| Project/Area Number |
12640139
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
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| Research Institution | Kyushu Dental College |
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Principal Investigator |
IIZUKA Masaru Kyushu Dental College, Faculty of Dentistry, Associate Professor, 歯学部, 助教授 (20202830)
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| Project Period (FY) |
2000 – 2002
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| Project Status |
Completed (Fiscal Year 2002)
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| Budget Amount *help |
¥1,500,000 (Direct Cost: ¥1,500,000)
Fiscal Year 2002: ¥400,000 (Direct Cost: ¥400,000)
Fiscal Year 2001: ¥500,000 (Direct Cost: ¥500,000)
Fiscal Year 2000: ¥600,000 (Direct Cost: ¥600,000)
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| Keywords | population genetics / stochastic processes / diffusion model / Wright-Fisher model / genealogy / fluctuation of population size / effective size of population / compensatory evolution / 集団遺伝子 / 環境変動 / 古人類学 / 弥生人 / ヘテロ接合度 / Kアレルモデル / 互助的中立突然変異 / 環境変動モデル / 自然淘汰 / 無限対立遺伝子モデル |
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| Research Abstract |
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.
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