2020.06.04 Alison Etheridge - Branching Brownian motion, mean curvature flow and hybrid zones
Channel: One World Probability
Date: 2020-06-04

Hybrid zones are narrow regions in which two genetically distinct
populations come together and interbreed, resulting in hybrids. They may be
maintained by an abrupt change in the environment or because of natural
selection against the hybrids, in which case the location of the zone can
change with time. If natural selection is acting at a single genetic locus,
then we can model the hybrid zone through a special case of the Allen-Cahn
equation. In this talk we present a probabilistic proof of a well known
connection between this version of  the Allen-Cahn equation and mean curvature
flow. The approach is quite flexible and, in particular, has the advantage
that it is readily adapted to incorporate another important force of
evolution, random genetic drift.