Hybrid zones are interfaces between populations which occur when two species interbreed, but the hybrids have a lower evolutionary fitness. We can model this situation using the spatial Lambda-Fleming-Viot process (SLFV), and study the behaviour using a dual process of branching and coalescing random walks. We use a duality relation with a Branching Brownian motion to give a probabilistic proof of a PDE result (originally proved by Chen) that in solutions to an Allen-Cahn equation, an interface forms which moves approximately according to curvature flow. Our proof of Chen's result is flexible enough that we can also apply it to the SLFV dual to prove that the hybrid zone evolves approximately according to curvature flow. Joint work with Alison Etheridge and Nic Freeman.

Joint seminar with Mathematical Physics. Followed at 16h00 by a lecture of Andrei Okounkov, in the same location.

# Curvature Flow, Allen-Cahn and the Spatial Lambda-Fleming-Viot

02/18/2016 - 15:00

02/18/2016 - 16:00

Speaker:

Sarah Penington, University of Oxford

Location:

Room 1205, Burnside Hall, McGill University, 805 Sherbrooke Street West

Abstract: