Advertisement

Environmental and Ecological Statistics

, Volume 17, Issue 3, pp 317–332 | Cite as

Bayesian analysis of abundance for binomial sighting data with unknown number of marked individuals

  • Brett T. McClintock
  • Jennifer A. Hoeting
Article

Abstract

The mark-resight method for estimating the size of a closed population can in many circumstances be a less expensive and less invasive alternative to traditional mark-recapture. Despite its potential advantages, one major drawback of traditional mark-resight methodology is that the number of marked individuals in the population available for resighting needs to be known exactly. In real field studies, this can be quite difficult to accomplish. Here we develop a Bayesian model for estimating abundance when sighting data are acquired from distinct sampling occasions without replacement, but the exact number of marked individuals is unknown. By first augmenting the data with some fixed number of individuals comprising a marked “super population,” the problem may then be reformulated in terms of estimating the proportion of this marked super population that was actually available for resighting. This then allows the data for the marked population available for resighting to be modeled as random realizations from a binomial logit-normal distribution. We demonstrate the use of our model to estimate the New Zealand robin (Petroica australis) population size in a region of Fiordland National Park, New Zealand. We then evaluate the performance of the proposed model relative to other estimators via a series of simulation experiments. We generally found our model to have advantages over other models when sample sizes are smaller with individually heterogeneous resighting probabilities. Due to limited budgets and the inherent variability between individuals, this is a common occurrence in mark-resight population studies. WinBUGS and R code to carry out these analyses is available from http://www.stat.colostate.edu/~jah/software.

Keywords

Individual heterogeneity Mark-resight Marking and sighting Markov chain Monte Carlo Population size 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Arnason AN, Schwarz CJ, Gerrard JM (1991) Estimating closed population size and number of marked animals from sighting data. J Wildl Manage 55: 716–730CrossRefGoogle Scholar
  2. Burnham KP, Anderson DR (2002) Model selection and multi-model inference: a practical information-theoretic approach. 2nd edn. Springer, New YorkGoogle Scholar
  3. Burnham KP, Anderson DR, White GC, Brownie C, Pollock KH (1987) Design and analysis methods for fish survival experiments based on release-recapture. American Fisheries Society Monograph 5, Bethesda, MD, 437 ppGoogle Scholar
  4. Gelman A (1996) Inference and monitoring convergence. In: Gilks WR, Richardson S, Spiegelhalter DJ(eds) Markov chain Monte Carlo in practice.. Chapman and Hall/CRC, Boca Raton, FL, pp 131–143Google Scholar
  5. Givens GH, Hoeting JA (2005) Computational statistics. Wiley, Hoboken, NJGoogle Scholar
  6. Kendall WL, Pollock KH, Brownie C (1995) A likelihood-based approach to capture-recapture estimation of demographic parameters under the robust design. Biometrics 51: 293–308CrossRefPubMedGoogle Scholar
  7. McClintock BT, White GC, Antolin MF, Tripp DW (2009) Estimating abundance using mark-resight when sampling is with replacement or the number of marked individuals is unknown. Biometrics 65:in pressGoogle Scholar
  8. McClintock BT, White GC, Burnham KP, Pryde MA (2008) A generalized mixed effects model of abundance for mark-resight data when sampling is without replacement. In: Thomson DL, Cooch EG, Conroy MJ(eds) Modeling demographic processes in marked populations.. Springer, New York, pp 271–289Google Scholar
  9. Minta S, Mangel M (1989) A simple population estimate based on simulation for capture-recapture and capture-resight data. Ecology 70: 1738–1751CrossRefGoogle Scholar
  10. Neal AK, White GC, Gill RB, Reed DF, Olterman JH (1993) Evaluation of mark-resight model assumptions for estimating mountain sheep numbers. J Wildl Manage 57: 436–450CrossRefGoogle Scholar
  11. Otis DL, Burnham KP, White GC, Anderson DR (1978) Statistical inference from capture data on closed animal populations. Wildlife Monogr 62: 1–135Google Scholar
  12. Royle JA, Dorazio RM, Link WA (2007) Analysis of multinomial models with unknown index using data augmentation. J Comput Graph Stat 16: 67–85CrossRefGoogle Scholar
  13. SAS Institute (2002) SAS OnlineDoc, Ver. 9. SAS Institute, Cary, NCGoogle Scholar
  14. Spiegelhalter DJ, Best NG, Carlin BP, van der Linde A (2002) Bayesian measures of model complexity and fit (with discussion). J R Stat Soc B 64: 1–34CrossRefGoogle Scholar
  15. White GC, Burnham KP (1999) Program MARK: survival estimation from populations of marked individuals. Bird Study 46: 120–139CrossRefGoogle Scholar
  16. White GC, Shenk TM (2001) Population estimation with radio-marked animals. In: Millspaugh J, Marzluff JM(eds) Radio tracking and animal populations. Academic Press, San Diego, CA, pp 329–350CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Department of StatisticsColorado State UniversityFort CollinsUSA
  2. 2.USGS Patuxent Wildlife Research CenterLaurelUSA

Personalised recommendations