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On the Bayesian Estimation of a Closed Population Size in the Presence of Heterogeneity and Model Uncertainty

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  • R. King
  • S. P. Brooks

Abstract

Summary We consider the estimation of the size of a closed population, often of interest for wild animal populations, using a capture–recapture study. The estimate of the total population size can be very sensitive to the choice of model used to fit to the data. We consider a Bayesian approach, in which we consider all eight plausible models initially described by Otis et al. (1978, Wildlife Monographs62, 1–135) within a single framework, including models containing an individual heterogeneity component. We show how we are able to obtain a model‐averaged estimate of the total population, incorporating both parameter and model uncertainty. To illustrate the methodology we initially perform a simulation study and analyze two datasets where the population size is known, before considering a real example relating to a population of dolphins off northeast Scotland.

Suggested Citation

  • R. King & S. P. Brooks, 2008. "On the Bayesian Estimation of a Closed Population Size in the Presence of Heterogeneity and Model Uncertainty," Biometrics, The International Biometric Society, vol. 64(3), pages 816-824, September.
    • Handle: RePEc:bla:biomet:v:64:y:2008:i:3:p:816-824
    DOI: 10.1111/j.1541-0420.2007.00938.x
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    References listed on IDEAS

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    1. S. E. Fienberg & M. S. Johnson & B. W. Junker, 1999. "Classical multilevel and Bayesian approaches to population size estimation using multiple lists," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 162(3), pages 383-405.
    2. Robert M. Dorazio & J. Andrew Royle, 2003. "Mixture Models for Estimating the Size of a Closed Population When Capture Rates Vary among Individuals," Biometrics, The International Biometric Society, vol. 59(2), pages 351-364, June.
    3. Elena Stanghellini & Peter G. M. van der Heijden, 2004. "A Multiple-Record Systems Estimation Method that Takes Observed and Unobserved Heterogeneity into Account," Biometrics, The International Biometric Society, vol. 60(2), pages 510-516, June.
    4. William A. Link, 2003. "Nonidentifiability of Population Size from Capture-Recapture Data with Heterogeneous Detection Probabilities," Biometrics, The International Biometric Society, vol. 59(4), pages 1123-1130, December.
    5. Shirley Pledger, 2000. "Unified Maximum Likelihood Estimates for Closed Capture–Recapture Models Using Mixtures," Biometrics, The International Biometric Society, vol. 56(2), pages 434-442, June.
    6. Brent A. Coull & Alan Agresti, 1999. "The Use of Mixed Logit Models to Reflect Heterogeneity in Capture-Recapture Studies," Biometrics, The International Biometric Society, vol. 55(1), pages 294-301, March.
    7. Francesco Bartolucci & Antonio Forcina, 2001. "Analysis of Capture-Recapture Data with a Rasch-Type Model Allowing for Conditional Dependence and Multidimensionality," Biometrics, The International Biometric Society, vol. 57(3), pages 714-719, September.
    8. Luca Tardella, 2002. "A new Bayesian method for nonparametric capture-recapture models in presence of heterogeneity," Biometrika, Biometrika Trust, vol. 89(4), pages 807-817, December.
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    Cited by:

    1. Riki Herliansyah & Ruth King & Stuart King, 2022. "Laplace Approximations for Capture–Recapture Models in the Presence of Individual Heterogeneity," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 27(3), pages 401-418, September.
    2. Jérôme A. Dupuis & Michel Goulard, 2011. "Estimating Species Richness from Quadrat Sampling Data: A General Approach," Biometrics, The International Biometric Society, vol. 67(4), pages 1489-1497, December.
    3. Mevin B. Hooten & Michael R. Schwob & Devin S. Johnson & Jacob S. Ivan, 2023. "Multistage hierarchical capture–recapture models," Environmetrics, John Wiley & Sons, Ltd., vol. 34(6), September.
    4. Matthew R. Schofield & Richard J. Barker & Nicholas Gelling, 2018. "Continuous†time capture–recapture in closed populations," Biometrics, The International Biometric Society, vol. 74(2), pages 626-635, June.
    5. Hannah Worthington & Rachel S. McCrea & Ruth King & Richard A. Griffiths, 2019. "Estimation of Population Size When Capture Probability Depends on Individual States," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 24(1), pages 154-172, March.
    6. Richard Arnold & Yu Hayakawa & Paul Yip, 2010. "Capture–Recapture Estimation Using Finite Mixtures of Arbitrary Dimension," Biometrics, The International Biometric Society, vol. 66(2), pages 644-655, June.

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