title: 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. (J Math Biol 67(3):569-607, 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 [Formula: see text], where K is the size of the population and [Formula: see text].
authors.affiliation: Institut für Angewandte Mathematik, Rheinische Friedrich-Wilhelms-Universität, Endenicher Allee 60, 53115, Bonn, Germany. rebecca.neukirch@iam.uni-bonn.de.
authors.forename: Rebecca
authors.initials: R
authors.lastname: Neukirch
authors.affiliation: Institut für Angewandte Mathematik, Rheinische Friedrich-Wilhelms-Universität, Endenicher Allee 60, 53115, Bonn, Germany.
authors.forename: Anton
authors.initials: A
authors.lastname: Bovier
mesh_terms: D000483:Alleles; D004171:Diploidy; D019143:Evolution, Molecular; D005808:Genes, Recessive / Q000235:genetics*; D008957:Models, Genetic; D011156:Population Density; D012641:Selection, Genetic
keywords: Adaptive dynamics; Diploid population; Genetic variability; Mendelian reproduction; Nonlinear birth-and-death process; Population genetics