Mutation-Selection Balance with Recombination: Convergence to Equilibrium for Polynomial Selection Costs
Mutation-Selection Balance with Recombination: Convergence to Equilibrium for Polynomial Selection Costs
复制标题
具有重组的突变选择平衡：多项式选择成本收敛到平衡
DOI：
--
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发表时间：
2007
影响因子：
1.9
通讯作者：
S. Evans
中科院分区：
文献类型：
--
作者：
Aubrey Clayton;S. Evans
我们研究了一个连续时间动力系统，该系统模拟了基因型在无限种群中的分布，其中基因组可能有无限多个甚至是连续的基因座，突变沿着沿着谱系积累而不发生回复突变，增加的突变降低了适应度，重组发生在比突变和选择更快的时间尺度上。该模型的一些特征，如解的存在性和唯一性以及收敛到离散时间模型的近似序列的动力系统，在早期的工作中由Evans，Steinsaltz和Wachter提出，用于相当一般的选择成本。在这里，我们研究了一个特殊的情况下，一个基因型的选择成本与给定的积累祖先突变从野生型祖先是一个总的成本可归因于每个单独的突变加上连续的相互作用的贡献，从每个$k$元组的突变$k$到一些有限的“度”。利用复杂化学反应网络的思想和一个新的李雅普诺夫函数，我们建立了突变选择平衡的现象发生在温和的条件下，这样的选择成本。也就是说，我们表明，动力系统有一个唯一的平衡，它收敛到这个平衡从所有的初始条件。
We study a continuous-time dynamical system that models the evolving distribution of genotypes in an infinite population where genomes may have infinitely many or even a continuum of loci, mutations accumulate along lineages without back-mutation, added mutations reduce fitness, and recombination occurs on a faster time scale than mutation and selection. Some features of the model, such as existence and uniqueness of solutions and convergence to the dynamical system of an approximating sequence of discrete time models, were presented in earlier work by Evans, Steinsaltz, and Wachter for quite general selective costs. Here we study a special case where the selective cost of a genotype with a given accumulation of ancestral mutations from a wild type ancestor is a sum of costs attributable to each individual mutation plus successive interaction contributions from each $k$-tuple of mutations for $k$ up to some finite ``degree''. Using ideas from complex chemical reaction networks and a novel Lyapunov function, we establish that the phenomenon of mutation-selection balance occurs for such selection costs under mild conditions. That is, we show that the dynamical system has a unique equilibrium and that it converges to this equilibrium from all initial conditions.
影响因子：
3.3
作者：
S. Sawyer;D. Hartl
通讯作者：
S. Sawyer;D. Hartl
自然选择的年龄特定力量和生物人口统计学的死亡之墙。
DOI：
10.1073/pnas.1306656110
发表时间：
2013
影响因子：
11.1
作者：
Wachter,KennethW;Evans,StevenN;Steinsaltz,David
通讯作者：
Steinsaltz,David