Biodiversity Estimation and Joint Species Distribution Modeling

Abstract

Ecology aims to quantify and predict interactions between organisms and their environment, necessitating rigorous statistical frameworks for reliable inference. This dissertation presents statistical methodologies for addressing two fundamental ecological problems: biodiversity estimation and joint species distribution modeling. In Chapter 2, we generalize the notion of biodiversity estimation by extending Hubbell’s fundamental biodiversity number α to σ-diversity and conditional σ-diversity. This extension allows for flexible taxon accumulation growth and enables biodiversity estimation across different layers of the Linnean taxonomy. In Chapter 3, we propose a Bayesian mixture framework for joint species distribution modeling. This approach explicitly accounts for rare and previously unobserved species, mitigating biases in traditional models that underestimate biodiversity. Together, these contributions provide a principled statistical foundation for biodiversity estimation and species distribution modeling. Theoretical and empirical results are provided.