A geometric approach to beta diversity

Beta diversity—the variation among community compositions in a region—is a fundamental measure of biodiversity. Most classic measures have posited that beta diversity is maximized when each community has a distinct, nonoverlapping set of species. However, this assumption overlooks the ecological significance of species interactions and non-additivity in ecological systems, where the function and behavior 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. Besides considering compositional distinctiveness as in classic metrics, this geometric measure explicitly incorporates species associations and captures the idea that adding a unique, species-rich community to a metacommunity increases beta diversity. We show that our geometric measure is closely linked to and naturally extends previous information- and variation-based measures. Additionally, we provide 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 classic approaches. In sum, our geometric approach offers a new and complementary perspective on beta diversity, is immediately applicable to existing data, and holds promise for advancing our understanding of the complex relationships between species composition, ecosystem functioning, and stability.