The Exact Distributions of FIS under Partial Asexuality in Small Finite Populations with Mutation

Reproductive systems like partial asexuality participate to shape the evolution of genetic diversity within populations, which is often quantified by the inbreeding coefficient FIS. Understanding how those mating systems impact the possible distributions of FIS values in theoretical populations helps to unravel forces shaping the evolution of real populations. We proposed a population genetics model based on genotypic states in a finite population with mutation. For populations with less than 400 individuals, we assessed the impact of the rates of asexuality on the full exact distributions of FIS, the probabilities of positive and negative FIS, the probabilities of fixation and the probabilities to observe changes in the sign of FIS over one generation. After an infinite number of generations, we distinguished three main patterns of effects of the rates of asexuality on genetic diversity that also varied according to the interactions of mutation and genetic drift. Even rare asexual events in mainly sexual populations impacted the balance between negative and positive FIS and the occurrence of extreme values. It also drastically modified the probability to change the sign of FIS value at one locus over one generation. When mutation prevailed over genetic drift, increasing rates of asexuality continuously increased the variance of FIS that reached its highest value in fully asexual populations. In consequence, even ancient asexual populations showed the entire FIS spectrum, including strong positive FIS. The prevalence of heterozygous loci only occurred in full asexual populations when genetic drift dominated.