环路的平均固定时间研究

Average Fixation Time on a Circulation

进化图可以动态刻画一个种群的动态演化,定置概率描述进入种群的新突变体占据整个种群的概率,而平均固定时间反映了该种群的平均进化速度.本文研究了环路的平均固定时间.在种群个体数量很大的情况下,给出了环路上单个突变体的平均固定时间及其性质.当相对适应度0<r<1时,随着r的增加,环路的固定概率和平均固定时间都增加;而在r>1时,随着r的增加,环路的固定概率增加了,而平均固定时间却减少了.

Evolutionary graph can be used to describe the evolution of a population dynamically. The fixation probability of an evolutionary graph is the probability that a new emerging mutant occupies the whole population, while its average fixation time reflectes the average evolutinary velocity of the population. The average fixation time of a new mutant on a circulation with large population is studied and its property is discussed. When the relative fitness 0 〈 r 〈 1, the fixation probability and the average fixaton time of the circulation increase with the increase of the relative fitness r. When r 〉 1, the fixation probability of a circulation increases, but the average fitness time decreases with the increase of the relative fitness r.