Kimura M, King J L
Proc Natl Acad Sci U S A. 1979 Jun;76(6):2858-61. doi: 10.1073/pnas.76.6.2858.
We consider a diploid population and assume two gene loci with two alleles each, A and a at one locus and B and b at the second locus. Mutation from wild-type alleles A and B to deleterious alleles a and b occurs with mutation rates va and vb, respectively. We assume that alleles are completely recessive and that only the double recessive genotype aabb shows a deleterious effect with relative fitness 1-epsilon. Then, it can be shown that if va greater than vb mutant a becomes fixed in the population by mutation pressure and a mutation-selection balance is ultimately attained with respect to the B/b locus alone. The main aim of this paper is to investigate the situation in which va = vb exactly. In this case a neutral equilibrium is attained and either locus can drift to fixation for the mutant allele. Diffusion models are developed to treat the stochastic process involved whereby the deleterious mutant eventually becomes fixed in one of the two duplicated loci by random sampling drift in finite populations. In particular, the equation for the average time until fixation of mutant a or b is derived, and this is solved numerically for some combinations of parameters 4Nev and 4Ne epsilon, where v is the mutation rate (va = vb = v) and Ne is the effective size of the population. Monte Carlo experiments have been performed (using a device termed "pseudo sampling variable") to supplement the numerical analysis.
我们考虑一个二倍体种群，并假设两个基因座，每个基因座有两个等位基因，一个基因座上是A和a，另一个基因座上是B和b。野生型等位基因A和B突变为有害等位基因a和b的突变率分别为va和vb。我们假设等位基因是完全隐性的，并且只有双隐性基因型aabb表现出有害效应，其相对适合度为1 - ε。那么，可以证明，如果va大于vb，突变型a会因突变压力在种群中固定下来，最终仅就B/b基因座达到突变 - 选择平衡。本文的主要目的是研究va恰好等于vb的情况。在这种情况下，会达到一个中性平衡，任何一个基因座都可能因随机抽样漂变在有限种群中使突变等位基因固定下来。我们开发了扩散模型来处理所涉及的随机过程，有害突变体最终会通过有限种群中的随机抽样漂变在两个重复基因座之一中固定下来。特别地，推导了突变型a或b固定所需平均时间的方程，并针对一些参数组合4Nev和4Neε进行了数值求解，其中v是突变率（va = vb = v），Ne是种群的有效大小。已经进行了蒙特卡罗实验（使用一种称为“伪抽样变量”的装置）来补充数值分析。
