Tran Tat Dat, Hofrichter Julian, Jost Jürgen
Max Planck Institute for Mathematics in the Sciences, 04103 Leipzig, Germany.
Theory Biosci. 2013 Jun;132(2):73-82. doi: 10.1007/s12064-012-0170-3. Epub 2012 Dec 14.
In this paper, we develop the mathematical structure of the Wright-Fisher model for evolution of the relative frequencies of two alleles at a diploid locus under random genetic drift in a population of fixed size in its simplest form, that is, without mutation or selection. We establish a new concept of a global solution for the diffusion approximation (Fokker-Planck equation), prove its existence and uniqueness and then show how one can easily derive all the essential properties of this random genetic drift process from our solution. Thus, our solution turns out to be superior to the local solution constructed by Kimura.
在本文中，我们以最简单的形式（即无突变或选择），在固定大小种群的随机遗传漂变下，推导了二倍体基因座上两个等位基因相对频率演化的赖特 - 费希尔模型的数学结构。我们为扩散近似（福克 - 普朗克方程）建立了全局解的新概念，证明了其存在性和唯一性，然后展示了如何从我们的解中轻松推导出这个随机遗传漂变过程的所有基本性质。因此，我们的解比木村构建的局部解更优越。
