Title: Maximizing diversity in biology and beyond (Part 1)
Speaker: Mark Meckes (Associate Professor, Case Western Reserve University)
Abstract: Entropy-like quantities have long been used as a measure of diversity in various fields. There is a spectrum of viewpoints on diversity, indexed by a real parameter q giving greater or lesser importance to rare species (to adopt ecological terminology). Leinster and Cobbold proposed a one-parameter family of diversity measures taking into account both this variation and the varying similarities between species. Because of this latter feature, diversity is not generally maximized by the uniform distribution on species. In this talk I’ll show that there is a single distribution which simultaneously maximizes diversity for all values of q. I will also discuss how this distribution can be computed; under what circumstances it has full support (so that all species are actually present when diversity is maximized); and connections with information theory, graph theory, and geometry. This is joint work with Tom Leinster.