Bayesian discovery of species in multiple areas

TL;DR

This paper introduces a Bayesian framework for analyzing species diversity across multiple areas, enabling out-of-sample predictions of unseen and shared species, with applications to ecological sampling.

Contribution

It extends Bayesian nonparametric methods to heterogeneous populations from two areas, providing distributional theory and out-of-sample prediction capabilities.

Findings

Distributional theory for in-sample analysis of two-area data

Out-of-sample prediction of unseen and shared species

Application to real-world ant population data

Abstract

In ecology, the description of species composition and biodiversity calls for statistical methods that involve estimating features of interest in unobserved samples based on an observed one. In the last decade, the Bayesian nonparametrics literature has thoroughly investigated the case where data arise from a homogeneous population. In this work, we propose a novel framework to address heterogeneous populations, specifically dealing with scenarios where data arise from two areas. This setting significantly increases the mathematical complexity of the problem and, as a consequence, it has received limited attention in the literature. While early approaches leverage computational methods, we provide a distributional theory for the in-sample analysis of any observed sample and enable out-of-sample prediction for the number of unseen distinct and shared species in additional samples of arbitrary sizes. The latter also extends the frequentist estimators, which solely deal with one-step-ahead prediction. Furthermore, our results can be applied to address sample size determination in sampling problems aimed at detecting distinct and shared species. Our results are illustrated in a real-world dataset concerning a population of ants in the city of Trieste.