Computer Simulation for the Crossing Time in the Three-State Coupled Discrete-Time, Mutation-Selection Model in an Infinitely Large Asexual Population

Most previous studies have focused on the two-state, haploid, coupled, discrete-time, mutation-selection (HCDMS) model. The present study examined the error threshold in the n-state HCDMS model in an infinitely large asexual population. The error threshold in a sharply-peaked landscape in the n-state HCDMS model is given as k/(n - 1) when $k{\ll}1$, where k is the fitness parameter. The crossing time in an asymmetric sharply-peaked landscape in the three-state HCDMS model was calculated by grouping the alleles into two-dimensional classes. The crossing time became saturated at a large fitness parameter when s > 0, scaled as a power law in the fitness parameter when s = 0, and diverged as the fitness parameter approached the critical fitness parameter when s < 0, where s is the selective advantage. The crossing time for the fixed extension parameter in the three-state model was saturated at a long sequence length when s > 0 and increased exponentially with increasing sequence length when s = 0. The method developed in this study can be extended to the four-state model describing four different nucleotides for a real DNA sequence.