A General Solution of the Wright-Fisher Model of Random Genetic Drift

被引：4

作者：

Tat Dat Tran ^{[1
]}

Hofrichter, Julian ^{[1
]}

Jost, Juergen ^{[1
,2
,3
]}

机构：

[1] Max Planck Inst Math Sci, D-04103 Leipzig, Germany

[2] Univ Leipzig, Dept Math, D-04081 Leipzig, Germany

[3] Santa Fe Inst Sci Complex, Santa Fe, NM 87501 USA

来源：

DIFFERENTIAL EQUATIONS AND DYNAMICAL SYSTEMS | 2019年 / 27卷 / 04期

基金：

芬兰科学院; 欧洲研究理事会;

关键词：

Random genetic drift; Fokker-Planck equation; Wright-Fisher model; Several alleles; DIFFUSION APPROXIMATIONS;

D O I：

10.1007/s12591-016-0289-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We introduce a general solution concept for the Fokker-Planck (Kolmogorov) equation representing the diffusion limit of the Wright-Fisher model of random genetic drift for an arbitrary number of alleles at a single locus. This solution will continue beyond the transitions from the loss of alleles, that is, it will naturally extend to the boundary strata of the probability simplex on which the diffusion is defined. This also takes care of the degeneracy of the diffusion operator at the boundary. We shall then show the existence and uniqueness of a solution. From this solution, we can readily deduce information about the evolution of a Wright-Fisher population.

引用

页码：467 / 492

页数：26

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