Selfing Shapes Fixation of a Mutant Allele Under Flux Equilibrium

Sexual reproduction with alternative generations in a life cycle is an important feature in eukaryotic evolution. Partial selfing can regulate the efficacy of purging deleterious alleles in the gametophyte phase and the masking effect in heterozygotes in the sporophyte phase. Here, we develop a new theory to analyze how selfing shapes fixation of a mutant allele that is expressed in the gametophyte or the sporophyte phase only or in two phases. In an infinitely large population, we analyze a critical selfing rate beyond which the mutant allele tends to be fixed under equilibrium between irreversible mutation and selection effects. The critical selfing rate varies with genes expressed in alternative phases. In a finite population with partial self-fertilization, we apply Wright's method to calculate the fixation probability of the mutant allele under flux equilibrium among irreversible mutation, selection, and drift effects and compare it with the fixation probability derived from diffusion model under equilibrium between selection and drift effects. Selfing facilitates fixation of the deleterious allele expressed in the gametophyte phase only but impedes fixation of the deleterious allele expressed in the sporophyte phase only. Selfing facilitates or impedes fixation of the deleterious allele expressed in two phases, depending upon how phase variation in selection occurs in a life cycle. The overall results help to understand the adaptive strategy that sexual reproductive plant species evolve through the joint effects of partial selfing and alternative generations in a life cycle.