A Bayesian theory for estimation of biodiversity

Tommaso Rigon, Ching-Lung Hsu, David Dunson

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 α, 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, build- ing on the literature on Gibbs-type priors. We argue that σ-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 model- ing 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.