Computer simulation for the dependence of the crossing time on the sequence length in a diploid, coupled, discrete-time, mutation-selection model for a finite population

Abstract

In a previous study, the crossing time for the overdominant case in an infinite population was found to be saturated at a long sequence length in the diploid, coupled, discrete-time, mutation-selection model. The present study focused on the effect of a finite population size on the crossing time for the overdominant case. The dependence of the crossing time on the sequence length was simulated for a range of dominance parameters and selective advantages by switching on a diploid, asymmetric, bridged landscape from an initial state, a steady state in a diploid, bridged landscape. The boundary between the deterministic and the stochastic regions in the diploid, coupled, discrete-time, mutation-selection model was characterized using the same formula as that in the haploid, coupled, discrete-time, mutation-selection model. The crossing time in a finite population with various population sizes, dominance parameters and selective advantages began to deviate from the crossing time for an infinite population at a critical sequence length. The crossing time for a finite population in the stochastic region was found to be an exponentially increasing function of the sequence length, whose rate was unchanged, regardless of changes in the population size, dominance parameter and selective advantage with a fixed extension parameter. Therefore, the saturation of the crossing time at a long sequence length, which was observed for the overdominant case in an infinite population, could not be realized for a finite population.