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

Abstract

Reproductive systems like partial asexuality participate to shape the evolution of genetic diversity within populations, which is often quantified by the inbreeding coefficient F IS. Understanding how those mating systems impact the possible distributions of F IS 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 F IS, the probabilities of positive and negative F IS, the probabilities of fixation and the probabilities to observe changes in the sign of F IS 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 F IS and the occurrence of extreme values. It also drastically modified the probability to change the sign of F IS value at one locus over one generation. When mutation prevailed over genetic drift, increasing rates of asexuality continuously increased the variance of F IS that reached its highest value in fully asexual populations. In consequence, even ancient asexual populations showed the entire F IS spectrum, including strong positive F IS. The prevalence of heterozygous loci only occurred in full asexual populations when genetic drift dominated.

Clonal structure and high genetic diversity at peripheral populations of Sorbus torminalis (L.) Crantz.

“…Our results confirmed this finding with inbreeding coefficients being consistently slightly negative across almost all SSR loci. This is reasonable given the self-incompatibility mating system of the species (Ludwig et al 2013, Stoeckel et al 2006; however, asexual reproduction may also affect FIS estimates (Stoeckel & Masson 2014).…”

Effects of complex life cycles on genetic diversity: cyclical parthenogenesis

“…The model used in this study is an adaptation of the mathematical model developed by Stoeckel and Masson (2014). This model describes a single biallelic locus (A and a) in a population of N diploid individuals for which genotypic frequencies rather than allelic frequencies are computed.…”

“…The genotypic frequencies at t+1 as functions of the genotypic frequencies at t under clonal ðp tþ1 ij Þ and sexual ðq tþ1 ij Þ reproduction are respectively given by Equations (1) and (2) of Stoeckel and Masson (2014):…”

“…Recently, Stoeckel and Masson (2014) proposed a forward-in-time stochastic model that exactly describes the full probabilistic distribution of genetic diversity in partially clonal organisms. This approach confirmed the existence of a small, nearly indistinguishable, difference in mean F IS values between populations with moderate levels of clonality and those with strict sexuality.…”

“…Third, because APC model outputs are often used to discuss results obtained for cyclical parthenogens, we compare genetic diversity under APC and CP with similar levels of clonality. Genetic diversity is modelled at one locus using an adaptation of the stochastic model of Stoeckel and Masson (2014) and simulated at two unlinked neutral loci using classical individual-based simulations.…”