Skip to main content
Log in

A unified approach for estimating population size in capture-recapture studies with arbitrary removals

  • Published:
Journal of Agricultural, Biological, and Environmental Statistics Aims and scope Submit manuscript

Abstract

A unified approach is suggested to estimate the population size for a closed population in discrete time. Individuals can be removed after capture at any time during the experiment. The usual recapture and removal experimentsare shown to be particular cases of the general formulation. The capture probability is assumed to have a logistic function that depends on individual covariates and can be time dependent. The unified approach involves a two-step procedure. A conditional likelihood function is used to estimate the covariates coefficients and a Horvitz-Thompson type estimator to estimate the population size. The asymptotic and small-sample properties of the resulting estimators are in vestigated. A real example is given.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Andersen, P. K., Borgan, O., Gill, R. D., and Keiding, N. (1993), Statistical Models Based on Counting Processes, New York: Springer-Verlag.

    MATH  Google Scholar 

  • Burnham, K. P., and Overton, W. S. (1978), “Estimation of the Size of a Closed Population When Capture Probabilities Vary Among Animals,” Biometrika, 65, 625–633. Correction, 68, 345.

    Article  MATH  Google Scholar 

  • Carothers, A. D. (1973), “The Effects of Unequal Catchability on Jolly-Seber Estimates,” Biometrics, 29, 79–100.

    Article  Google Scholar 

  • Chao, A. (1987), “Estimating the Population Size for Capture-Recapture Data With Unequal Capturability,” Biometrics, 43, 783–791.

    Article  MATH  MathSciNet  Google Scholar 

  • Chao, A., and Lee, S. M. (1992), “Estimating the Number of Classes via Sample Coverage,” Journal of the American Statistical Assocition, 87, 210–217.

    Article  MATH  MathSciNet  Google Scholar 

  • Cormack, R. M. (1968), “The Statistics of Capture-Recapture Methods,” Oceanography and Marine Biology: An Annual Review, 6, 455–506.

    Google Scholar 

  • Cox, D. R., and Hinkley, D. V. (1974), Theoretical Statistics, London, Chapman and Hall.

    MATH  Google Scholar 

  • Horvitz, D. G., and Thompson, D. J. (1952), “A Generalization of Sampling Without Replacement From a Finite Universe,” Journal of the American Statistical Association, 47, 663–685.

    Article  MATH  MathSciNet  Google Scholar 

  • Huggins, R. M. (1989), “On the Statistical Analysis of Capture Experiments,” Biometrika, 76, 133–140.

    Article  MATH  MathSciNet  Google Scholar 

  • — (1991), “Some Practical Aspects of a Conditional Likelihood Approach to Capture-Recapture Models,” Biometrics, 47, 725–732.

    Article  Google Scholar 

  • Huggins, R. M., and Yi, P. S. F. (1997), “Statistical Analysis of Removal Experiments With the Use of Auxiliary Variables,” Statistica Sinica, 7, 705–712.

    MATH  Google Scholar 

  • Lee, S. M., and Chao, A. (1994), “Estimating Population Size via Sample Coverage for Closed Capture-Recapture Methods,” Biometrics, 50, 88–97.

    Article  MATH  Google Scholar 

  • Lloyd, C., Yip, P. S. F., and Chan, K. S. (1998), “A Comparison of Recapturing, Removal and Resighting Designs for Population Size Estimation,” Journal of Statistical Inference and Planning, 71, 363–373.

    Article  MATH  MathSciNet  Google Scholar 

  • Manly, B. F. J. (1970), A Simulation Study of Animal Population Estimation Using the Capture-Recapture Method,” Journal of Applied Ecology, 7, 13–39.

    Article  Google Scholar 

  • Nayak, T. K. (1988), “Estimating Population Size by Recapture Sampling,” Biometrika, 75, 113–120.

    Article  MATH  MathSciNet  Google Scholar 

  • Otis, D. L., Burnham, K. P., White, G. C., and Anderson, D. R. (1978), “Statistical Inference From Capture Data on Closed Animal Populations,” Wildlife Monograph, 62, Washington, DC: The Wildlife Society.

    MATH  Google Scholar 

  • Pollock, K. H. (1993), “Modeling Capture, Recapture and Removal Statistics for Estimation of Demographic Parameters for Fish and Wildlife Populations: Past, Present and Future,” Journal of the American Statistical Association, 86, 225–238.

    Article  Google Scholar 

  • Pollock, K. H., Hines, J. E., and Nichols, J. D. (1984), “The Use of Auxillary Variables in Capture-Recapture and Removal Experiments,” Biometrics, 40, 329–340.

    Article  MATH  Google Scholar 

  • Yip, P. S. F. (1995), “Estimating Number of Errors in a Computer Program,” IEEE Transactions on Reliability 44, 322–326.

    Article  Google Scholar 

  • Yip, P. S. F., Chan, K. S., and Lin, D. Y. (1996), “Regression Models for Discrete-Time Recapture and Removal Studies,” ASA Proceedings, Biopharmaceutical Section, 103–107.

  • Yip, P. S. F., Huggins, R., and Lin, D. Y. (1996), “An Inference Procedure for Capture-Recapture Experiments in Continuous Time With Variable Capture Rates,” Biometrika, 83, 477–483.

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Paul S. F. Yip.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Yip, P.S.F., Wan, E.C.Y. & Chan, K.S. A unified approach for estimating population size in capture-recapture studies with arbitrary removals. JABES 6, 183–194 (2001). https://doi.org/10.1198/108571101750524698

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1198/108571101750524698

Key Words

Navigation