The fate of a recessive allele in a Mendelian diploid model

Abstract

The omnipresence of sexual reproduction in a highly competitive world is a fascinating phenomenon. Its evolution and maintenance is up to now not completely understood since it is known that sexual reproduction require from organisms a lot more costs and energy than asexual reproduction would do.<br /> In this thesis we show mathematically that sexual reproduction provides populations an evolutionary advantage because they can better adapt to a changing ecological system.To this end, we study a stochastic individual based model which describes the genetic evolution of a diploid hermaphroditic population reproducing sexually according to Mendelian laws.This single locus model describes a population of interacting individuals that incorporate the canonical genetic mechanisms of birth, death, mutation, and competition. <br /> In the first part of this thesis the genetic evolution of the population with two alleles is studied under the assumption that a dominant allele is also the fittest one. It is shown that after the invasion of a dominant allele in a resident population of homozygous recessive genotypes, the recessive allele survives in heterozygous individuals for a time of order at least <em>K^1/2-α</em>, where <em>K</em> is the carrying capacity and <em>α>0</em>.<br /> This time of survival of the unfit allele is much longer than it would be in a population reproducing asexually. <br /> Therefore, a suitable rescaling of the mutation rate made the appearance of a new advantageous mutation possible before the extinction of the recessive allele.<br /> In the second part of this thesis, we study the fate of the recessive allele after the occurrence of a further mutation to a more dominant allele. It is proven that resulting changes in the composition of the population indeed opens the possibility that individuals of homozygous recessive genotype can reinvade and that coexistence of different genotypes is possible. <br /> This leads to genetic variability and can be seen as a statement of genetic robustness exhibited by diploid populations performing sexual reproduction as well as an indicator for the overwhelming biodiversity in nature.