自然交配群体的基因频率和基因型频率

Gene Frequency and Genotype Frequency of Natural Mating Population

采用理论推算方法,对基因频率(A=p,a=q)和基因型频率各不相同的若干原始群体(Aa=m0),在自交率(x)和异交率(y)各不相同的情况下进行自然交配时,后代群体中基因型频率的变化进行了研究。结果表明,后代群体中Aa的基因型频率Aa(m)可以用公式Aa(m)=[m0×(1/2x)m]+(2pq×y)[1+m-1∑1(1/2x)m-1]表示,并根据公式对Aa(m)进行了实际计算。原始群体的基因型频率(m0)对后代群体的基因型频率影响最小,并随着繁殖世代(m)的增加渐趋于0;当m0对后代的影响渐趋于0时,若2pq不变,则x(y)对后代中Aa(m)的影响渐趋于与y[1+m-1∑1(1/2x)m-1]成正比,若x(y)不变,则p(q)对后代中Aa(m)的影响渐趋于与2pq成正比。m2及以后各代群体中的Aa(m)还可以用公式Aa(m)=m1-(m0-m1)m-1∑1(1/2x)m-1表示,由此可知,当m1=m0时,则各世代中Aa(m)保持不变,即这样的群体为遗传平衡群体。

The variations of genotype frequency of progeny populations in a certain number initial populations were studied using the pure theory computed method,in which gene frequency （A=p,a=q）and genotype frequency were different,and percentage of self pollination and percentage of cross pollination as well.The results showed that the genotype frequency Aa（m） of Aa in progeny populations could be indicated by the formula Aa（m）=[m0×（/2x）m]＋（2pqxy）[1＋∑1m-1 （1/2x）^m-1]. According to the formula,Aa （m） has been actually computed. From the formula and actual results computed,two conclusions could be drawn：the effect of genotype frequency （m0） of initial population to progeny populations was smallest,which was getting to 0 with the increase of reproduction generations;When the effect of m0 to the progeny tends to 0 ,if 2pq was not changed,the effect of x （y） to Aa （m） in progenies is getting to direct ratio with 2pq m2 and Aa （m） of generations could also be ex pressed as the formula Aa（m）=m1-（m0-m1） ∑1m-1 （1/2x）^m-1. So Aa（m） would be unchangeable when m0=m1, then it was genetic equilibrum population.