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.
A branching random walk related to population genetics
16.11.2021 17:45 - 19:00
Organiser:
M. Beiglböck, N. Berestycki, L. Erdös, J. Maas, F. Toninelli
Location: