Diversity - the degree to which individuals in a populations are different—has a central role in many disciplines, in particular in the life science. In evolutionary biology, genetic and phenotypic diversity drive evolution and are key to understanding human traits. In ecology, diversity reflects ecosystem health and the ability to adapt to environmental changes, such as climate change. In oncology, genetic diversification of tissues plays a central role in tumor initiation and progression, and intra-tumor heterogeneity is a key predictor of response to treatment and relapse. Nevertheless, there is considerable debate regarding which diversity metric should be used to quantify diversity.
I will present a recent body of work studying the mathematical properties of various diversity metrics—in particular the conditions under which they are maximized or minimized—and show how this analysis reconciles their sometimes apparently contradictory behaviors. I will show how this allows to lift apparent contradictions in multiple fields, including debates on the extent of genetic differences among Human populations, the level of diversity in threatened species, and the impact of carcinogens on tumor DNA.
