An information-geometric framework for mapping maximum potential biodiversity

2026-06-05

AI Summary

This study addresses a critical gap in biodiversity assessment: the absence of site-specific benchmarks for potential diversity that enable quantification of the disparity between observed communities and their ecological capacity. The authors propose a theoretical framework grounded in information geometry, which integrates Hill diversity and Rao’s quadratic entropy within a constrained variational principle on the probability simplex to construct a continuous, abundance-weighted baseline of potential diversity. This approach unifies evenness, functional traits, and phylogenetic dissimilarity into a single coherent measure, representing the first synthesis of information geometry with ecological capacity and linking explicitly to the concept of “dark diversity.” The resulting model cleanly distinguishes current diversity from attainable potential and supports dynamic extensions under scenarios of species migration and climate change, thereby providing a robust theoretical foundation for regional biodiversity conservation.

Abstract

Biodiversity measures are often used descriptively: one computes a diversity index from an observed or estimated community composition and maps the resulting values across space. Conservation planning, however, also requires a site-specific benchmark against which the observed community can be compared. This chapter develops an information-geometric framework for such \emph{potential diversity} and the associated \emph{diversity gap}. The central object is a pair of probability vectors on the species simplex: an observed or realized composition \(p^{\mathrm{obs}}\), and a potential composition \(p^{\mathrm{pot}}\) obtained by a constrained variational principle. The gap is then defined by comparing a diversity functional at these two compositions. The framework is developed for both Hill-type diversity, which measures abundance and evenness, and Rao's quadratic entropy, which incorporates trait, phylogenetic, or ecological dissimilarities among species. A spatial point-process interpretation clarifies how local ecological capacities can be defined before passing to the simplex. Escort constraints, capacity constraints, and divergence projections then provide a unified way to define nontrivial benchmarks beyond the uniform distribution. The resulting formulation separates two distinct questions: how diverse a community is, and how far it is from a locally admissible potential benchmark. It also connects the ecological idea of dark diversity with a continuous, abundance-weighted comparison on the probability simplex. We also outline a dynamic extension in which capacities, species migration, and climate-driven shifts vary over time. Empirical implementation with large-scale citizen-science biodiversity data and trait databases is left for future work.

Problem

• potential diversity
• diversity gap
• information geometry
• biodiversity benchmark
• species simplex

Innovation

• information geometry
• potential diversity
• diversity gap
• constrained variational principle
• Rao's quadratic entropy