IDEAS home Printed from https://ideas.repec.org/a/spr/jagbes/v24y2019i1d10.1007_s13253-018-00347-x.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13253-018-00347-x
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s13253-018-00347-x?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. 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. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. B. J. T. Morgan & M. S. Ridout, 2008. "A new mixture model for capture heterogeneity," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 57(4), pages 433-446, September.
    10. 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.
    11. Jerome A. Dupuis & Carl James Schwarz, 2007. "A Bayesian Approach to the Multistate Jolly–Seber Capture–Recapture Model," Biometrics, The International Biometric Society, vol. 63(4), pages 1015-1022, December.
    12. R. M. Fewster & P. E. Jupp, 2009. "Inference on population size in binomial detectability models," Biometrika, Biometrika Trust, vol. 96(4), pages 805-820.
    13. 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.
    14. R. King, 2003. "Closed-form likelihoods for Arnason--Schwarz models," Biometrika, Biometrika Trust, vol. 90(2), pages 435-444, June.
    15. Ruth King & Roland Langrock, 2016. "Semi-Markov Arnason–Schwarz models," Biometrics, The International Biometric Society, vol. 72(2), pages 619-628, June.
    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. B. J. T. Morgan & M. S. Ridout, 2008. "A new mixture model for capture heterogeneity," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 57(4), pages 433-446, September.
    2. 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.
    3. Chang Xuan Mao & Na You, 2009. "On Comparison of Mixture Models for Closed Population Capture–Recapture Studies," Biometrics, The International Biometric Society, vol. 65(2), pages 547-553, June.
    4. Shirley Pledger & Kenneth H. Pollock & James L. Norris, 2010. "Open Capture–Recapture Models with Heterogeneity: II. Jolly–Seber Model," Biometrics, The International Biometric Society, vol. 66(3), pages 883-890, September.
    5. 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.
    6. Alessio Farcomeni, 2015. "Latent class recapture models with flexible behavioural response," Statistica, Department of Statistics, University of Bologna, vol. 75(1), pages 5-17.
    7. 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.
    8. Fodé Tounkara & Louis‐Paul Rivest, 2015. "Mixture regression models for closed population capture–recapture data," Biometrics, The International Biometric Society, vol. 71(3), pages 721-730, September.
    9. 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.
    10. 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.
    11. J. Andrew Royle, 2006. "Site Occupancy Models with Heterogeneous Detection Probabilities," Biometrics, The International Biometric Society, vol. 62(1), pages 97-102, March.
    12. Jakub Stoklosa & Wen-Han Hwang & Sheng-Hai Wu & Richard Huggins, 2011. "Heterogeneous Capture–Recapture Models with Covariates: A Partial Likelihood Approach for Closed Populations," Biometrics, The International Biometric Society, vol. 67(4), pages 1659-1665, December.
    13. Dankmar Böhning, 2010. "Some General Comparative Points on Chao's and Zelterman's Estimators of the Population Size," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(2), pages 221-236, June.
    14. Orasa Anan & Dankmar Böhning & Antonello Maruotti, 2017. "Population size estimation and heterogeneity in capture–recapture data: a linear regression estimator based on the Conway–Maxwell–Poisson distribution," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 26(1), pages 49-79, March.
    15. 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.
    16. 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.
    17. 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.
    18. Jennifer B Smith & Bryan S Stevens & Dwayne R Etter & David M Williams, 2020. "Performance of spatial capture-recapture models with repurposed data: Assessing estimator robustness for retrospective applications," PLOS ONE, Public Library of Science, vol. 15(8), pages 1-16, August.
    19. William A. Link, 2006. "The author replied as follows:," Biometrics, The International Biometric Society, vol. 62(3), pages 936-939, September.
    20. 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.

    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:spr:jagbes:v:24:y:2019:i:1:d:10.1007_s13253-018-00347-x. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.