Abstract
Sexual selection and divergent selection are among the major driving forces of reproductive isolation, which could eventually result in speciation. A magic trait is defined such that a single trait is subject to both divergent selection and mate choice through phenotype-based assortative mating. We are here interested in the evolutionary behavior of alleles at a genetic locus responsible for a magic trait in a finite population. We assume that, in a pair of homogeneous subpopulations, a mutant allele arises at the magic trait locus, and theoretically obtain the probability that the new allele establishes in the population, or the establishment probability. We also show an analytical expression for the trajectory of allele frequency along the establishment, from which the time required for the establishment is obtained, or the establishment time. Under this model, divergent selection simply favors the new allele to fix where it is beneficial, whereas assortative mating works against rare alleles. It is theoretically demonstrated that the fate of the new allele is determined by the relative contributions of the two selective forces, divergent selection and assortative mating, when the allele is rare so that the two selective forces counteract. Our theoretical results for the establishment probability and time allow us to understand the relative role of random genetic drift in the establishment process of a magic trait allele in a finite population.
Highlights
Several theoretical models indicated that sexual selection alone can lead speciation even in the face of gene flow (Wu 1985; Turner and Burrows 1995; Higashi et al 1999; Takimoto et al 2000), but these results largely rely on their assumptions such as ample genetic variation, symmetric distribution of female preference or strong female choice (Arnegard and Kondrashov 2004; Gavrilets 2004), and empirically not well supported yet as reviewed in Ritchie (2007)
Establishment of a locally adaptive mutation could lead stable genetic divergence between local populations in different environments, even in the face of gene flow between them. If there is another locus that is involved in sexual selection, it reduces gene flow between populations. This effect is strong when the locus is genetically linked to the target locus of local adaptation and an extreme case is that a single locus is pleiotropically subject to both divergent selection and sexual selection
The location of the gray region is quite constant over the range of α. This robustness to α should be because the eventual fate of A is mainly determined by divergent selection because assortative mating works efficiently only when allele A is rare, namely, shortly after it arises in the population
Summary
The initial state is that all individuals have allele a in both subpopulations. First, we derive the establishment probability of allele A which arises in subpopulation I with initial frequency N11. The location of the gray region is quite constant over the range of α This robustness to α should be because the eventual fate of A (i.e., cases C or F) is mainly determined by divergent selection because assortative mating works efficiently only when allele A is rare, namely, shortly after it arises in the population. We obtain almost the same result as the haploid model when h = 1 (Figure 3A), and u1 and u2 decrease as h decreases (Figures 3B and C) This trend can be explained if we consider how selection works on allele A in the very early phases, namely, when the frequency is very low. This pattern is globally observed both in the haploid and diploid models
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