James D. Nichols has made enormous contributions to population estimation in many different areas. He is also a tremendous supporter and friend to those lucky enough to have worked with him.

Mike Conroy, Ken Williams, Jim Nichols celebrating the book completion in serious style. 
Williams is an expert on adaptive management and Head of the Coop Unit Program in USGS. Conroy has made important contributions to band return models and other population estimation methods. He is an expert in adaptive management methods and population biology.

TOTAL   100

Homework Set 1. Due Thursday Sept 7, 2006

1. A scientist wishes to estimate the mean number of individuals of a rare cactus plant per 1-ha plot on a 500-ha study area. The goal is to collect enough samples to estimate the population mean to within 15% of the true value using a 90% confidence interval (i.e., a = 0.10). Based on an earlier study the CV was 0.26. Note: We are assuming that the plant is large enough that the detection probability is 1

Calculate the sample size required, ignoring the finite population correction.

Calculate the sample size required, allowing for the finite population correction.

Calculate the approximate Expected Value, Bias, SE, and MSE of the Chapman estimator using your simulation replicate values. Also calculate the expected value and bias of the Lincoln-Petersen Estimates if you ignore the infinite values. Comment on why this shows the value of the Chapman modification.

3.      3. In an aerial survey of 10 plots or sampling units, selected by simple random sampling without replacement, the numbers of elk detected were     62,  22, 88, 43, 69, 88, 93, 75, 13, and 17. The study area or population consists of 50 plots. A random sub-sample of 4 plots was then selected for a complete ground count. The plots selected were 2, 4, 5, and 10 and they had 27, 43, 87, and 21 elk counted.

(i)     Estimate the probability of detection of an elk in the aerial survey.

(ii)    What assumption is being made about the ground count?

(iii)    Estimate the total number of elk in the study area unadjusted for visibility bias and then adjusted for visibility bias.

Calculate the population size estimate and its SE (see p. 292. for equation)

Calculate the detection probability estimate for observer 1 and also for observer 2.

1. When one is interested in conducting an aerial survey of a population of objects (say eagle nests to make it simple) there are several approaches available for accounting for visibility bias (i.e., non-detection of all animals from the air). Discuss the advantages and disadvantages of the following methods:

(iii)               Aerial count plus complete ground counts on a sub-sample of plots

(iv)              Ground and air counts by two observers with mapping objects seen in common.

(v)                Two (independent) observers in the same plane with mapping of objects seen in common, and

(vi)              Line transects (distance sampling).

Note: Give about one page or so on each one.

2. More questions being developed.

General

Ricker, W. E. (1958). Handbook of computations for biological statistics of fish populations. Fisheries Research Bulletin of Canada, Bulletin 119. 300pp.

Lancia, R. A., Nichols, J. D., and Pollock, K. H.  (1994).  Estimating the number of animals in wildlife populations in T.A. Bookout, ed. Research and management techniques for wildlife and habitats. Fifth ed.  The Wildlife Society, Bethesda, MD, 215-253. (Introductory)

Seber (1982). The Estimation of Animal Abundance and Related Parameters.Macmillan, New York.( Very detailed).

Schwarz, C. J., and Seber, G. A. F. (1999). A review of estimating animal abundance III, Statistical Science 14, 427-456.

Burnham, K. P., and Anderson, D. R. (2002). Model Selection and Inference: A Practical Information Theoretic Approach, New York: Springer-Verlag.

Pollock, K. H., Marsh, H., Bailey, L. L., Farnsworth, G. L., Simons, T. L., and Alldredge, M. W. (2004) Separating components of detection probability in abundance estimation: An overview with diverse examples. In W. L Thompson Ed. Sampling Rare and Elusive Species: Concepts, Designs and Techniques for Estimating Population Parameters. Island Press, Washington D. C

Dave Anderson, Ken Burnham and Gary White from Colorado State University have made enormous contributions to population estimation 
in so many areas. One special mention should be the creation of MARK!
A marvellous program which has revolutionised the field!

Sampling Theory
Cochran, W. G ( 1967) Sampling Techniques, Wiley, New York.

Thompson, S. K. (2002) Sampling, 2nd Edition, Wiley, New York.

Angler Surveys and Survey Methodology
Pollock, K. H., Jones, C. M. and Brown, T. L. (1994).  Angler Surveys and their application to fisheries management.  American Fisheries Society Special Publication 25, Bethesda, Maryland.

Cynthia Jones

Aerial Surveys
Pollock, K. H., and Kendall, W. L.  (1987).  Visibility bias in aerial surveys: A review of estimation procedures. Journal of  Wildlife  Management 51, 502-510.

Adaptive Sampling
Thompson, S. K. and Seber, G. A.F.(1996)  Adaptive Sampling, 2nd Edition, Wiley, New York.

Distance Sampling Methods

S.T. Buckland, D.R. Anderson, K.P. Burnham, J.L Laake, D.L. Borchers and L. Thomas (2001).Introduction to Distance Sampling:Estimating Abundance of Biological Populations.  Oxford University Press.

Alpizar-Jara, R. & Pollock, K.H. (1996).  A combination line transect and capture- recapture sampling model for multiple observers in aerial surveys,  Journal of Environmental and Ecological Statistics 3, 311-327.

Alpizar-Jara, R.(1997). Assessing assumption violations in line transect sampling. Ph  D Dissertation, Biomathematics Program, North Carolina State University, Raleigh, North Carolina, U. S. A.

Arnason, A.N. & Schwartz, C.J. (1999). Using POPAN-5 to analyse banding data. Bird Study, 46, S157-S168. 

Borchers, D. L., Zucchini, W., and Fewster, R. M.. (1998). Mark-Recapture Models for Line Transect Surveys, Biometrics, 54, 1207-1220.
 

Stephen Buckland                              David Borchers

 

Capture-Recapture Methods
Monographs

Burnham, K. P., Anderson, D. R., White, G. C., Brownie, C., and Pollock, K. H. (1987). Design and Analysis Methods for Fish Survival Experiments based on Release-Recapture.  American Fisheries Society Monographs 5, Bethesda, Maryland. (ISSN 0362-1715).

Lebreton, J.-D., Burnham, K. P., Clobert, J., and Anderson, D. R. (1992). Modelling Survival and Testing Biological Hypotheses Using Marked Animals: A Unified Approach with Case Studies, Ecological Monographs, 62, 67-118.

Otis, Burnham, White and Anderson (1978).Statistical Inference from Capture Data on Closed Animal Populations.Wildlife Monograph 62.

Pollock, K. H., Nichols, J. D., Brownie, C., and Hines, J. E.  (1990).  Statistical Inference for Capture-Recapture Experiments, Wildlife Society Monographs (No. 107).

White, G.C., Anderson, D.R., Burnham, K.P. and Otis, D.L. (1982). Capture-Recapture and Removal Methods for Sampling Closed Populations. Los Alamos National Lab, LA-8787-NERP, Los Alamos, New Mexico, USA.

Cooch , E. Online book on program MARK. An invaluable resource!

Some Classic Papers 

Laplace, P.S. (1786). Sur les naissances, les mariages et les morts in Memoires  de L’Academie Royale des Sciences, 1783, Paris, pp. 693-702. 

Petersen, C.G.J. (1896).  The yearly immigration of young plaice into the Limfjiord from the German Sea, Report of Danish Biological Station 6, 1-48. 

Lincoln, F.C. (1930).  Calculating Waterfowl Abundance on the Basis of Banding Returns. United States Department of Agriculture Circular, No. 118.

Schnabel, Z.E. (1938). The estimation of the total fish population of a lake. American Mathematical Monthly 45: 348-52.

Jackson, C. H. N. (1939). The analysis of an animal population. Journal of Animal Ecology, 8, 238-246.

Jackson, C. H. N. (1940). The analysis of a tsetse fly population:I. Annals of Eugenics 10,332-369.

Jackson, C. H. N. (1944). The analysis of a tsetse fly population:II. Annals of Eugenics 12, 176-205.

Jackson, C. H. N. (1948). The analysis of a tsetse fly population:III. Annals of Eugenics 14, 91-108.

Fisher, R. A.  and  Ford, E. B. (1947). The spread of a gene in natural conditions in a colony of the moth Panaxia dominula. Heredity , 1, 143-174.

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.

Bailey, N.T.J. (1951). On estimating the size of mobile populations from recapture data.  Biometrika 38: 293-306.

Cormack, R.M. (1964).  Estimates of survival from the sighting of marked animals, Biometrika 51, 429-38. 

Darroch, J.N. (1958). The multiple-recapture census I. Estimation of a closed population. Biometrika 45: 343-59.

Darroch, J.N.  1959.  The multiple-recapture census: II. Estimation when there is immigration or death. Biometrika 46:336-351. 

Jolly, G. M. (1965). Explicit Estimates From Capture-Recapture Data With Both Death and Immigration – Stochastic Model, Biometrika, 52, 225-247.

Seber, G. A. F. (1965), A Note on the Multiple Recapture Census, Biometrika, 52, 249-259.

Manly, B.F.J. and Parr, M.J. (1968). A new method of estimating population size, survivorship and birth rate from capture-recapture data. Transactions of the Society for British Entomology 18, 81-89.

Robson, D. S. (1969). Mark-recapture methods of population estimation. Pages 120-140 in N. L. Johnson and H. Smith, Jr., eds. New developments in survey sampling. John Wiley and Sons, New York, New York.

Fienberg, S. E. (1972). The multiple-recapture census for closed populations and incomplete contingency tables. Biometrika, 59,591-603. 

Arnason, A.N.  1973.  The estimation of population size, migration rates and survival in a stratified population.  Researches on Population Ecology 15:1-8.

Carothers, A.D. (1973). Capture-recapture methods applied to a population with known parameters. Journal of Animal Ecology 42: 125-46.

Pollock, K.H. (1975). A K-sample tag-recapture model allowing for unequal survival and catchability. Biometrika 62, 577-583.

Burnham, K. P., and Overton, W. S. (1978). Estimation of the Size of a Closed Population When Capture probabilities Vary Among Animals, Biometrika, 65, 625-633.

Pollock, K.H. (1981). Capture-recapture models allowing for age-dependent survival and capture rates. Biometrics 37, 521-529.

Pollock, K. H. (1982), A Capture-Recapture Design Robust to Unequal Probability Capture, Journal of Wildlife Management, 46: 752-757.

White, G.C. 1983.  Numerical estimation of survival rates from band recovery and biotelemetry data.  J. Wildl. Manage. 47:716-728.

Pollock, K. H., Hines, J. E. and Nichols J.N. (1985). Goodness of fit tests for open capture-recapture models. Biometrics 41, 399-410.

Huggins, R. M. (1989). On the Statistical Analysis of Capture Experiments, Biometrika, 76, 133-140.

Chao, A. (1989). Estimating population size for sparse data in capture-recapture experiments. Biometrics 45: 427-38.

Huggins, R. M. (1991). Some Practical Aspects of a Conditional Likelihood Approach to Capture Experiments, Biometrics, 47, 725-732.

Important Recent Papers (Incomplete)

Arnason, A.N. & Schwartz, C.J. (1999). Using POPAN-5 to analyse banding data. Bird Study, 46, S157-S168.

Bailey, L. L., T. R. Simons, and K. H. Pollock.(2004).  Estimating detectability parameters for plethodon salamanders using the robust capture-recapture design. Journal of Wildlife Management, 68: 1-13.

Bailey, L. L., T. R. Simons, and K. H. Pollock.(2004). Spatial and temporal variation in detection probability of plethodon salamanders using the robust capture-recapture design. Journal of Wildlife Management, 68: 14-24.

Barker, R. J. (1997). Joint Modelling of Live Recapture, Tag-Resight and Tag-Recovery Data , Biometrics, 53, 666-677.

Brownie, C., Hines, J. E., Nichols, J. D., Pollock, K. H., and Hestbeck, J. B. (1993).  Capture-recapture studies for multiple strata including non-Markovian transition probabilities.  Biometrics 49, 1173-1187.

Burnham, K. P. (1993). A Theory for Combined Analysis of Ring Recovery and Recapture Data. Pages 199-213, In J.-D. Lebreton and P. M. North editors. Marked Individuals in the Study of Bird Population. Birkhauser. Verlag, Basel, Switzerland.

Chao, A. (2001). An overview of closed capture-recapture models. Journal of Agricultural, Biological and Environmental Statistics 6: 158-75.

Chao, A., Lee, S.-M., and Jeng, S. L. (1992). Estimating population size for capture-recapture data when capture probabilities vary by time and individual animal. Biometrics, 48, 201-216. 

Dorazio and Royle. (2003). Mixture models for estimating the size of a closed population when capture rates vary among individulas. Biometrics, 59, 351-364.

Hestbeck,  J. G., Nichols, J. D., and Malecki, R. A. (1991). Estimates of movement and site fidelity using mark-resight data of wintering Canada Geese, Ecology, 72,523-533.

Kendall, W. L., Pollock, K. H., and Brownie, C. (1995). A likelihood-based approach to capture-recapture estimation of demographic parameters under the Robust design.  Biometrics , 51, 293-308.

Kendall, W. L., and  Nichols, J. D.(1995). On the use of secondary capture-recapture samples to estimate temporary  emigration and breeding proportions. Journal of Applied Statistics 22, 751-762. 

Kendall, W. L. , Nichols, J. D. and Hines. J. E. (1997). Estimating temporary emigration using capture-recapture data with Pollock’s robust design. Ecology , 78, 563-578.

Lebreton, J.-D., and Pradel, R. (2001). Multi-stratum capture-recapture models: modeling incomplete capture histories. Journal of Applied  Statistics This Volume.

Lee, S.-M., and Chao, A. (1994). Estimating Population Size via Sample Coverage for Closed Capture-Recapture Models, Biometrics, 50, 88-97.

Link, W. A. (2003). Nonidentifiability of population size from capture-recapture data with heterogeneous detection probabilities. Biometrics, 59, 1123-1130.

Nichols, J. D., Sauer, J. R., Pollock, K. H., and Hestbeck, J. B. (1992).  Estimating transition probabilities for stage based population projection matrices using capture-recapture data.  Ecology 73, 306-312.

Nichols, J. D., and Hines, J. E. (2001) Approaches for the direct estimation of lambda and demographic contributions to lambda using capture-recapture data.. Journal of Applied  Statistics 

Norris, J. L., and Pollock, K. H.  (1995).  Capture-recapture model Mbh:  Bivariate MLE of capture-recapture distribution and resulting model selection.  Journal of Environmental and Ecological Statistics 2, 305-313.

Norris, J. L., and Pollock, K. H.  (1996).  Nonparametric maximum likelihood estimators for population size under two closed capture-recapture models with heterogeneity.  Biometrics 52, 639-649.

Pine, W. E.,  Pollock, K. H., Hightower, J. E., Kwak, T. J., and Rice, J. A. (2003). A review of tagging methods for estimating fish population size and components of mortality. Fisheries 28: 10-23.

Pledger, S. (2000). Unified Maximum Likelihood Estimates for Closed Capture-Recapture Models Using Mixtures, Biometrics, 56, 443-450..

Pledger, S., Pollock, K. H.,Norris, J. L. (2003). Open Capture-recapture models with heterogeneity. 1. Cormack-Jolly-Seber model. Biometrics 59: 786-794.

Pollock, K. H. (2000). Capture-Recapture Models, Journal of the American Statistical Association, 95, 293-296.

Pradel, R. (1996),  Utilization of Capture-Mark-Recapture for the Study of Recruitment and Population Growth Rate, Biometrics, 52, 703-709.

Schwarz, C. J., and Arnason, A. N. (1996), A General Methodology for the Analysis of Capture-Recapture Experiments in Open Populations, Biometrics, 52, 860-873.

White, G. C., and Burnham, K. P. (1999), Program MARK: Survival Estimation from Populations of Marked Animals, Bird Study, 46, S120-S139.

Yip, P. S. F.(1991). A martingale estimating equation for a capture-recapture experiment in discrete time,  Biometrics, 47, 1081-1088.

Pollock, Burnham, Pledger, Wellendorf and Norris have all worked on capture-recapture models.
Picture taken at a recent ASA meeting.

Carl Schwarz

 

Paul Yip

Anne Chao, Paul Yip and Postgraduate Students

Bill Kendall

Removal or Depletion and Catch-Effort Methods

Gould, W. R., and Pollock, K. H.  (1997).  Catch-effort maximum likelihood estimation of population parameters.  Canadian Journal of Fisheries and Aquatic Science 54, 890-897.

Gould, W. R., and Pollock, K. H.  (1997).  Catch-effort estimation of population parameters under the robust design.  Biometrics 53, 207-216.

White, G.C., Anderson, D.R., Burnham, K.P. and Otis, D.L. (1982). Capture-Recapture and Removal Methods for Sampling Closed Populations. Los Alamos National Lab, LA-8787-NERP, Los Alamos, New Mexico, USA.

Zippin, C. (1956). An evaluation of the removal method of estimating animal populations, Biometrics 12, 163-189.

Bill Gould

Selective Removal Methods ( Change in Ratio)

Paulik and Robson (1969). Statistical calculations for change-in-ratio estimators of population parameters.  Journal of Wildlife Management 33, 1-27.

Hoenig, J. M., and Pollock, K. H.  (1998).  Index-removal estimators.  Encyclopedia of Statistics Update Volume 2, p. 342-346.

Lancia, R. A., Nichols, J. D., and Pollock, K. H.  (1994).  Estimating the number of animals in wildlife populations in T.A. Bookout, ed. Research and management techniques for wildlife and habitats. Fifth ed.  The Wildlife Society, Bethesda, MD, 215-253.

Pollock, K. H., and Hoenig, J. M.  (1998).  Change-in-ratio estimators.  Encyclopedia of Statistics Update Volume 2, p. 109-112.

Nest Survival and Radio-Telemetry Survival Methods

Mayfield, H.(1961). Nesting success calculated from exposure.Wilson Bulletin, 73, 255-261.

Pollock, K. H., and Cornelius, W. L.  (1988).  A distribution free nesting survival model. Biometrics 44, 397-404.

Trent, T. T., and Rongstad, O. J. (1974), Home Range and Survival of Cottontail Rabbits in Southwestern Wisconsin, Journal of Wildlife Management, 38, 459-472.

Heisey, D. M., and Fuller, T. K. (1985). Evaluation of Survival and Cause Specific mortality Rates Using Telemetry Data,  Journal of Wildlife Management, 49, 668-674.

Pollock, K. H., Winterstein, S. R., Bunck, C. M., and Curtis, P. D.  (1989).  Survival analysis in telemetry studies: the staggered entry design.  Journal of  Wildlife  Management 53, 7-15.

Pollock, K. H., Winterstein, S. R., and Conroy, M. J. (1989).  Estimation and analysis of survival distributions for radio-tagged animals.  Biometrics 45, 99-109.

Pollock, K. H., Bunck, C. M., Winterstein, S. R., and Chen, C. L.  (1995).  A capture-recapture survival analysis model for radio-tagged animals.  Journal of Applied Statistics, 22, 661-672.

Joe Hightower

Tag-Return Models

Brownie, C., Anderson, D. R., Burnham, K. P., and Robson, D. S. (1985), Statistical Inference From band-Recovery Data: A handbook (2nd ed, Resource publication 156), Washington, DC: Fish and Wildlife Service, U.S. Department of the Interior.

Cavell Brownie

Hoenig, J. M., Barrowman, N. J., Hearn, W. S. and Pollock, K. H.  (1998).  Multiyear tagging studies incorporating fishing effort data.  Canadian Journal of Fisheries and Aquatic Sciences 55, 1466-1476.

Hoenig, J. M., Barrowman, N. J., Pollock, K. H., Brooks, E. N. and Hearn, W. S., and Polacheck, T.  (1998).  Models for tagging data that allow for incomplete mixing of newly tagged animals.  Canadian Journal of Fisheries and Aquatic Sciences 55, 1477-1483.
John Hoenig 

Bill Hearn

Program Mark

Mark Online Book

Patuxent Software Site

Distance

Popan