How do variable patch sizes hold higher beta diversity?

Abstract

Beta diversity is a fundamental component of regional biodiversity that accumulates from compositional differences between local species assemblages. Although beta diversity is increasingly applied across spatial scales, its scale dependence remains incompletely synthesized, particularly concerning variation in spatial scale used to define alpha diversity (grain size). Using tree community data from Barro Colorado Island, we find that both additive and multiplicative beta diversity are consistently higher for unequal than equal grain divisions across different spatial extents and numbers of grains. These results can be explained by Jensen's inequality based on the concave-down relationship of alpha diversity with area that in turn increases beta diversity through the scaling relationship between alpha and gamma diversity. Combined with our additional analysis showing that this prediction is robust to more general models of species richness, including species--area and species--sampling-effort curves, these results reveal a previously unrecognized, predictable range of beta diversity variation.