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arXiv · 2502.01333

A Bayesian theory for estimation of biodiversity

Tommaso Rigon·Ching-Lung Hsu·David B. Dunson
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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.

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Tommaso Rigon, Ching-Lung Hsu, David B. Dunson. 2025-02-03. A Bayesian theory for estimation of biodiversity. https://arxiv.org/abs/2502.01333

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