Event
Amandine Veber, Ecole Polytechnique Paris
Wednesday, November 1, 2017 10:00to11:00
Burnside Hall
Room 1205, 805 rue Sherbrooke Ouest, Montreal, QC, H3A 0B9, CA
The effects of a weak selection pressure in a spatially structured population.
One of the motivations for the introduction of the Fisher-KPP equation was to model the wave of advance of a favourable (genetic) type in a population distributed over some continuous space. This model relies on the fact that reproductions occur very locally in space, so that if we assume that individuals can be of two types only, the drift term modelling the competition between the types is of the form sp_{t,x}(1-p_{t,x}). Here, s is the strength of the selection pressure and p_{t,x} is the frequency of the favoured type at location x and time t. However, large-scale extinction-recolonisation events may happen at some nonnegligible frequency, potentially disturbing the wave of advance. In this talk, we shall address and compare the effect of weak selection in the presence or absence of occasional large-scale events, based on a model of evolution in a spatial continuum called the spatial Lambda-Fleming-Viot process. This is a joint work with Alison Etheridge and Feng Yu.