Numerical Survival Rate Estimation for Capture-Recapture Models Using SAS PROC NLIN

  • Kenneth P. Burnham
Part of the Lecture Notes in Statistics book series (LNS, volume 55)

Abstract

This paper discusses and illustrates recent developments in the modeling and analysis of capture-recapture data for open populations. Results are presented using a unified theory of cohort survival processes. The statistical models for survival rate estimation are represented as products of conditionally independent multinomials; this is achieved by always conditioning on the known number of releases initiating the cohorts. This approach facilitates extension of the Jolly-Seber model to control-treatment studies, or other contexts where comparison of population survival rates is of most interest. Numerical computation of maximum likelihood survival and capture rate estimators, under any model, is easily achieved using iteratively-reweighted nonlinear least squares in SAS PROC NLIN. In his classical paper, Jolly (1965) illustrated his methods using summary statistics on female black-kneed capsids (Blepharidopterus angulatus). Here I use the entire data set on males and females to illustrate survival rate estimation and flexible modeling of capture-recapture data.

Keywords

Open Population Daily Survival Rate Capture History Survival Rate Estimation Proc NLIN 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Arnason, A. N., & L. Baniuk. 1980. A computer system for mark-recapture analysis of open populations. J. Wildl. Mgt.44: 325 – 332CrossRefGoogle Scholar
  2. Brownie, C., D. R. Anderson, K. P. Burnham, & D. S. Robson. 1985. Statistical inference from band recovery data — a handbook, 2nd edition. U.S. Fish and Wildlife Service Resource Publication 156.Google Scholar
  3. Brownie, C., J. E. Hines, & J. D. Nichols. 1986. Constant parameter capture—recapture models. Biometrics42: 561 – 574.MathSciNetMATHCrossRefGoogle Scholar
  4. Brownie, C., & D. S. Robson. 1983. Estimation of time—specific survival rates from tag—resighting samples: a generalization of the Jolly—Seber model. Biometrics39: 437 – 453.MathSciNetMATHCrossRefGoogle Scholar
  5. Buckland, S. T. 1980. A modified analysis of the Jolly—Seber capture—recapture model. Biometrics36: 419 – 435.CrossRefGoogle Scholar
  6. Burnham, K. P., D. R. Anderson, G. C. White, C. Brownie, & K. H. Pollock. 1987. Design and analysis methods for fish survival experiments based on capture—recapture. Monograph 5, American Fisheries Society, Bethesda, Maryland.Google Scholar
  7. Clobert, J., J. D. Lebreton, & D. Allaine. 1987. A general approach to survival rate estimation by recaptures or resightings of marked birds. Ardea75: 113 – 142.Google Scholar
  8. Cormack, R. M. 1964. Estimates of survival from sighting of marked animals. Biometrika51: 429 – 438.MATHGoogle Scholar
  9. Cormack, R. M. 1981. Loglinear models for capture—recapture experiments on open populations. Pages 217–235. In R. W. Hiorns and D. Cooke [eds.]. The mathematical theory of the dynamics of biological populations. Academic Press, London.Google Scholar
  10. Ciosbie, S. F., & B. F. J. Manly. 1985. A new approach for parsimonious modeling of capture—recapture studies. Biometrics41: 385 – 398.CrossRefGoogle Scholar
  11. Green, P. J. 1984. Iteratively reweighted least squares maximum likelihood estimation and some robust and resistant alternatives. J. Royal Statist Soc., Series B 46: 149 – 192.MATHGoogle Scholar
  12. Jennrich, R. I., & R. H. Moore. 1975. Maximum likelihood estimation by means of nonlinear least squares. Pages 57–65 in American Statistical Association 1975 Proceedings of the Statistical Computing Section. American Statistical Association, Washington, D. C.Google Scholar
  13. Jolly, G. M. 1965. Explicit estimates from capture—recapture data with both death and immigration — stochastic models. Biometrika52: 225 – 247.MathSciNetMATHGoogle Scholar
  14. Jolly, G. M. 1982. Mark—recapture models with parameters constant in time. Biometrics38: 301 – 321.MathSciNetMATHCrossRefGoogle Scholar
  15. Manly, B. F. J. 1984. Obtaining confidence limits on parameters of the Jolly—Seber model for capture—recapture data. Biometrics40: 749 – 758.MathSciNetCrossRefGoogle Scholar
  16. Muir, R. C. 1957. On the application of the capture-recapture method to an orchard population of Blepharidopterus angvlatatus(Fall.) (Hemiptera—Heteroptera, Miridae). East Mailing Annual Report 1957: 140 – 147.Google Scholar
  17. Pollock, K. H. 1975. A K—sample tag—recapture model allowing for unequal survival and catchability. Biometrika62: 577 – 583.MathSciNetMATHGoogle Scholar
  18. Pollock, K. H. 1981a. Capture—recapture models allowing for age—dependent survival and capture rates. Biometrics37: 521 – 529.MATHCrossRefGoogle Scholar
  19. Pollock, K. H. 1981b. Capture-recapture models: a review of current methods, assumptions, and experimental design. Studies in Avian Biology 6: 426 – 435.Google Scholar
  20. Pollock, K. H., J. E. Hines, & J. D. Nichols. 1985. Goodness—of—fit tests for open capture—recapture models. Biometrics41: 399 – 410.MATHCrossRefGoogle Scholar
  21. Pollock, K. H., J. D. Nichols, C. Brownie, & J. E. Hines. (in prep). Statistical inference for capture-recapture experiments. Wildlife Monographs, The Wildlife Society, Washington, D. C.Google Scholar
  22. Ralston, M. L., & R. I. Jennrich. 1978. Dud, a derivative—free algorithm for nonlinear least squares. Technometrics20: 7 – 14.MATHCrossRefGoogle Scholar
  23. Robson, D. S. 1969. Mark-recapture methods of population estimation. Pages 129–140 in N. L. Johnson and H. Smith, Jr. [eds.]. New developments in survey sampling. Wiley Int er science, New York.Google Scholar
  24. SAS Institute Inc. 1985. SAS user’s guide: statistics, version 5 edition. SAS Institute Inc., Cary, NC 27511.Google Scholar
  25. Sandland, R. L., & P. Kirkwood. 1981. Estimation of survival in marked populations with possibly dependent sighting probabilities. Biometrika68: 531 – 541.MathSciNetMATHCrossRefGoogle Scholar
  26. Seber, G. A. F. 1965. A note on the multiple—recapture census. Biometrika52: 249 – 259.MathSciNetMATHGoogle Scholar
  27. White, G. C. 1983. Numerical estimation of survival rates from band—recovery and biotelemetry data. J. Wildlife Mgt.47: 716 – 728.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Kenneth P. Burnham
    • 1
  1. 1.USDA-Agricultural Research Service, and Department of StatisticsNorth Carolina State UniversityRaleighUSA

Personalised recommendations