对于含有两类个体A和B的有限种群,研究群体在中性漂变作用下达到吸收态的平均到达时间问题。借助随机模拟的数学方法和Matlab软件,选取大小为N=20,40,60,80,100的五类有限种群,在初始A类个体的数量依次为i=1,2,…,N-1情况下,分别进行两组重复10000次的随机模拟试验。试验平均结果具有较好的稳定性,当种群中A类个体的数量很大或者很小时,会较快地到达吸收态;当种群中A类个体的数量与占类个体的数量相当时,到达吸收态的过程较慢。所得结果对于种群数量不大的群体来说均适用,当群体大小足够大时,群体接近无限群体,会趋于一种平衡状态,而不会到达吸收态,上述模拟结果不成立。数据拟合结果表明平均到达时间与种群初始时A类个体数量呈现出明显的二次曲线关系,借助于拟合曲线可以给出到达吸收态所需平均到达时间的一般形式。
This paper studies on arriving-average time of neutral drift in finite populations with two kinds of individuals. Based on random simulation method and Matlab software, 10 000 random simulation experiments were made twice for each finite population that contains N=20,40,60,80,100 individuals divided into two kinds of individuals A and B,and that initial value of A was from 1 to N-1. Each finite population could sharply arrive absorbing states if initial value of A is near 1 or N;and could vary slowly arrive absorbing states if initial value of A was near N/2. All above conclusions from simulation and analysis apply to finite populations whose individual quantity was less. Or else,they were not fit if individual quantity of populations was tremendous. The quadratic curve based on least square data fitting could reflect the relationship between arriving-average time and initial value of A, and was a general type of arriving-average time from initial state to absorbing states.