UBC Math Department Rising Stars Colloquium: Sarah Penington

Suppose two populations with different genetic types live close to each other and can interbreed, but hybrid offspring have a lower evolutionary fitness. The interface between such populations is known as a hybrid zone. We can model this situation using a stochastic process. I will discuss a result on the motion of the interface, which is related to a well-known PDE result connecting the Allen-Cahn equation and mean curvature flow.

If we take a simplified model in only one spatial dimension, we can trace the ancestral lineages of individuals backwards in time and (in some cases) determine the asymptotic behaviour of the genealogy (or family tree) of a set of individuals. Several interesting questions about the genealogies remain open. Partly based on joint work with Alison Etheridge and Nic Freeman.