Mathematical theories of the population dynamics of sex-determining alleles in honey bees are developed. It is shown that in an infinitely large population the equilibrium frequency of a sex allele is 1/n, where n is the number of alleles in the population, and the asymptotic rate of approach to this equilibrium is 2/(3n) per generation. Formulae for the distribution of allele frequencies and the effective and actual numbers of alleles that can be maintained in a finite population are derived by taking into account the population size and mutation rate. It is shown that the allele frequencies in a finite population may deviate considerably from 1/n. Using these results, available data on the number of sex alleles in honey bee populations are discussed. It is also shown that the number of self-incompatibility alleles in plants can be studied in a much simpler way by the method used in this paper. A brief discussion about general overdominant selection is presented.

译文

:发展了蜜蜂性别决定等位基因种群动态的数学理论。结果表明,在无限大的种群中,性等位基因的平衡频率为1 / n,其中n是种群中等位基因的数目,并且达到该平衡的渐近速率为每代2 /(3n)。通过考虑种群数量和突变率,得出等位基因频率分布的公式以及可以在有限种群中维持的等位基因的有效和实际数目。结果表明,有限群体中的等位基因频率可能会大大偏离1 / n。使用这些结果,讨论了蜜蜂种群中性等位基因数量的可用数据。还表明,通过本文使用的方法,可以以更简单的方式研究植物中自交不亲和性等位基因的数量。简要讨论了一般的主导选择。

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