Measuring diversity: species similarity

Traditional measures of the diversity of an ecological community depend only on how abundant the species are, not the similarities or differences between them. To better reflect biological reality, species similarity should be incorporated. Mathematically, this corresponds to moving from probability distributions on sets to probability distributions on metric spaces. I will explain how to do this and how it can change ecological judgements. Finally, I will describe a surprising theorem on maximum diversity (joint with Meckes and Roff), which reveals close connections between maximum diversity and invariants of geometric measure.