  Wildlife monitoring for open populations can be performed using a number of
different survey methods. Each survey method gives rise to a type of data and,
in the last five decades, a large number of associated statistical models have
been developed for analysing these data. Although these models have been
parameterised and fitted using different approaches, they have all been
designed to model the pattern with which individuals enter and exit the
population and to estimate the population size. However, existing approaches
rely on a predefined model structure and complexity, either by assuming that
parameters are specific to sampling occasions, or by employing parametric
curves. Instead, we propose a novel Bayesian nonparametric framework for
modelling entry and exit patterns based on the Polya Tree (PT) prior for
densities. Our Bayesian non-parametric approach avoids overfitting when
inferring entry and exit patterns while simultaneously allowing more
flexibility than is possible using parametric curves. We apply our new
framework to capture-recapture, count and ring-recovery data and we introduce
the replicated PT prior for defining classes of models for these data.
Additionally, we define the Hierarchical Logistic PT prior for jointly
modelling related data and we consider the Optional PT prior for modelling long
time series of data. We demonstrate our new approach using five different case
studies on birds, amphibians and insects.
