Growth behavior of additional offspring with a beneficial reversal allele in the asymmetric sharply-peaked landscape in the coupled discrete-time mutation-selection model

Abstract

The probability of additional offspring with a beneficial reversal allele for growing to a size NC for a range of population sizes N, sequence lengths L, selective advantages s, and measuring parameters C was calculated for a haploid, asexual population in the coupled discrete-time mutation-selection model in an asymmetric sharply-peaked landscape with a positive selective advantage of the reversal allele over the optimal allele. The growing probability in the stochastic region was inversely proportional to the measuring parameter when C < 1/Ns, bent when C ≈ 1/Ns and saturated when C > 1/Ns. The crossing time and the time dependence of the increase in relative density of the reversal allele in the coupled discrete-time mutation-selection model was approximated using the Wright-Fisher two-allele model with the same selective advantage and corresponding effective mutation rate. The growth behavior of additional offspring with the reversal allele in the asymmetric sharply-peaked landscape in the coupled discrete-time mutation-selection model was controlled by the selective advantage of the reversal allele compared to the optimal allele and could be described by using the Wright-Fisher two-allele model, in spite of there being many other alleles with lower fitness, and in spite of there being two alleles, the optimal and reversal allele, separated by a low-fitness valley with a tunable depth and width.