Kimura M
Proc Natl Acad Sci U S A. 1978 Apr;75(4):1934-7. doi: 10.1073/pnas.75.4.1934.
By incorporating a population number regulating mechanism into the formulation of genic selection involving a pair of alleles (A1 and A2) with respective frequencies x and I-x, it is shown that the change of x in one generation is given by deltax = sx(1-x)/W, in which W is the mean absolute selective value (in Wright's sense). It is also shown that, in the process in which advantageous allele (say A1) increases from a low frequency to a high frequency, quasi-equilibrium is rapidly attained where deltaW approximately 0. In this state we have W approximately 1 + (s2/c)x(1-x) in the case of logarithmic population number regulation, and W approximately 1 + s2x(1-x)/(cN) in the case of logistic regulation. In these expressions, s is the selective advantage of A1 over A2, and c is a coefficient relating to the total population number regulation. It is pointed out that the approximation formula deltax = sx(1-x) is valid under wider circumstances than usually suggested by the conventional treatment of genic selection.
通过将种群数量调节机制纳入涉及一对等位基因（A1和A2）、各自频率为x和1 - x的基因选择公式中，结果表明x在一代中的变化由Δx = sx(1 - x)/W给出，其中W是平均绝对选择值（在赖特意义上）。还表明，在有利等位基因（如A1）从低频增加到高频的过程中，当ΔW近似为0时，会迅速达到准平衡状态。在这种状态下，对于对数种群数量调节，我们有W近似为1 + (s²/c)x(1 - x)；对于逻辑斯蒂调节，W近似为1 + s²x(1 - x)/(cN)。在这些表达式中，s是A1相对于A2的选择优势，c是与总体种群数量调节相关的系数。需要指出的是，近似公式Δx = sx(1 - x)在比基因选择的传统处理通常所建议的更广泛情况下是有效的。
