休厄尔·赖特的方程Δq = (q(1 - q)∂w/∂q)/2w 。

Sewall Wright's equation Deltaq=(q(1-q) partial differentialw/ partial differentialq)/2w.

作者信息

Edwards A W

出版信息

Theor Popul Biol. 2000 Feb;57(1):67-70. doi: 10.1006/tpbi.1999.1437.

Abstract

An equation of Sewall Wright's expresses the change in the frequency of an allele under selection at a multiallelic locus as a function of the gradient of the mean fitness "surface" in the direction in which the relative proportions of the other alleles do not change. An attempt to derive this equation using conventional vector calculus shows that this description leads to a different equation and that the purported gradient in Wright's equation is not a gradient of the mean fitness surface except in the diallelic case, where the two equations are the same. It is further shown that if Fisher's angular transformation is applied to the diallelic case the genic variance is exactly equal to one-eighth of the square of the gradient of the mean fitness with respect to the transformed gene frequency.

摘要

休厄尔·赖特的一个方程将多等位基因位点在选择作用下一个等位基因频率的变化表示为平均适应度“曲面”在其他等位基因相对比例不变方向上的梯度的函数。尝试用传统向量微积分推导这个方程表明,这种描述会得出一个不同的方程,并且赖特方程中所谓的梯度并非平均适应度曲面的梯度,除非在双等位基因的情况下,此时两个方程是相同的。进一步表明,如果将费希尔角变换应用于双等位基因情况,基因方差恰好等于平均适应度相对于变换后的基因频率的梯度平方的八分之一。

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