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On the estimation of population sizes in capture–recapture experiments

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  • Yauck, Mamadou
  • Rivest, Louis-Paul

Abstract

This work considers a nested mark–recapture experiment with two levels of sampling: within each primary sampling period of an open population model, there are secondary capture occasions to estimate the size of the population at that primary period. This scheme is known as Pollock’s robust design. Two sources of information are then available to estimate the population size for a primary period: the within and the between primary period data. This work proves that the population size estimators derived from these two sources are asymptotically independent for a large class of closed population models. In this context, the robust design maximum likelihood estimator of population size is shown to be asymptotically equivalent to a weighted sum of the estimators for the open population Jolly–Seber model (Jolly, 1965; Seber, 1965) and for the closed population model. This article shows that the weighted estimator is more efficient than the moment estimator of Kendall et al. (1995). A closed form expression for the efficiency associated with this estimator is given and evaluated in a Monte Carlo study and in a numerical example about the estimation of the size of dolphin populations discussed by Santostasi et al. (2016).

Suggested Citation

  • Yauck, Mamadou & Rivest, Louis-Paul, 2019. "On the estimation of population sizes in capture–recapture experiments," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 512-524.
    • Handle: RePEc:eee:jmvana:v:173:y:2019:i:c:p:512-524
    DOI: 10.1016/j.jmva.2019.04.010
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    References listed on IDEAS

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    1. Louis-Paul Rivest & Gaétan Daigle, 2004. "Loglinear Models for the Robust Design in Mark–Recapture Experiments," Biometrics, The International Biometric Society, vol. 60(1), pages 100-107, March.
    2. A. Farcomeni, 2016. "A general class of recapture models based on the conditional capture probabilities," Biometrics, The International Biometric Society, vol. 72(1), pages 116-124, March.
    3. R. M. Fewster & P. E. Jupp, 2009. "Inference on population size in binomial detectability models," Biometrika, Biometrika Trust, vol. 96(4), pages 805-820.
    4. Louis-Paul Rivest & Sophie Baillargeon, 2007. "Applications and Extensions of Chao's Moment Estimator for the Size of a Closed Population," Biometrics, The International Biometric Society, vol. 63(4), pages 999-1006, December.
    5. Baillargeon, Sophie & Rivest, Louis-Paul, 2007. "Rcapture: Loglinear Models for Capture-Recapture in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 19(i05).
    6. Nina Luisa Santostasi & Silvia Bonizzoni & Giovanni Bearzi & Lavinia Eddy & Olivier Gimenez, 2016. "A Robust Design Capture-Recapture Analysis of Abundance, Survival and Temporary Emigration of Three Odontocete Species in the Gulf of Corinth, Greece," PLOS ONE, Public Library of Science, vol. 11(12), pages 1-21, December.
    7. Hsin-Chou Yang & Anne Chao, 2005. "Modeling Animals' Behavioral Response by Markov Chain Models for Capture–Recapture Experiments," Biometrics, The International Biometric Society, vol. 61(4), pages 1010-1017, December.
    8. Mamadou Yauck & Louis-Paul Rivest & Greg Rothman, 2019. "Capture-Recapture Methods for Data on the Activation of Applications on Mobile Phones," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(525), pages 105-114, January.
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