Dependence of the Crossing Time on the Sequence Length in the Wright-Fisher Multiple Allele Model

作者：Gill Wonpyong^*

来源：Journal of the Korean Physical Society, 2010, 57(1): 192-199.

DOI：10.3938/jkps.57.192

• Crossing time
• Wright-Fisher model
• Sequence length
• Multiple allele
• Asymmetric sharply-peaked landscape

This study examined the dependence of the crossing time on the sequence length in the Wright-Fisher multiple allele model by switching on an asymmetric sharply-peaked landscape with a positive asymmetry parameter from the initial state, a quasispecies in a sharply-peaked landscape. The sequence length was varied with the fixed extension parameter E; which is defined as the average Hamming distance from the optimal allele of the initial quasispecies divided by the sequence length. An approximate formula was proposed for the crossing time in a stochastic region and was found to describe the computer simulation results of the crossing time for a broad range of population sizes, measuring parameters, and asymmetry parameters in the stochastic region, whose condition could be satisfied by increasing the sequence length above a critical sequence length, even near the error threshold. The computer simulation result for the crossing time in the stochastic region was found to be an exponentially increasing function of the sequence length, whose rate was unchanged, even though the population size and the asymmetry parameter were varied with a fixed extension parameter. The maximum sequence length for a finite population, which could evolve through the fitness barrier, e.g., within 10(7) generations, increased by approximately six sequence elements as the population size or the asymmetry parameter was increased by a factor of a hundred when E = 0.1 and the selective advantage, s, of the reversal allele compared with the optimal allele was much less than 1.

• 出版日期2010-7