Reconceptualizing beta diversity: a hypervolume geometric approach

Beta diversity--the variation among community compositions in a region--is a fundamental measure of biodiversity. Despite a diverse set of measures to quantify beta diversity, most measures have posited that beta diversity is maximized when each community has a single distinct species. However, this assumption overlooks the ecological significance of species interactions and non-additivity in ecological systems, where the function and behaviour of species depend on other species in a community. Here, we introduce a geometric approach to measure beta diversity as the hypervolume of the geometric embedding of a metacommunity. This approach explicitly accounts for non-additivity and captures the idea that introducing a unique, species-rich community composition to a metacommunity increases beta diversity. We show that our hypervolume measure is closely linked to and naturally extends previous information- and variation-based measures while providing a unifying geometric framework for widely adopted extensions of beta diversity. Applying our geometric measures to empirical data, we address two long-standing questions in beta diversity research--the latitudinal pattern of beta diversity and the effect of sampling effort--and present novel ecological insights that were previously obscured by the limitations of traditional approaches. In sum, our geometric approach reconceptualizes beta diversity, offering an alternative and complementary perspective to previous measures, with immediate applicability to existing data.