A branching random walk related to population genetics

16.11.2021 17:45 - 19:00

Emmanuel Schertzer (Universität Wien)

Consider an ancestral population made of N individuals. Assume that each individual carries a single chromosome characterised by a distinct color (there is a red, blue, etc. chromosome). Because of recombination, individuals at generation 1 will carry a chromosome carrying the two parental colors. As time evolves, more complex coloring patterns may emerge. The question I would like to address in this talk is the following: how do those patterns look like at large times?
To answer this question, I will introduce the standard Wright-Fisher dynamics with recombination which modelizes the propagation of ancestral genetic material in a neutral and well-mixed population. Despite its simplicity, few analytical results are known about this model. In this talk, I will present some recent progress on this topic. I will also present the branching random walk approximation of Baird, Barton and Etheridge (03), and present a spinal method which allows to get very precise asymptotics in the large population, large chromosome regime. 
This is is joint work with  F. Foutel—Rodier, A. Lambert and V. Miro Pina.

Organiser:
M. Beiglböck, N. Berestycki, L. Erdös, J. Maas, F. Toninelli
Location:

HS 5, EG., OMP 1