Department of Mathematics and Department of Molecular and Population Genetics, University of Georgia.
Genetics. 1981 Oct;99(2):337-56. doi: 10.1093/genetics/99.2.337.
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.
我们分析了在各种确定性选择模型中，中性和选择位点之间的连锁不平衡（D）的动态行为。D 的时变行为由选择位点上的基因频率（p）和选择（s）和重组（r）参数决定。Thomson（1977）通过数值显示，在某些初始条件下，D 可能会增加。我们给出了 D 随时间增加的精确条件，这要求选择强度超过重组分数（s>r），并且 p 接近于零或一。从这个结果可以得出结论，当一个新的有利突变体进入一个群体时，基因频率搭便车最有可能是重要的。我们还表明，对于可以有广泛的基因频率范围，D 将以比中性速率更快的速率衰减。因此，随着选择基因变得更加普遍，搭便车效应可能会迅速消失。-分析方法允许对 D 作为 s 和 r 的函数的动态进行完整的定性描述。两个主要发现涉及选择位点上 D 随时间增加或比中性更快衰减的基因频率范围。对于考虑的所有模型，D 增加的区域（i）随着选择强度的增加而先扩大后缩小，（ii）随着 r 的增加而稳定缩小。相比之下，加速衰减的区域随着选择强度的增加而不断扩大。该区域将随着 r 的增加而缩小或扩大，这取决于作用力的选择形式。
