The Λ-lookdown model with selection

The goal of this paper is to study the lookdown model with selection in the case of a population containing two types of individuals, with a reproduction model which is dual to the A-coalescent. In particular we formulate the infinite population "Lambda-lookdown model with selection". When the measure Lambda gives no mass to 0, 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. We show that one of the two types fixates in finite time if and only if the A-coalescent comes down from infinity. We give precise asymptotic results in the case of the Bolthausen-Sznitman coalescent. We also consider the general case of a combination of the Kingman and the Lambda-lookdown model. (C) 2014 Elsevier B.V. All rights reserved.