Why are deleterious mutations maintained in selfing populations? An analysis of the effects of early- and late-acting mutations by a two-locus two-allele model

Frequencies of deleterious mutations are higher than expected in many plants. Here, by developing a two-locus two-allele model, I examine the effects of differential timing of the expression of deleterious mutations (two-stage effects) on the maintenance of mutations. I assume early- and late-acting loci to distinguish whether maintenance of mutations in populations with high selfing rates is explained better by two-stage effects of single mutations, or by separate mutations in both early- and late-acting loci. I found that, when ovules are overproduced, the stable frequency of early-acting mutations is higher if mutations also occur in a late-acting locus than if a late-acting mutation is lacking. The stable frequency of late-acting mutations is higher if mutations also occur in an early-acting locus than if an early-acting mutation is lacking. Selective interference does not account for these results because analyses in which the number of loci subject to mutations is equalized are included. Overproduction of ovules has little effect on maintenance if either early- or late-acting mutations are lacking, whereas when ovules are not overproduced, the two-stage effect does not enhance the maintenance of mutations. Hence, mutations occurring in both loci coupled with overproduction of ovules enhances the maintenance of mutations in populations with high selfing rates. The detailed mechanisms underlying the two-stage effect were also analyzed.