Bayesian Estimation of the Size of a Closed Population Using Photo-ID Data with Part of the Population Uncatchable

Abstract

We develop a Bayesian statistical model for estimating bowhead whale population size from photo-identification data when most of the population is uncatchable. The proposed conditional likelihood function is a product of Darroch's model, formulated as a function of the number of good photos, and a binomial distribution of captured whales given the total number of good photos at each occasion. The full Bayesian model is implemented via adaptive rejection sampling for log concave densities. We apply the model to data from 1985 and 1986 bowhead whale photographic studies and the results compare favorably with the ones obtained in the literature. Also, a comparison with the maximum likelihood procedure with bootstrap simulation is considered using different vague priors for the capture probabilities.

Keywords:

• Capture–recapture
• Closed uncatchable populations
• Bayesian models

Acknowledgments

The authors are grateful to Judy Zeh and Anthony Davison and to the anonymous referees for a careful reading of the manuscript and for constructive suggestions which considerably improved the article. Data for this analysis were provided through photographic aerial surveys conducted by LGL Limited (King City, Ontario, Canada) and the National Marine Mammal Laboratory (NMFS, NOAA, Seattle, Washington, USA). We particularly thank Bill Koski and Gary Miller of LGL and Dave Rugh of the National Marine Mammal Laboratory for their work on the surveys, the scoring and matching of photographs, and creation of the data base. The first author was partially funded by PRPq-UFMG, Brazil.