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Estimation of Population Size When Capture Probability Depends on Individual States

Author

Listed:
  • Hannah Worthington

    (University of St Andrews)

  • Rachel S. McCrea

    (University of Kent)

  • Ruth King

    (University of Edinburgh)

  • Richard A. Griffiths

    (University of Kent)

Abstract

We develop a multi-state model to estimate the size of a closed population from capture–recapture studies. We consider the case where capture–recapture data are not of a simple binary form, but where the state of an individual is also recorded upon every capture as a discrete variable. The proposed multi-state model can be regarded as a generalisation of the commonly applied set of closed population models to a multi-state form. The model allows for heterogeneity within the capture probabilities associated with each state while also permitting individuals to move between the different discrete states. A closed-form expression for the likelihood is presented in terms of a set of sufficient statistics. The link between existing models for capture heterogeneity is established, and simulation is used to show that the estimate of population size can be biased when movement between states is not accounted for. The proposed unconditional approach is also compared to a conditional approach to assess estimation bias. The model derived in this paper is motivated by a real ecological data set on great crested newts, Triturus cristatus. Supplementary materials accompanying this paper appear online.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jagbes:v:24:y:2019:i:1:d:10.1007_s13253-018-00347-x
    DOI: 10.1007/s13253-018-00347-x
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    References listed on IDEAS

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    1. Robert M. Dorazio & J. Andrew Royle, 2005. "Rejoinder to "The Performance of Mixture Models in Heterogeneous Closed Population Capture-Recapture"," Biometrics, The International Biometric Society, vol. 61(3), pages 874-876, September.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
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    9. Hajo Holzmann & Axel Munk & Walter Zucchini, 2006. "On Identifiability in Capture–Recapture Models," Biometrics, The International Biometric Society, vol. 62(3), pages 934-936, September.
    10. Roger Pradel, 2005. "Multievent: An Extension of Multistate Capture–Recapture Models to Uncertain States," Biometrics, The International Biometric Society, vol. 61(2), pages 442-447, June.
    11. Shirley Pledger, 2005. "The Performance of Mixture Models in Heterogeneous Closed Population Capture–Recapture," Biometrics, The International Biometric Society, vol. 61(3), pages 868-873, September.
    12. Wen-Han Hwang & Richard Huggins, 2005. "An examination of the effect of heterogeneity on the estimation of population size using capture-recapture data," Biometrika, Biometrika Trust, vol. 92(1), pages 229-233, March.
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