Kimura M, Ohta T
Genetics. 1973 Sep;75(1):199-212. doi: 10.1093/genetics/75.1.199.
Formulae for the mean and the mean square age of a neutral allele which is segregating with frequency x in a population of effective size N(e) have been obtained using the diffusion equation method, for the case of 4N(e)v<1 where v is the mutation rate. It has been shown that the average ages of neutral alleles, even if their frequencies are relatively low, are quite old. For example, a neutral mutant whose current frequency is 10% has the expected age roughly equal to the effective population size N(e) and the standard deviation 1.4N(e) (in generations), assuming that this mutant has increased by random drift from a very low frequency. Also, formulae for the mean "first arrival time" of a neutral mutant to a certain frequency x have been presented. In addition, a new, approximate method has been developed which enables us to obtain the condition under which frequencies of "rare" polymorphic alleles among local populations are expected to be uniform if the alleles are selectively neutral.-It was concluded that exchange of only a few individuals on the average between adjacent colonies per generation is enough to bring about such a uniformity of frequencies.
对于有效种群大小为(N(e))的群体中，频率为(x)的中性等位基因，在(4N(e)v < 1)（其中(v)是突变率）的情况下，已使用扩散方程方法得出其平均年龄和平均平方年龄的公式。研究表明，即使中性等位基因的频率相对较低，其平均年龄也相当大。例如，一个当前频率为(10%)的中性突变体，假设它是从极低频率通过随机漂变增加到当前频率的，其预期年龄大致等于有效种群大小(N(e))，标准差为(1.4N(e))（以世代为单位）。此外，还给出了中性突变体达到特定频率(x)的平均“首次到达时间”的公式。另外，已开发出一种新的近似方法，该方法使我们能够得出在等位基因是选择中性的情况下，预期局部种群中“稀有”多态等位基因频率均匀的条件。得出的结论是，每代相邻群体之间平均仅交换少数个体就足以实现这种频率的均匀性。
