IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v173y2019icp512-524.html
   My bibliography  Save this article

On the estimation of population sizes in capture–recapture experiments

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X19302325
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.jmva.2019.04.010?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Farcomeni, Alessio & Dotto, Francesco, 2021. "A correction to make Chao estimator conservative when the number of sampling occasions is finite," Statistics & Probability Letters, Elsevier, vol. 176(C).
    2. Alessio Farcomeni, 2015. "Latent class recapture models with flexible behavioural response," Statistica, Department of Statistics, University of Bologna, vol. 75(1), pages 5-17.
    3. Donald T McKnight & Day B Ligon, 2017. "Correcting for unequal catchability in sex ratio and population size estimates," PLOS ONE, Public Library of Science, vol. 12(8), pages 1-13, August.
    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. Danilo Alunni Fegatelli & Luca Tardella, 2016. "Flexible behavioral capture–recapture modeling," Biometrics, The International Biometric Society, vol. 72(1), pages 125-135, March.
    6. Linda Altieri & Alessio Farcomeni & Danilo Alunni Fegatelli, 2023. "Continuous time‐interaction processes for population size estimation, with an application to drug dealing in Italy," Biometrics, The International Biometric Society, vol. 79(2), pages 1254-1267, June.
    7. repec:jss:jstsof:19:i05 is not listed on IDEAS
    8. J. Andrew Royle, 2009. "Analysis of Capture–Recapture Models with Individual Covariates Using Data Augmentation," Biometrics, The International Biometric Society, vol. 65(1), pages 267-274, March.
    9. Neil Stewart & Christoph Ungemach & Adam J. L. Harris & Daniel M. Bartels & Ben R. Newell & Gabriele Paolacci & Jesse Chandler, 2015. "The average laboratory samples a population of 7,300 Amazon Mechanical Turk workers," Judgment and Decision Making, Society for Judgment and Decision Making, vol. 10(5), pages 479-491, September.
    10. Olivier Binette & Rebecca C. Steorts, 2022. "On the reliability of multiple systems estimation for the quantification of modern slavery," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(2), pages 640-676, April.
    11. Brett T. McClintock & Gary C. White & Michael F. Antolin & Daniel W. Tripp, 2009. "Estimating Abundance Using Mark–Resight When Sampling Is with Replacement or the Number of Marked Individuals Is Unknown," Biometrics, The International Biometric Society, vol. 65(1), pages 237-246, March.
    12. repec:cup:judgdm:v:10:y:2015:i:5:p:479-491 is not listed on IDEAS
    13. Yee, Thomas W. & Stoklosa, Jakub & Huggins, Richard M., 2015. "The VGAM Package for Capture-Recapture Data Using the Conditional Likelihood," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 65(i05).
    14. Yuzi Zhang & Howard H. Chang & Qu Cheng & Philip A. Collender & Ting Li & Jinge He & Justin V. Remais, 2023. "A hierarchical model for analyzing multisite individual‐level disease surveillance data from multiple systems," Biometrics, The International Biometric Society, vol. 79(2), pages 1507-1519, June.
    15. Francesco Bartolucci & Fulvia Pennoni, 2007. "A Class of Latent Markov Models for Capture–Recapture Data Allowing for Time, Heterogeneity, and Behavior Effects," Biometrics, The International Biometric Society, vol. 63(2), pages 568-578, June.
    16. Santostasi, Nina Luisa & Ciucci, Paolo & Bearzi, Giovanni & Bonizzoni, Silvia & Gimenez, Olivier, 2020. "Assessing the dynamics of hybridization through a matrix modelling approach," Ecological Modelling, Elsevier, vol. 431(C).
    17. Jolynn Pek & Hao Wu, 2015. "Profile Likelihood-Based Confidence Intervals and Regions for Structural Equation Models," Psychometrika, Springer;The Psychometric Society, vol. 80(4), pages 1123-1145, December.
    18. Yang Liu & Yukun Liu & Yan Fan & Han Geng, 2018. "Likelihood ratio confidence interval for the abundance under binomial detectability models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(5), pages 549-568, July.
    19. Camille Le Roy & Camille Roux & Elisabeth Authier & Hugues Parrinello & Héloïse Bastide & Vincent Debat & Violaine Llaurens, 2021. "Convergent morphology and divergent phenology promote the coexistence of Morpho butterfly species," Nature Communications, Nature, vol. 12(1), pages 1-9, December.
    20. Rivest Louis-Paul, 2011. "A Lower Bound Model for Multiple Record Systems Estimation with Heterogeneous Catchability," The International Journal of Biostatistics, De Gruyter, vol. 7(1), pages 1-21, May.
    21. Fewster, R.M. & Jupp, P.E., 2013. "Information on parameters of interest decreases under transformations," Journal of Multivariate Analysis, Elsevier, vol. 120(C), pages 34-39.
    22. Rivest, Louis-Paul, 2021. "Limiting properties of an equiprobable sampling scheme for 0–1 matrices," Statistics & Probability Letters, Elsevier, vol. 172(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:173:y:2019:i:c:p:512-524. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.