Event
Boubacar Bah, AIMS-Cameroon
Monday, January 29, 2018 14:00to15:00
Burnside Hall
Room 1214, 805 rue Sherbrooke Ouest, Montreal, QC, H3A 0B9, CA
Lambda-coalescent and lookdown model with selection
We study the lookdown model with selection in the case of a population containing two types of individuals, where the genealogy backward in time is described by the standard Lambda-coalescent with a non-trivial "Kingman part". We show that the proportion of one of the two types converges, as the population size N tends to infinity, towards the solution to a stochastic differential equation driven by a Poisson point process (the same equation, in case without selection, already appeared in the work of Bertoin and Le Gall). We show that one of the two types fixates in finite time if and only if the Lambda-coalescent comes down from infinity. In the case of no fixation, we prove that for a certain selection pressure, the disadvantage allele will vanish asymptotically with probability one. This phenomenon cannot occur in the classical Wright-Fisher diffusion. We give precise asymptotic results in the case of the Bolthausen-Sznitman coalescent. In particular we obtain in that case an explicit formula for the probability that one of the two alleles fixates, which is different from the classical one for the Wright-Fisher model.