Article

Journal of Agricultural, Biological, and Environmental Statistics

, Volume 18, Issue 4, pp 556-577

Insights Into the Latent Multinomial Model Through Mark-Resight Data on Female Grizzly Bears With Cubs-of-the-Year

  • Megan D. HiggsAffiliated withDepartment of Mathematical Sciences, Montana State University Email author 
  • , William A. LinkAffiliated withPatuxent Wildlife Research Center, U.S. Geological Survey
  • , Gary C. WhiteAffiliated withDepartment of Fish, Wildlife, and Conservation Biology, Colorado State University
  • , Mark A. HaroldsonAffiliated withNorthern Rocky Mountain Science Center, Interagency Grizzly Bear Study Team, U.S. Geological Survey
  • , Daniel D. BjornlieAffiliated withLarge Carnivore Section, Wyoming Game and Fish Department

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Abstract

Mark-resight designs for estimation of population abundance are common and attractive to researchers. However, inference from such designs is very limited when faced with sparse data, either from a low number of marked animals, a low probability of detection, or both. In the Greater Yellowstone Ecosystem, yearly mark-resight data are collected for female grizzly bears with cubs-of-the-year (FCOY), and inference suffers from both limitations. To overcome difficulties due to sparseness, we assume homogeneity in sighting probabilities over 16 years of bi-annual aerial surveys. We model counts of marked and unmarked animals as multinomial random variables, using the capture frequencies of marked animals for inference about the latent multinomial frequencies for unmarked animals. We discuss undesirable behavior of the commonly used discrete uniform prior distribution on the population size parameter and provide OpenBUGS code for fitting such models. The application provides valuable insights into subtleties of implementing Bayesian inference for latent multinomial models. We tie the discussion to our application, though the insights are broadly useful for applications of the latent multinomial model.

Key Words

Bayesian Discrete uniform Greater Yellowstone Ecosystem (GYE) Mark-recapture Population size