A Polya Tree Based Model for Unmarked Individuals in an Open Wildlife Population

Many ecological sampling schemes do not allow for unique marking of individuals. Instead, only counts of individuals detected on each sampling occasion are available. In this paper, we propose a novel approach for modelling count data in an open population where individuals can arrive and depart from the site during the sampling period. A Bayesian nonparametric prior, known as Polya Tree, is used for modelling the bivariate density of arrival and departure times. Thanks to this choice, we can easily incorporate prior information on arrival and departure density while still allowing the model to flexibly adjust the posterior inference according to the observed data. Moreover, the model provides great scalability as the complexity does not depend on the population size but just on the number of sampling occasions, making it particularly suitable for data-sets with high numbers of detections. We apply the new model to count data of newts collected by the Durrell Institute of Conservation and Ecology, University of Kent.