# On the Bayesian Estimation of a Closed Population Size
in the Presence of Heterogeneity and Model Uncertainty

### Ruth King, Stephen P. Brooks

### Universities of St. Andrews and Cambridge

## Summary

We consider the estimation of the size of a closed population, often
of interest for wild animal populations, using a capture-recapture
study. The estimate of the total population size can be very
sensitive to the choice of model used to fit to the data. We
consider a Bayesian approach, in which we consider all eight
plausible models initially described by *Otis et al.* (1978) within a
single framework, including models containing an individual
heterogeneity component. We show how we are able to obtain a
model-averaged estimate of the total population, incorporating both
parameter and model uncertainty. To illustrate the methodology we
initially perform a simulation study and analyse two datasets where
the population size is known, before considering a real example
relating to a population of dolphins based in North East Scotland.

### Keywords:

Bayesian approach, Heterogeneity,
Model-averaging, Population size, Reversible jump Markov chain Monte
Carlo.