Lou Jost (EcoMinga Foundation)
Abstract. Diversity plays a central role in ecology, conservation biology, genetics, and other fields. Yet most of the classical measures of compositional complexity, generalized entropy, and diversity, and the measures of compositional differentiation and similarity that biologists derived from them, do not support the rules of inference typically applied to them in biology. This mismatch between concept and measure means that the biological literature is full of nonsensical reasoning on this subject. I'll give some examples from ecology and genetics. To fix the problem, I examine the common forms of inference biologists apply to diversity, and find a set of diversity measures (the Hill numbers) that really makes these inferences valid. I then develop a rigorous mathematical framework for partitioning these “true diversities” into independent within- and between-group components, and construct real measures of differentiation from these components. These derivations validate some previous measures and dispose of others; what remains is a beautiful, united field relating compositional complexity, diversity, differentiation, similarity, concentration, inequality, and evenness. These measures can be applied to standard ecological and genetic models, such as the finite island model of genetics and Hubbell’s neutral model of biodiversity, yielding new causal explanations for genetic and ecological divergence. These new formulas reveal that classical population genetics has a mistaken understanding of fundamental evolutionary processes such as speciation. The new perspective allow us to fix these problems. As my main example, I will use the new math to identify the real factors controlling genetic divergence between populations, and confirm my predictions using simulations and real data.