TY - JOUR

T1 - Mean and variance of FST in a finite number of incompletely isolated populations

AU - Nei, Masatoshi

AU - Chakravarti, Aravinda

AU - Tateno, Yoshio

N1 - Funding Information:
Part of this work was done while the senior author was a visitor to the National Institute of Genetics, Japan. He is grateful to Dr. Takeo Maruyama for a helpful discussion. This work was supported by a grant from the U.S. National Institute of Health and the U.S. National Science Foundation.
Copyright:
Copyright 2014 Elsevier B.V., All rights reserved.

PY - 1977/6

Y1 - 1977/6

N2 - In the presence of migration FST in a finite number of incompletely isolated populations first increases, but after reaching a certain maximum value, it starts to decline and eventually becomes 0. The mean and variance of FST in this process are studied by using the recurrence formulas for the moments of gene frequencies in the island model of finite size as well as by using Monte Carlo simulation. The mean and variance in the early generations can be predicted by the approximate formulas developed. On the other hand, if we exclude the cases of an allele being fixed in all subpopulations, the mean of FST eventually reaches a steady-state value. This value is given by 1 - 2NT(1 - λ) approximately, where NT is the total population size and λ is the rate of decay of heterozygosity at steady state. It is shown that the mean and variance of FST depend on the initial gene frequency and when this is close to 0 or 1, Lewontin and Krakauer's test of the neutrality of polymorphic genes is not valid.

AB - In the presence of migration FST in a finite number of incompletely isolated populations first increases, but after reaching a certain maximum value, it starts to decline and eventually becomes 0. The mean and variance of FST in this process are studied by using the recurrence formulas for the moments of gene frequencies in the island model of finite size as well as by using Monte Carlo simulation. The mean and variance in the early generations can be predicted by the approximate formulas developed. On the other hand, if we exclude the cases of an allele being fixed in all subpopulations, the mean of FST eventually reaches a steady-state value. This value is given by 1 - 2NT(1 - λ) approximately, where NT is the total population size and λ is the rate of decay of heterozygosity at steady state. It is shown that the mean and variance of FST depend on the initial gene frequency and when this is close to 0 or 1, Lewontin and Krakauer's test of the neutrality of polymorphic genes is not valid.

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U2 - 10.1016/0040-5809(77)90013-2

DO - 10.1016/0040-5809(77)90013-2

M3 - Article

C2 - 877908

AN - SCOPUS:0017506437

SN - 0040-5809

VL - 11

SP - 291

EP - 306

JO - Theoretical Population Biology

JF - Theoretical Population Biology

IS - 3

ER -