The dynamic behavior of the linkage disequilibrium (D) between a neutral and a selected locus is analyzed for a variety of deterministic selection models. The time-dependent behavior of D is governed by the gene frequency at the selected locus (p) and by the selection (s) and recombination (r) parameters. Thomson (1977) showed numerically that D may increase under certain initial conditions. We give exact conditions for D to increase in time, which require that the selection intensity exceed the recombination fraction (s > r) and that p be near zero or one. We conclude from this result that gene frequency hitchhiking is most likely to be important when a new favorable mutant enters a population. We also show that, for what can be a wide range of gene frequencies, D will decay at a faster rate than the neutral rate. Consequently, the hitchhiking effect may quickly diminish as the selected gene becomes more common.—The method of analysis allows a complete qualitative description of the dynamics of D as a function of s and r. Two major findings concern the range of gene frequencies at the selected locus for which D either increases over time or decays at a faster rate than under neutrality. For all models considered, the region where D increases (i) first enlarges then shrinks as selection intensifies, and (ii) steadily shrinks as r increases. In contrast, the region of accelerated decay constantly enlarges as the selection intensity increases. This region will either shrink or enlarge as r increases, depending upon the form of selection in force.
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机译:针对各种确定性选择模型,分析了中性位点和选定位点之间的连锁不平衡(D)的动态行为。 D的时间依赖性行为受选定基因座(p)的基因频率以及选择(s)和重组(r)参数的控制。汤姆森(Thomson,1977)从数字上表明,在某些初始条件下,D可能会增加。我们给出D随时间增加的确切条件,这要求选择强度超过重组分数(s> r),并且p接近零或一。我们从这个结果得出结论,当新的有利突变体进入种群时,基因频率搭便车最可能重要。我们还表明,对于可能存在广泛范围的基因频率,D的衰变速率将比中性速率快。因此,随着所选基因变得更加普遍,搭便车的作用可能会迅速消失。-分析方法允许对D动力学作为s和r的函数进行完整的定性描述。有两个主要发现涉及所选位点的基因频率范围,其中D随时间增加或以比中性条件下更快的速度衰减。对于所有考虑的模型,D增大的区域(i)先扩大然后扩大,然后随着选择的增强而缩小,(ii)随着 r em>的增加而稳定缩小。相反,随着选择强度的增加,加速衰减的区域不断扩大。该区域将随着 r em>的增加而收缩或扩大,具体取决于有效选择的形式。
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