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Minimum chi-square method for estimating population size in capture-recapture experiments

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  • Yuyan Zheng
  • Yongfei Mao
  • Min Tsao
  • Laura L E Cowen

Abstract

Closed population capture-recapture estimation of population size is difficult under heterogeneous capture probabilities. We introduce the minimum chi-square method which can handle multi-occasion capture-recapture data. It complements likelihood methods with elements that can lead to confidence intervals and assessment of goodness-of-fit. We conduct a comprehensive study on the minimum chi-square method for estimating the size of a closed population using multiple-occasion capture-recapture data under heterogeneous capture probability. We also develop two different bootstrap techniques that can be combined with any underlying estimator, be it the minimum chi-square estimator or a likelihood estimator, to perform useful inference for estimating population size. We present a simulation study on the minimum chi-square method and apply it to analyze white stork multiple capture-recapture data. Under certain conditions, the chi-square method outperforms the likelihood based methods.

Suggested Citation

  • Yuyan Zheng & Yongfei Mao & Min Tsao & Laura L E Cowen, 2023. "Minimum chi-square method for estimating population size in capture-recapture experiments," PLOS ONE, Public Library of Science, vol. 18(10), pages 1-17, October.
    • Handle: RePEc:plo:pone00:0292622
    DOI: 10.1371/journal.pone.0292622
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    References listed on IDEAS

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    1. 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.
    2. Brent A. Coull & Alan Agresti, 2000. "Random Effects Modeling of Multiple Binomial Responses Using the Multivariate Binomial Logit-Normal Distribution," Biometrics, The International Biometric Society, vol. 56(1), pages 73-80, March.
    3. Huggins, Richard, 2001. "A note on the difficulties associated with the analysis of capture-recapture experiments with heterogeneous capture probabilities," Statistics & Probability Letters, Elsevier, vol. 54(2), pages 147-152, September.
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