  Capture-recapture studies are widely used to obtain information about
abundance (population size or density) of animal populations. A common design
is that in which multiple distinct populations are sampled, and the research
objective is modeling variation in population size $N_{s}; s=1,2,...,S$ among
the populations such as estimating a treatment effect or some other source of
variation related to landscape structure. The problem is naturally resolved
using hierarchical models. We provide a Bayesian formulation of such models
using data augmentation which preserves the individual encounter histories in
the model and, as such, is amenable to modeling individual effects. We
formulate the model by conditioning on the total population size among all
populations. In this case, the abundance model can be formulated as a
multinomial model that allocates individuals among sites. MCMC is easily
carried out by the introduction of a categorical individual effect, $g_{i}$,
which partitions the total population size. The prior distribution for the
latent variable $g$ is derived from the model assumed for the population sizes
$N_{s}$.
