A Bayesian theory for estimation of biodiversity

TL;DR

This paper introduces Bayesian nonparametric methods for biodiversity estimation, extending ecological theory with novel models based on Gibbs-type priors and hierarchical taxonomy, demonstrated on Amazon tree data.

Contribution

It develops new Bayesian nonparametric tools for biodiversity inference, including methods for estimating the fundamental biodiversity number and $\sigma$-diversity, using Gibbs-type priors and hierarchical models.

Findings

Effective estimation of biodiversity parameters from complex data

Hierarchical models improve biodiversity quantification

Application to Amazon tree flora dataset demonstrates practical utility

Abstract

Statistical inference on biodiversity has a rich history going back to RA Fisher. An influential ecological theory suggests the existence of a fundamental biodiversity number, denoted $\alpha$, which coincides with the precision parameter of a Dirichlet process (DP). In this paper, motivated by this theory, we develop Bayesian nonparametric methods for statistical inference on biodiversity, building on the literature on Gibbs-type priors. We argue that $\sigma$-diversity is the most natural extension of the fundamental biodiversity number and discuss strategies for its estimation. Furthermore, we develop novel theory and methods starting with an Aldous-Pitman (AP) process, which serves as the building block for any Gibbs-type prior with a square-root growth rate. We propose a modeling framework that accommodates the hierarchical structure of Linnean taxonomy, offering a more refined approach to quantifying biodiversity. The analysis of a large and comprehensive dataset on Amazon tree flora provides a motivating application.