Iizuka Masaru, Tachida Hidenori, Matsuda Hirotsugu
Division of Mathematics, Kyushu Dental College, Kitakyushu 803-8580, Japan.
Genetics. 2002 May;161(1):381-8. doi: 10.1093/genetics/161.1.381.
We consider a diffusion model with neutral alleles whose population size is fluctuating randomly. For this model, the effects of fluctuation of population size on the effective size are investigated. The effective size defined by the equilibrium average heterozygosity is larger than the harmonic mean of population size but smaller than the arithmetic mean of population size. To see explicitly the effects of fluctuation of population size on the effective size, we investigate a special case where population size fluctuates between two distinct states. In some cases, the effective size is very different from the harmonic mean. For this concrete model, we also obtain the stationary distribution of the average heterozygosity. Asymptotic behavior of the effective size is obtained when the population size is large and/or autocorrelation of the fluctuation is weak or strong.
我们考虑一个具有中性等位基因的扩散模型，其种群大小随机波动。对于该模型，研究了种群大小波动对有效大小的影响。由平衡平均杂合度定义的有效大小大于种群大小的调和均值，但小于种群大小的算术均值。为了明确看出种群大小波动对有效大小的影响，我们研究了种群大小在两个不同状态之间波动的特殊情况。在某些情况下，有效大小与调和均值有很大差异。对于这个具体模型，我们还得到了平均杂合度的平稳分布。当种群大小较大和/或波动的自相关性较弱或较强时，得到了有效大小的渐近行为。
