A modified Crow-Kimura evolution model with reduced fitness for the smooth distribution of population

摘要

We investigate an evolution model in which the fitness depends on the steepness of population distribution via Hamming classes (the absolute value of the logarithm of the probability ratios for the neighbor Hamming classes). The model has a rather rich phase structure with observed oscillations of the mean fitness in the dynamics. Specifically, the fitness is reduced (compared to the standard Crow-Kimura model) when the steepness is less than a certain value, d. We compare the mean fitness of our model with the mean fitness of Crow-Kimura model with the same parameters. Our work reveals that there is a threshold value, d(c) for which d > d(c), there are no oscillations of the mean fitness, and it is less than the corresponding fitness in the Crow-Kimura model with the same parameters. For d < d(c), the mean fitness oscillates with time. The time averaged mean fitness is identical to the mean fitness in Crow-Kimura model, and there is a wider distribution than in the case of Crow-Kimura model. This is a significant advantage in dynamic environment. (C) 2019 Elsevier B.V. All rights reserved.