Survival of a recessive allele in a Mendelian diploid model

Abstract

In this paper we analyse the genetic evolution of a diploid hermaphroditic population, which is modelled by a three-type nonlinear birth-and-death process with competition and Mendelian reproduction. In a recent paper, Collet et al., 2013 have shown that, on the mutation time-scale, the process converges to the Trait-Substitution Sequence of adaptive dynamics, stepping from one homozygotic state to another with higher fitness. We prove that, under the assumption that a dominant allele is also the fittest one, the recessive allele survives for a time of order at least K^{1/4-a}, where K is the size of the population and a>0.

References in corpus (2)

• A microscopic probabilistic description of a locally regulated population and macroscopic approximations
• T. E. Harris and branching processes

Cited by in corpus (3)

• From Adaptive Dynamics to Adaptive Walks
• Effective growth rates in a periodically changing environment: From mutation to invasion
• Looking for the right mate in diploid species: how dominance relationships affect population differentiation in sexual trait?