Afternoon Seminar & Reception with Dr. Lou Jost - The mathematics of diversity: How fundamental mathematical misconceptions distort conservation biology, ecology, and population genetics

Dr. Lou Jost, EcoMinga Foundation

The mathematics of diversity: How fundamental mathematical misconceptions distort conservation biology, ecology, and population genetics

Many common measures of diversity give misleading advice to conservation biologists, ecologists, and geneticists, because the rules of inference used by many biologists are mathematically incompatible with these measures. Biologists compound the problem by partitioning non-additive diversity measures into additive within- and between-group components, which are then incorrectly converted to measures of compositional similarity and differentiation, such as Wright’s fixation index FST and Nei’s GST, and some measures of beta diversity in ecology. When diversity is high, these measures will indicate low differentiation even when the subpopulations or communities are completely differentiated (no shared alleles or species). Widespread misconceptions regarding statistical paradigms exacerbate these problems. Conservation decisions and even our basic understanding of the population genetics of speciation are often based on these wildly misleading measures.

The mathematics of diversity and compositional differentiation can be derived from first principles, by observing the rules of inference biologists implicitly apply to diversity, and finding the measures which make these forms of reasoning valid. This new mathematics provides a logically consistent foundation for analysis of population structure in genetics and ecology. This yields new biological insights into the finite island model of population genetics and neutral models in ecology. For example, the “one migrant per generation” rule for panmixia in genetics is not true even when the finite island model strictly applies. I derive the correct rule and validate it by computer simulations. This new rule allows us to identify the genetic and demographic factors which facilitate speciation.