Mathematics of Planet Earth

One of the most compelling images to result from Darwin’s theory of evolution is that of the tree of life. Inherent in this picture is the idea that when members of a species are geographically separated, over time they may evolve to a point where it makes sense to view them as different species – these are the branch points in the tree of life. Probability theory has developed powerful stochastic spatial models that can be used to understand and model the behavior of such migrating and evolving populations. In particular, the theories of branching random walk and branching diffusions are fundamental in population biology and genetics. Furthermore, there has been substantial recent progress on understanding the typical genealogy of spatially extreme species in these models. For example, at the moment when our first ancestors left Africa, it is likely that a majority of the human population stayed close to home and only a relatively small group left the continent. Understanding how these exceptional, frontier individuals likely split up as they made their way around the globe would yield deeper understanding of the genetic diversity between extant human populations. The mathematical tools for such a study are actively being developed on several fronts, and these will be presented in the workshop.