 07 94 10 30 26 64444444444444444444464444444444444444444444444444444444444744444444444444 44 dg g7 5 Monte Car5 Continue Do not save output gt 444444444444444444445 File Output saved to a file Guesstimate of population size Expected number of sighting occasions Expected proportion of population to be marked Number of replicates to simulate Random number seed to initiate simulations Simulation Results Number of Valid Simulations 1000 95 Conf Interval Coverage 95 90 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 9 Expected proportion of population to be seen on each occasions 0 70 Alpha level for Confidence Interval Construction 0 01 0 50 0 05 Estimated Bias 0 60 or 0 3 animals 95 Conf Interval Length 29 43 or 13 2 ani
34. ransmitters The initial sample of animals is captured and marked with radios but recaptures of these animals are obtained by only observing them not actually recapturing them The limitation of this procedure is that unmarked animals are not marked on subsequent occasions The advantage of this procedure is that resighting occasions are generally much cheaper to acquire than when the animals must be physically captured and handled The mark resight procedure has been tested with known populations of mule deer Bartmann et al 1987 and used with white tailed deer Rice and Harder 1977 mountain sheep Furlow et al 1981 Neal et al 1993 black and grizzly bears Miller et al 1987 and coyotes Hein 1992 Eberhardt 1990 further investigated the Petersen estimator with the Chapman correction Chapman 1951 for small population sizes where animals could immigrate emigrate from the study area Here I present a user s manual for Program NOREMARK a program to compute mark resight estimators of population abundance Four estimators of abundance are provided the joint hypergeometric maximum likelihood estimator JHE Bartmann et al 1987 White and Garrott NOREMARK Reference Manual 2 1990 Neal et al 1993 the joint hypergeometric maximum likelihood estimator extended to incorporate animals moving on and off the study area Neal et al 1993 White 1993 the Minta Mangel estimator Minta and Mangel 1989 and Bowden s estimator Bowden 1993
35. ress bar is shown on the screen to allow the user to see that progress is being made Once the bootstrap procedure is completed the following screen appears NOREMARK Reference Manual O2 701794 G3 S57 S35 64444444444444444444444444444444444444444444444444444444444444444444444444444447 5 27444444444444444444444444444444444444444444444444444444444444444 5 4444444 444444 lt Compute Robbins Monro CI Buckland and Garthwaite 1990 3 5 x And 2 7 Cancel x x x x A B444444444444444444444444444444 4d 4g4ggggggggggggggggggggggggggdga Number of marked animal sightings 162 Population Estimate 119 95 Confidence Interval 112 128 Percent Complete 0 20 40 60 80 100 SSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSSS S 4 The ESC key takes you back one menu screen You can get context sensitive help with the F1 key 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 944444444444444444444444444T0p4444 Bot4 444 Help4444Pgup4444PgDn4444Return4444EsSc4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 8 This screen reports the Minta Mangel estimate of population size and the 95 confidence interval determined from the bootstrap sampling distribution The program is asking whether to compute the Robbins Monro confidence interval procedure discussed in White 1993 a more precise estimator of the confidence interval If you select OK this interval is then computed and reported as shown in the fol
36. rk Resight Estimation for Populations with Immigration Emigration 5 Aad ddd ddd add add gdg ggg agg ggg gggagggggggdgggggggagdggddagdgagdgagdgaggggddadgaddgddadag Enter a title to identify the data 5 Andrea Neal s Mountain Sheep Data Alpha level for Confidence Interval Construction 0 01 0 50 oRoS Enter number of sighting occasions 14 Total Marked Marked Unmarked Lin Pet 95 Confidence Marked Available Seen Estimate Interval ME 14 SI 2444444444444444444444444444444444444444 More data entry or edit screen Proceed Edit T oot Vount 1 key 4ZAAAAAAAAAAAAAA AAA ABA ddd ddd ddddgdddgdgggggggggdgdgggagagagggggggdpddddReturn4444kEsc4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 a 1095 5 5 20 10 42 100 2 65 3 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 9 8 NOREMARK Reference Manual One difference between this screen for the Immigration Emigration Estimator and the Closed Estimator is that the total number of radios must be specified followed by the number of radios available to be sighted on the study area As with the Closed estimator the Lincoln Petersen estimate for each occasion is computed to allow you to evaluate the data you ve entered After you have entered data for all occasions the program computes the Immigration 12 Emigration estimates Before this process is conducted the program gives you a chance to save the data you have input as shown in the following screen 02 01 94 VORS rene i 64444444
37. rtion of popul Expected proportion of popul Estimated bias is 0 16 Expected 99 confidence Expected 90 confidence Expected 80 confidence Expected confidence int The ESC key ta You can get conte 5 5 5 5 5 5 5 5 5 5 5 Expected 95 confidence 5 5 5 5 5 5 5 5 5 9 44444444444444444444444444 Top4444Bot4444Help4444 Pgup4444PgdDn4444Return4444Esc4 NOREMARK has generated the output and is now asking how to dispose of these results using exit back to main menu ze occasions ation to be marked ation to be seen on each occasions or 0 7 animals interval is 18 4 or 83 0 animals interval is 13 9 or 62 4 animals interval is 11 6 or 5 1 animals interval is 9 0 or 40 3 animals erval coverage is l alpha 100 kes you back one menu screen xt sensitive help with the F1 key 450 8 0415 0 65 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 8 the same menu as shown previously to continue print or file the output Note in the output that the confidence interval length is reported as a percent of the estimate and as the number of animals Confidence interval length is the difference of the upper and low limits For all the estimators in NOREMARK the confidence intervals are not symmetric around the estimate Often confidence interval length is reported as a percent of the estimate This approach is not really valid for an asymmetric confidence interval Thus
38. s The files NOREMARK EXE and IE_NRM EXE are executable files for the program DOSXMSF EXE is the DOS memory extender file for TE_NRM EXE INTERP DBF is the dBase database for interpolations with the design procedure HELP DBF and HELP DBT are the help documents in dBase HI format The next 7 files are example input from Minta and Mangel 1989 Bowden 1993 or just a test case based on a simple experiment with marked macaroni The last file USERMAN WP is this document in WordPerfect 6 0 format NOREMARK Reference Manual 28 Literature Cited Arnason A N Schwarz C J and Gerrard J M 1991 Estimating closed population size and number of marked animals from sighting data J Wildl Manage 55 716 730 Bartmann R M G C White L H Carpenter and R A Garrott 1987 Aerial mark recapture estimates of confined mule deer in pinyon juniper woodland J Wildl Manage 51 41 46 Bowden D C 1993 A simple technique for estimating population size Dept of Statistics Colorado State Univ Fort Collins Colo 17pp Buckland S T and P H Garthwaite 1990 Algorithm AS 259 Estimation confidence intervals by the Robbins Monro search process Applied Statistics 39 413 424 Burnham K P and W S Overton 1978 Estimation of the size of a closed population when capture probabilities vary among animals Biometrika 65 625 633 Burnham K P and W S Overton 1979 Robust estimation of population size when capture probabili
39. s input on the number of times each marked animal was observed NOREMARK Reference Manual Each column appears as you complete the proceeding column of entries For the example here 02 01 94 MOSSO 644444444444444444444444444444444ddgddggdgggggdgggggggggggdggdgggggdggdgddgggaaT 5 Mark Resight Population Estimation for Minta Mangel Estimator 5 Aad ddddgdd add add gdg ggg gdg ggg gdgggdggdggagdggdggagdggdgagdggdgagdgggdgddgddgaddaddaddadag 5 Enter a title to identify the data Andrea Neal s Mountain Sheep Data for Minta Mangel Estimator Enter number of marked animals 25 Enter number of unmarked animal sightings SS Alpha level for confidence interval construction 0 05 Enter number of bootstraps to perform 10000 Animal Animal Times Animal Number Aba LZ 13 14 LS 16 10 The ESC key takes you back one menu screen You can get context sensitive help with the F1 key 4aaddgdd add add add add agdddaddTops444pot4444Help4444Ppqgup4444Pgdn4444Return4444Esc4 OAAIKDUBWNE WADHDWHO SB 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 9 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 8 15 an additional page of input is requested because 25 animals were marked After the user hits the Enter key for the last animals the program performs the bootstrap process This process can take from a few minutes to several hours depending on the number of unmarked animals observed and the number of bootstraps requested A prog
40. sumes a geographically closed population with each animal in the population having the same sighting probability on a particular occasion In addition animals are assumed to be sampled without replacement i e no animal is observed or counted twice during the survey for a particular occasion The immigration emigration estimator extends this model to the situation where the study area is no longer geographically closed but each animal in the population still has NOREMARK Reference Manual 25 the same sighting probability on a particular occasion and is sampled without replacement For both these estimators it is inappropriate to apply them to data collected by sampling with replacement i e animals are seen more than once during a particular occasion Bowden s estimator allows each animal s sighting probability to differ from the others and sampling can be with or without replacement Sighting heterogeneity allows to a certain degree that the study area does not have to be geographically closed in that some animals can be off the study area for a particular occasion s and hence have a zero sighting probability The resulting estimate is the total population using the study area which is not the same as the average density of animals on the study area Thus the estimate resulting from Bowden s estimator may not be exactly what the researcher had in mind if the study area is not closed The Minta Mangel estimator requires the same assumptions
41. terval instead of a 95 interval enter the value 0 10 in this field After the correct value is entered move to the number of sighting occasions field with the Enter key In this field you enter the number of sighting occasions For the JHE estimator a sighting occasion is an attempt to view animals in the population keeping track of the number of marked and unmarked animals observed For the example here I ll assume that 14 sighting occasions were conducted After the value 14 has been entered the user could proceed to the next data entry screen by hitting the Enter key However you might have noted a mistake in one of the previous fields This mistake could be corrected by using the up arrow to move the cursor to the field with the error and making the change To exit the data screen you could hit the Enter key until you reach the last field or you can use the short cut key PgDn which takes you immediately to the next data entry screen The following shows the screen just prior to hitting return to specify 14 resighting occasions for the data set described in Neal et al 1993 These data are not the best example to illustrate this estimator with because the population was not closed as is assumed by this estimator However I believe it is informative to see the difference in the results from this estimator and the immigration emigration estimator which is appropriate for these data The user has specified a title to identify the data In a
42. ties vary among animals Ecology 60 927 936 Chao A 1988 Estimating animal abundance with capture frequency data J Wildl Manage 52 295 300 Chapman D G 1951 Some properties of the hypergeometric distribution with applications to zoological sample censuses University of California Publication in Statistics 1 131 160 Darroch J N 1958 The multiple recapture census I Estimation of a closed population Biometrika 45 343 359 Eberhardt L L 1990 Using radio telemetry for mark recapture studies with edge effects J Applied Ecol 27 259 271 Furlow R C M Haderlie and R Van den Berge 1981 Estimating a bighorn sheep population by mark recapture Desert Bighorn Council Transactions 1981 31 33 Gill P E W Murray M A Saunders and M H Wright 1986 User s guide for NPSOL Version 4 0 a FORTRAN package for nonlinear programming Tech Rep SOL 86 2 Systems Optimization Laboratory Dept of Operations Research Stanford Univ Stanford Calif 54pp Hein E W 1992 Evaluations of coyote attractants and a density estimate on the Rocky Mountain Arsenal M S Thesis Colorado State Univ Fort Collins 58pp NOREMARK Reference Manual 29 Hudson D J 1971 Interval estimation from the likelihood function J Royal Stat Soc Series B 33 256 262 Leslie D M Jr and C L Douglas 1979 Desert bighorn sheep of the River Mountains Nevada Wildl Monogr 66 1 56 Leslie D M Jr and C L Douglas 1
43. tion size and average daily population size An example output for this estimator is shown in the following screen NOREMARK Reference Manual 24 04 07 94 19 48 42 64444444444444444444dG4gddgddgdgggggggggggggggggggggggggggg7agdagddgdgdagdgggdggggaaT 5 Monte Carl5 Continue Do not save output 5Estimator 5 444444444444444444445 File Output saved to a file 54444444444444444444 lt 5 Print Output saved to printer 5 5 Enter the expect944444444444444444444444444444444444448criment Guesstimate of total population size 150 Expected proportion of population on study area 0 90 Expected number of sighting occasions 4 Expected proportion of population to be marked 0 30 Expected proportion of population to be seen on each occasions 0 70 Alpha level for Confidence Interval Construction 0 01 0 50 0 05 Number of replicates to simulate 1000 Random number seed to initiate simulations 2922875 Total Population Daily Population Estimated Bias 0 26 or 0 4 animals 0 14 or 0 2 animals 95 CI Length 20 05 or 30 1 animals 17 43 or 23 5 animals 95 CI Coverage 95 40 93 40 The ESC key takes you back one menu screen You can get context sensitive help with the F1 key 44444444444444444444444444Top4444B0t4444He1p4444 PguUp4444Pgdn4444Return4444EsSc4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 9 5 5 5 5 5 5 5 5 5 5 Simulation Results Number of Valid Simulations Was 1000 5 5 5 5 5 5 5 5 5 8
44. ts the Enter key on this last input value the following screen appears 02 01 94 Gre 1G 644444444444444444444444444444444d4gddgddgggggdggggggggggggggdggdgggggdggggggaay7 5 Mark Resight Population Estimation for Bowden s Minta Mangel Estimator 5 Aad dddadd add add agdgg ggg ggg gggagggagdgggdgggggggggggdgagdgagdgagdgggdggadggddaddaddaddadag 5 Enter a title to identify the data Andrea Neal s Mountain Sheep Data for Minta Mangel Estimator Enter number of marked animals 25 Enter number of marked but unidentified animals 0 Enter number of unmarked animal sightings 615 Alpha level for confidence interval construction 0 050 Animal Animal Times Animal Times Number TL LZ T3 14 T5 16 10 The ESC key takes you back one menu screen You can get context sensitive help with the F1 key 4aadddgdd add add gddgddagddaddTops444pot4444Help4444Ppqgup4444Pgdn4444Return4444Esc4 AIAIHDUBPWNE WADNADADWHO FB 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 9 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 8 NOREMARK Reference Manual 19 The user is being asked to enter the number of times each of the 25 marked animals were sighted When the number of sightings for the 24th animal is entered a second screen appears that asks about animal number 25 02 01 94 C44 add dd ddd add add ggg ggadddgddaddggddggddgddgddgddgddagdggggaag 5 Mark Resight Pop5 Continue Do not save output gt 444444444444444444445 File Outp
45. ut saved to a file 5 IPieaLiote Output saved to printer Enter a tit94444444444444444444444444444444444444 Enter number of marked animals JAS Enter number of unmarked animal sightings 615 Alpha level for confidence interval construction Number of marked animal sightings 162 5 5 3 5 3 5 5 5 3 5 5 5 3 5 5 5 5 5 5 5 9 When the last animal is entered the program computes Bowden s estimator shown in the above screen along with the log based confidence interval The program then asks how to dispose of the output with the standard options of Continue File or Print Andrea Neal s Mountain Sheep Data for Minta Mangel Estimator Enter number of marked but unidentified animals 0 Population Estimate 119 95 Confidence Interval 101 140 The ESC key takes you back one menu screen You can get context sensitive help with the F1 key 4aadd ddd add add add gddagddagddTop4444Bpot4444 Hel p4444Ppgup4444Pgdn4444Return4444Esc4 USAT S LG 744444444444444444447 5angel Estimator 5 54444444444444444ddd lt 5 5 8 0 050 5 3 5 3 b 5 5 5 5 3 5 3 b 5 5 5 5 5 5 8 After this question is answered another query requests whether to save the input in a file for later use with this estimator or the Minta Mangel estimator NOREMARK Reference Manual 02 01 94 AEs AG 81KG 64444444444444444444444 444d 4dggdgggggggggggggggdgggggggggggggggdggdggdggdgggggg7T 5 Mark Res
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