Iizuka M
Division of Mathematics, Kyushu Dental College, 2-6-1 Manazuru, Kokurakita-ku, Kitakyushu 803-8580, Japan.
Theor Popul Biol. 2001 Jun;59(4):281-6. doi: 10.1006/tpbi.2001.1521.
We consider a Wright-Fisher model whose population size is an autocorrelated stochastic process. Our interest is in the effects of autocorrelated fluctuations of the population size on the effective size. We define the inbreeding effective size and the variance effective size and show that these effective sizes are the same for this model. In the literature, it is said that the effective size is equal to the harmonic mean of population size when the size fluctuates. We will show, however, that the effective size is not the same as the harmonic mean of population size unless the fluctuations of population size are uncorrelated. The effective size is larger (resp. smaller) than the harmonic mean when the fluctuations of population size are positively (resp. negatively) autocorrelated. Further, we obtain some asymptotic expressions for effective size when the population size is very large and/or the autocorrelation of the fluctuation is very strong.
我们考虑一个群体大小为自相关随机过程的赖特-费希尔模型。我们感兴趣的是群体大小的自相关波动对有效大小的影响。我们定义了近交有效大小和方差有效大小，并表明对于该模型这些有效大小是相同的。在文献中，据说当群体大小波动时，有效大小等于群体大小的调和均值。然而，我们将证明，除非群体大小的波动是不相关的，否则有效大小与群体大小的调和均值并不相同。当群体大小的波动是正（或负）自相关时，有效大小大于（或小于）调和均值。此外，当群体大小非常大且/或波动的自相关性非常强时，我们得到了一些关于有效大小的渐近表达式。
