An Eco-Evolutionary approach of Adaptation and Recombination in a large population of varying size

We identify the genetic signature of a selective sweep in a population described by a birth-and-death process with density dependent competition. We study the limit behaviour for large K, where K scales the population size. We focus on two loci: one under selection and one neutral. We distinguish a soft sweep occurring after an environmental change, from a hard sweep occurring after a mutation, and express the neutral proportion variation as a function of the ecological parameters, recombination probability r\_K, and K. We show that for a hard sweep, two recombination regimes appear according to the order of r\_K log K.