Individual heterogeneity in capture probabilities and time dependence are fundamentally important for estimating the closed animal population parameters in capture-recapture studies. A generalized estimating equations (GEE) approach accounts for linear correlation among capture-recapture occasions, and individual heterogeneity in capture probabilities in a closed population capture-recapture individual heterogeneity and time variation model. The estimated capture probabilities are used to estimate animal population parameters. Two real data sets are used for illustrative purposes. A simulation study is carried out to assess the performance of the GEE estimator. A Quasi-Likelihood Information Criterion (QIC) is applied for the selection of the best fitting model. This approach performs well when the estimated population parameters depend on the individual heterogeneity and the nature of linear correlation among capture-recapture occasions.
Agresti, A. (1994) Simple capture-recapture models permitting unequal catchability and variable sampling effort. Biometrics, 50(2), 494-500.
Akanda, M.A.S. & Alpizar-Jara, R. (2014a) A generalized estimating equations approach for capture-recapture closed population models. Environmental and Ecological Statistics, 21(4), 667-688.
Akanda, M.A.S. & Alpizar-Jara, R. (2014b) Estimation of capture probabilities using generalized estimating equations and mixed effects approaches. Ecology and Evolution, 4(7), 1158-1165.
Briand, L.C., Emam, K.E., Freimut, B. & Oliver (1997) Quantitative evaluation of capture-recapture models to control software inspections, Proceedings of the Eighth International Conference on Software Reliability Engineering, Albuquerque, NM, 234-244.
Chao, A., Lee, S.M. & Jeng, S.L. (1992) Estimating population size for capture-recapture data when capture probabilities vary by time and individual animal. Biometrics, 48(1), 201-216.
Chao, A. & Lee, S.M. (1993) Estimating population size for continuous time capture-recapture models via sample coverage. Biometrical Journal, 35(1), 29-45.
Chao, A., Tsay, P.K., Lin, S.H., Shau, W.Y. & Chao, D.Y. (2001) The applications of capture-recapture models to epidemiological data. Stat. Med., 20(20), 3123-57.
Chao, A. & Huggins, R.M. (2005) Modern closed-population capture-recapture models. In: C. Amstrup, T.L. McDonald and B.F.J. Manly (eds), Handbook of capture-recapture analysis. Princeton University Press, Princeton, NJ, 58-87.
Diggle, P., Heagerty, P., Liang, K.Y. & Zeger, S. (2013) Analysis of longitudinal data. 2nd Edition, Oxford University Press, New York.
Hardin, J. W. & Hilbe, J.M. (2013) Generalized estimating equations, 2nd Edition. Chapman and Hall/CRC Press, Boca Ratan, FL.
Horvitz, D.G. & Thompson, D.J. (1952) A generalization of sampling without replacement from a finite universe. J. Amer. Statist. Assoc., 47(260), 663-685.
Huggins, R.M. (1989) On the statistical analysis of capture experiments. Biometrika, 76(1), 133-140.
Huggins, R.M. (1991) Some practical aspects of a conditional likelihood approach to capture experiments. Biometrics, 47(2), 725-732.
Huggins, R.M. & Yip, P.S.F. (1997) Statistical analysis of removal experiments with the use of auxillary variables. Stat. Sin., 7(3), 705-712.
Hwang, W.H. & Huggins, R.M. (2005) An examination of the effect of heterogeneity on the estimation of population size using capture- recapture data. Biometrika, 92(1), 229-233.
King, R. & Brooks, S.P. (2008) On the Bayesian estimation of a closed population size in the presence of heterogeneity and model uncertainty. Biometrics, 64(3), 816-824.
Liang, K.Y. & Zeger, S.L. (1986) Longitudinal data analysis using generalized linear models. Biometrika, 73(1), 13-22.
Lloyd, C. & Yip, P. (1991) A unification of inference from capture-recapture studies through martingale estimating functions. In: Godambe, V.P. (eds) Estimating functions. Oxford: Clarendon Press, 65-88.
Otis, D.L., Burnham, K.P., White, G.C. & Anderson, D.R. (1978) Statistical inference from capture data on closed animal populations. Wildlife Monographs, 62, 1-135.
Pan, W. (2001) Akaike’s information criterion in generalized estimating equations. Biometrics, 57(1), 120-125.
Pledger, S. (2000) Unified maximum likelihood estimates for closed capture-recapture models using mixtures. Biometrics, 56(2), 434-442.
Pollock, K., Hines, J. & Nichols, J. (1984) The use of auxiliary variables in capture-recapture and removal experiments. Biometrics, 40(2), 329-340.
Pradel, R. & Sanz-Aguilar, A. (2012) Modeling trap-awareness and related phenomena in capture-recapture studies. PLoS ONE, 7(3), e32666.
Qaqish, B.F. (2003) A family of multivariate binary distributions for simulating correlated binary variables with specified marginal means and correlations. Biometrika, 90(2), 455-463.
R Development Core Team (2016) R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. ISBN 3-900051-07-0. Available from: http:// www.r-project.org/.
Rexstad, E. & Burnham, K. (1991) User’s guide for interactive program CAPTURE. Colorado Cooperative Fish and Wildlife Research Unit, FortCollins.
Seber, G.A.F. (2002) The estimation of animal abundance and related parameters. 2nd Edition, The Blackburn Press, London, Edward Arnold.
Stanley, T.R. & Richards, J.D. (2005) Software review: a program for testing capture-recapture data for closure. Wildlife Society Bulletin, 33(2), 782-785.
Stoklosa, J. & Huggins, R.M. (2012) A robust p-spline approach to closed population capture-recapture models with time dependence and heterogeneity. Comput. Stat. Data Anal., 56(2), 408-417.
Williams, B.K., Nichols, J.D. & Conroy, M.J. (2002) Analysis and management of animal populations. Academic Press, San Diego, California.
Yang, H.C. & Chao, A. (2005) Modeling animals behavioral response by Markov chain models for capture-recapture experiments. Biometrics, 61(4), 1010-1017.
Zeger, S.L. & Liang, K.Y. (1986) Longitudinal data analysis for discrete and continuous outcomes. Biometrics, 42(1), 121-130.
Zhang, S. (2012) A GEE approach for estimating size of hard-to-reach population by using capture-recapture data. Statistics, 46(2), 175-183.