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.

翻译：生物多样性度量常被用于描述性目的：从观测或估算的群落组成计算多样性指数，并将结果值空间映射。然而，保护规划还需要一个特定地点的基准，用于与观测群落进行比较。本章为这种“潜在多样性”及相关的“多样性差距”建立了一个信息几何框架。其核心是物种单形上的两个概率向量：一个观测或实现组成 \(p^{\mathrm{obs}}\)，以及通过约束变分原理获得的潜在组成 \(p^{\mathrm{pot}}\)。然后通过比较这两个组成处的多样性函数来定义差距。该框架既适用于衡量丰度和均匀度的希尔型多样性，也适用于纳入物种间性状、系统发育或生态差异的拉奥二次熵。空间点过程解释阐明了如何在过渡到单形之前定义局部生态容量。随后，伴随约束、容量约束和散度投影提供了一种超越均匀分布定义非平凡基准的统一方法。所得公式分离了两个不同的问题：一个群落有多多样，以及它距离局部可接受的潜在基准有多远。它还将黑暗多样性的生态学概念与概率单形上的连续、丰度加权比较联系起来。我们还概述了一个动态扩展，其中容量、物种迁徙和气候驱动的变化随时间变化。基于大规模公民科学生物多样性数据和性状数据库的实证实现留待未来工作。