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

Citation: Stoeckel S, Masson J-P ( The Exact Distributions of F IS under Partial Asexuality in Small Finite Populations with Mutation Solenn Stoeckel 0 Jean-Pierre Masson 0 Paul Hohenlohe, University of Idaho, United States of America 0 INRA, UMR1349 Institute for Genetics , Environment and Plant Protection, Le Rheu , France 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. - Funding: This study was funded by the French National Research Agency (project CLONIX: ANR-11-BSV7-007) and by the Plant Health and Environment division of the French National Institute of Agricultural Research. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing Interests: The authors have declared that no competing interests exist. Reproductive systems define how genetic diversity is transmitted through generations thus they highly constrain the evolution of species. Many species relevant to human activities and ecosystems are partially asexual, meaning that they can reproduce both through sexual and asexual (equally named clonal) events [13]. Theoretical population genetics of partially asexual species has received little attention so far [4] and there is an ongoing debate on the effects of asexuality on genetic diversity and how such effects can be used to identify asexual species [5]. Indeed, theoretical studies about the genetic consequences of partial and full asexuality have only focused on the mean expected values of some population genetics parameters. In consequence, to disentangle evolutionary forces acting on such populations, applied studies may only compare their multiple quantitative measures of genetic diversity to theoretical average tendencies [68] and a large amount of the quantitative information contained within molecular data is wasted for evolutionary interpretations. Applied population genetics studies of partially asexual species lack of full frames of reference to compare their measured distributions of genetic parameters. Moreover, while we know that reproductive systems may have deep implications for the ecology and the evolution of species [9], we cannot rationally assess the evolutionary interests of sex, including genetic segregation, gamete fusion and massive recombination without understanding the full genetic consequences of partial and full asexuality [2,1014]. The population inbreeding coefficient, FIS [15], is a classical measure of genetic diversity for polyploid organisms that allows biologists to assess the evolutionary processes acting on a population. FIS is known to vary markedly according to mating systems, especially with the relative importance of sexuality and asexuality within populations [16,17]. It constitutes the lowest level of F-statistics [15] and stands for the excess or deficit of heterozygotes occurring in a population as compared to HardyWeinberg proportions. Asexual events are expected to maintain heterozygosity within the offspring because, by limiting the segregation of alleles, it conserves the ancestral heterozygosity through generations. Moreover, asexuality is even expected to increase heterozygosity and decrease the probability of allele identity since alleles of the same gene may independently accumulate mutations over generations. However, this process known as the Meselson effect was formulated considering only one genome rather than a population of genomes [18]. Extending the same argument to many individuals shows that the mean heterozygosity of asexual populations should also increase [19,20]. Empirical and theoretical results suggest that the effective rates of asexuality, the effective frequency of asexual events involved in producing the next generation in a population, is a key feature to understand the genetic evolution of those species [16]. The rate of asexuality is denoted c [19]. It ranges from 0, when populations reproduce only sexually, to 1 when populations reproduce only asexually. This rate is identical to A in [21], and shares common notion with d [22] and with the length of the asexual seasons, c [23] but may have different impacts and implications. The insights gained by mathematical and simulation modeling [19,20,2226] raise unsolved questions, mainly because the theoretical expectations were previously formalized only for the first moment (mean) of the possible distributions of FIS. Intermediate asexual populations, defined as populations producing 0 to 90 percent of their descents using asexuality, are expected to exhibit similar mean FIS values and variance to those obtained from fully sexual populations [19,24]. This implies that intermediate rates of asexuality should have no effects on the average level of genetic diversity expected within populations. If true on the full range of genetic diversity, a strategy with a low frequency of sex (c around 0.9) would be optimal, considering that it would combine the potential genetic benefits of mixis in terms of heritability of genetic diversity and would reduce the costs of sex [27]. Conversely, to explain why we can still observe populations that steadily reproduce through partial asexuality, we may suppose that the balance between the genetic benefits of mixis and the costs of sex should vary with different rates of asexuality [12]. Empirical and field studies observe that partially asexual species show low (...truncated)