A Generalized Mixed Effects Model of Abundance for Mark-Resight Data When Sampling is Without Replacement

  • Brett T. McClintock
  • Gary C. White
  • Kenneth P. Burnham
  • Moira A. Pryde
Part of the Environmental and Ecological Statistics book series (ENES, volume 3)


In recent years, the mark-resight method for estimating abundance when the number of marked individuals is known has become increasingly popular. By using field-readable bands that may be resighted from a distance, these techniques can be applied to many species, and are particularly useful for relatively small, closed populations. However, due to the different assumptions and general rigidity of the available estimators, researchers must often commit to a particular model without rigorous quantitative justification for model selection based on the data. Here we introduce a nonlinear logit-normal mixed effects model addressing this need for a more generalized framework. Similar to models available for mark-recapture studies, the estimator allows a wide variety of sampling conditions to be parameterized efficiently under a robust sampling design. Resighting rates may be modeled simply or with more complexity by including fixed temporal and random individual heterogeneity effects. Using information theory, the model(s) best supported by the data may be selected from the candidate models proposed. Under this generalized framework, we hope the uncertainty associated with mark-resight model selection will be reduced substantially. We compare our model to other mark-resight abundance estimators when applied to mainland New Zealand robin (Petroica australis) data recently collected in Eglinton Valley, Fiordland National Park and summarize its performance in simulation experiments.


Population size Logit-normal Program NOREMARK Sighting probability Mark-recapture Bowden’s estimator 


  1. Abramowitz M, Stegun I (1964) Handbook of Mathematical Functions, with Formulas, Graphs and Math Tables. Applied Math Series 55, National Bureau of Standards, U.S. Government Printing Office, Washington, DC.Google Scholar
  2. Bartmann RM, White GC, Carpenter LH, Garrott RA (1987) Aerial mark-recapture estimates of confined mule deer in pinyon-juniper woodland. Journal of Wildlife Management 51:41–46.CrossRefGoogle Scholar
  3. Bowden DC, Kufeld RC (1995) Generalized mark-resight population size estimation applied to Colorado moose. Journal of Wildlife Management 59:840–851.CrossRefGoogle Scholar
  4. Burnham KP, Anderson DR (2002) Model Selection and Multi-Model Inference: A Practical Information-Theoretic Approach. 2nd edition. Springer-Verlag, New York.Google Scholar
  5. Burnham KP, Anderson DR (2004) Multimodel inference: understanding AIC and BIC in model selection. Sociological Methods and Research 33:261–304.CrossRefMathSciNetGoogle Scholar
  6. Cochran WG (1977) Sampling Techniques. 3rd edition. Wiley, New York.Google Scholar
  7. Givens GH, Hoeting JA (2005) Computational Statistics. Wiley, Hoboken, NJ.Google Scholar
  8. Hocking RR (2003) Methods and Applications of Linear Models. 2nd edition. Wiley, Hoboken, NJ.CrossRefGoogle Scholar
  9. Kendall WL, Pollock KH, Brownie C (1995) A likelihood-based approach to capture–recapture estimation of demographic parameters under the robust design. Biometrics 51: 293–308.CrossRefzbMATHGoogle Scholar
  10. Link WA, Barker RJ (2006) Model weights and the foundations of multimodel inference. Ecology 87:2626–2635.CrossRefGoogle Scholar
  11. Magle SM, McClintock BT, Tripp DW, White GC, Antolin MF, Crooks KR (2007) Mark‐resight methodology for estimating population densities for prairie dogs 71:2067–2073.Google Scholar
  12. McClintock BT, White GC (2007) Bighorn sheep abundance following a suspected pneumonia epidemic in Rocky Mountain National Park. Journal of Wildlife Management 71: 183–189.CrossRefGoogle Scholar
  13. McClintock BT, White GC, Burnham KP (2006) A robust design mark-resight abundance estimator allowing heterogeneity in resighting probabilities. Journal of Agricultural, Biological, and Environmental Statistics 11:231–248.CrossRefGoogle Scholar
  14. Minta S, Mangel M (1989) A simple population estimate based on simulation for capture-recapture and capture–resight data. Ecology 70:1738–1751.CrossRefGoogle Scholar
  15. Neal AK, White GC, Gill RB, Reed DF, Olterman JH (1993) Evaluation of mark-resight model assumptions for estimating mountain sheep numbers. Journal of Wildlife Management 57:436–450.CrossRefGoogle Scholar
  16. Otis DL, Burnham KP, White GC, Anderson DR (1978) Statistical inference from capture data on closed animal populations. Wildlife Monographs 62.Google Scholar
  17. Pollock KH (1982) A capture–recapture design robust to unequal probability of capture. Journal of Wildlife Management 46:752–760.CrossRefGoogle Scholar
  18. SAS Institute (2002) SAS OnlineDoc, Version 9. SAS Institute, Inc., Cary, NC.Google Scholar
  19. Schwarz G (1978) Estimating the dimension of a model. Annals of Statistics 6:461–464.CrossRefzbMATHMathSciNetGoogle Scholar
  20. White GC (1993) Evaluation of radio tagging marking and sighting estimators of population size using Monte Carlo simulations. In Marked Individuals in the Study of Bird Populations, Lebreton JD, North PM, eds. Birkhauser-Verlag, Basel, Switzerland, pp. 91–103.Google Scholar
  21. White GC, Shenk TM (2001) Population estimation with radio-marked animals. In Radio Tracking and Animal Populations, Millspaugh J, Marzluff JM eds. Academic Press, San Diego, pp. 329–350.Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  • Brett T. McClintock
    • 1
  • Gary C. White
  • Kenneth P. Burnham
  • Moira A. Pryde
  1. 1.USGS Patuxent Wildlife Research CenterLaurelUSA

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