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A study on stochastic models for the interaction between random drift and selection in population genetics

群体遗传学中随机漂移与选择相互作用的随机模型研究

基本信息

批准号：
12640139
负责人：
IIZUKA Masaru
金额：
$ 0.96万
依托单位：
Kyushu Dental College
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
2000
资助国家：
日本
起止时间：
2000 至 2002
项目状态：
已结题

项目摘要

In this study, the effects of the stochastic fluctuation of population size on the effective size of population are investigated. For this end, three models (Wright-Fisher mode, diffusion mode, coalescent model) with the fluctuation of population size are formulated and their properties are studied. In the literature, it is said that the effective size is equal to the harmonic mean of fluctuating population size when population size is not constant. J. H. Gillespie (University of California at Davis) found, however, some examples where the effective size is not equal to the harmonic mean when the population size fluctuates stochastically. In the case where population size fluctuates stochastically, it is important to know how the effective size is related to the harmonic mean and the arithmetic mean and the condition under which the effective size is equal to the harmonic mean. It is shown that the effective size is larger than the harmonic mean but it is smaller than the arithmetic mean for the diffusion model and the coalescent model. For the Wright-Fisher model, the effective size is larger (resp. smaller) than the harmonic mean if the fluctuation of population size is positively (resp. negatively) autocorrelated. The effective size is equal to the harmonic mean if and only if the fluctuation of population size is independent from generation to generation. The conditions on the parameters of the models under which the effective size is asymptotically equal to the harmonic mean or the arithmetic mean are obtained.

研究了种群规模的随机波动对种群有效规模的影响。为此，我们建立了三种具有种群规模涨落的模型（Wright-Fisher模型、扩散模型和聚结模型），并研究了它们的性质。文献中说，当种群大小不恒定时，有效大小等于波动种群大小的调和平均。J. H.然而，吉莱斯皮（加州大学戴维斯分校）发现，当种群规模随机波动时，有效规模不等于调和平均数。在种群大小随机波动的情况下，重要的是要知道有效大小与调和平均值和算术平均值的关系以及有效大小等于调和平均值的条件。结果表明，对于扩散模型和聚结模型，有效尺寸大于调和平均值，但小于算术平均值。对于Wright-Fisher模型，有效尺寸较大（分别为如果种群大小的波动是正的，则其小于调和平均值（分别为自相关（autocorrelated）。当且仅当种群规模的波动代际独立时，有效规模等于调和平均值。得到了模型参数的有效尺寸渐近等于调和平均或算术平均的条件。