Rebecca Neukirch

Adaptive dynamics are well studied for the haploid reproduction model. In this talk we are interested in the genetic evolution of a diploid hermaphroditic population, which is modeled by a three-type nonlinear birth-and-death process with competition and Mendelian reproduction. In a recent paper, Collet, Méléard and Metz (2013) have shown that on the mutation timescale the process converges to the Trait-Substitution Sequence of adaptive dynamics, stepping from one homozygotic state to another with higher fitness. In the first part of the talk, we prove that, under the assumption that the dominant allele is also the fittest one, the recessive allele survives for a time of order at least $K^{1/6}$, where $K$ is the size of the population. In the second part we give a sufficient condition on the competition such that the recessive aallele can recover after the occurrence of a new fitter mutant. This leads to genetic variability in the populations.