University of Hawai'i at Manoa, Honolulu, USA.
Bull Math Biol. 2011 Jun;73(6):1227-70. doi: 10.1007/s11538-010-9557-9. Epub 2010 Aug 25.
A model of mutation rate evolution for multiple loci under arbitrary selection is analyzed. Results are obtained using techniques from Karlin (Evolutionary Biology, vol. 14, pp. 61-204, 1982) that overcome the weak selection constraints needed for tractability in prior studies of multilocus event models.A multivariate form of the reduction principle is found: reduction results at individual loci combine topologically to produce a surface of mutation rate alterations that are neutral for a new modifier allele. New mutation rates survive if and only if they fall below this surface-a generalization of the hyperplane found by Zhivotovsky et al. (Proc. Natl. Acad. Sci. USA 91, 1079-1083, 1994) for a multilocus recombination modifier. Increases in mutation rates at some loci may evolve if compensated for by decreases at other loci. The strength of selection on the modifier scales in proportion to the number of germline cell divisions, and increases with the number of loci affected. Loci that do not make a difference to marginal fitnesses at equilibrium are not subject to the reduction principle, and under fine tuning of mutation rates would be expected to have higher mutation rates than loci in mutation-selection balance.Other results include the nonexistence of 'viability analogous, Hardy-Weinberg' modifier polymorphisms under multiplicative mutation, and the sufficiency of average transmission rates to encapsulate the effect of modifier polymorphisms on the transmission of loci under selection. A conjecture is offered regarding situations, like recombination in the presence of mutation, that exhibit departures from the reduction principle. Constraints for tractability are: tight linkage of all loci, initial fixation at the modifier locus, and mutation distributions comprising transition probabilities of reversible Markov chains.
分析了任意选择下多个基因座突变率进化的模型。使用 Karlin（Evolutionary Biology，第 14 卷，第 61-204 页，1982）的技术获得了结果，这些技术克服了在先前多基因座事件模型研究中需要的弱选择约束，以便于处理。发现了一个多元形式的约化原理：个体基因座的约化结果在拓扑上组合，产生一个新修饰等位基因的突变率改变的表面，该表面是中性的。新的突变率只有在低于这个表面的情况下才能存活——这是 Zhivotovsky 等人（Proc. Natl. Acad. Sci. USA 91, 1079-1083, 1994）发现的多基因座重组修饰剂的超平面的推广。如果某些基因座的突变率增加得到其他基因座的降低补偿，则可以进化。修饰体的选择强度与生殖细胞分裂次数成正比，并随受影响基因座数量的增加而增加。在平衡时对边缘适合度没有影响的基因座不受约化原理的约束，并且在突变率的微调下，预计比处于突变选择平衡的基因座具有更高的突变率。其他结果包括在乘法突变下不存在“类似于生存力，Hardy-Weinberg”修饰多态性，以及平均传输率足以封装修饰多态性对选择下的基因座的传输的影响。对于像存在突变的重组等偏离约化原理的情况，提出了一个猜想。可处理性的约束条件是：所有基因座的紧密连锁，修饰基因座的初始固定，以及包含可逆马尔可夫链转移概率的突变分布。
