Genetic diversity in facultatively sexual populations and its implications for the origins of self-incompatibility in algae and fungi

The evolutionary mechanism that drove the establishment of self-incompatibility in early sexual eukaryotes is still a debated topic. While a number of competing hypotheses have been proposed, many have not received detailed theoretical attention. In particular, the hypothesis that self-incompatibility increases the benefits of genetic recombination in sexual haploids has been comparatively understudied. In this paper we address this topic by mathematically deriving how the probability of mating with a genetically distinct individual changes as a function of the presence or absence of self-incompatible mating type classes. We find that although populations with mating types successfully engage in sexual reproduction less frequently than their self-compatible competitors, they can nevertheless engage in useful sex with genetically distinct partners more frequently. This conclusion holds when the number of sexual reproductive events per generation is low (i.e. in small populations with low rates of facultative sexual reproduction). Finally we demonstrate the potential for frequency-dependent selection in competitive dynamics between self-compatible and self-incompatible types. These analytic results provide a baseline for studying the sex advantage enhancer model for the evolutionary origin of mating types within each specific hypothesis for the evolution of recombination. PACS 87.23.-n Ecology and evolution, 87.23.Kg Dynamics of evolution, 02.50.Ey Stochastic processes 2000 MSC 37N25: Dynamical systems in biology, 60J70: Applications of diffusion theory (population genetics, absorption problems, etc.) ### Competing Interest Statement The authors have declared no competing interest.