An Eco-Evolutionary approach of Adaptation and Recombination in a large population of varying size
Résumé
We identify the genetic signature left by a selective sweep in the vicinity of an allele fixed by positive selection. We consider a sexually reproducing haploid population with non constant population size described by a birth and death process with density dependent competition between individuals. Parameter K scales the population size, and we study the limit behaviour for large K. We focus on two linked loci: one under selection and a neutral one. We distinguish soft selective sweep occurring after an environmental change, from hard selective sweep occurring after a new mutation. In the first case, we express the variations of neutral allele proportions as a function of the ecological parameters, recombination probability and solutions of a deterministic two-dimensional Lotka-Volterra system with competition. In the case of strong selective sweep, we find two recombination regimes. In the strong one, the recombination probability per reproductive event is large with respect to 1/log K and the selective sweep does not modify the neutral proportions. In the weak regime, the recombination probability per reproductive event is of order 1/logK, and the natural selection on the mutant drives an increase in frequency of the neutral allele carried by the first mutant. We express this increase as an explicit function of the ecological parameters, recombination probability and K.
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