A general modelling framework for open wildlife populations based on the Polya Tree prior

TL;DR

This paper introduces a flexible Bayesian nonparametric framework using Polya Tree priors to model entry and exit patterns in open wildlife populations, improving over traditional parametric models.

Contribution

It develops a novel Polya Tree-based Bayesian approach for modeling wildlife population dynamics, allowing greater flexibility and avoiding overfitting compared to existing parametric models.

Findings

Successfully applied to diverse data types including capture-recapture, count, and ring-recovery data.

Demonstrated improved modeling flexibility with five case studies on various species.

Introduced hierarchical and optional PT priors for complex data structures.

Abstract

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.