Multilocus selection in subdivided populations I. Convergence properties for weak or strong migration
Multilocus selection in subdivided populations I. Convergence properties for weak or strong migration
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DOI：
10.1007/s00285-008-0236-5
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发表时间：
2009-06-01
影响因子：
1.9
通讯作者：
Buerger, Reinhard
中科院分区：
文献类型：
--
作者：
Buerger, Reinhard
研究了一个作用于多个多等位基因位点的迁移和选择的确定性种群遗传模型的动力学和平衡结构。大量的二倍体个体分布在由迁徙连接的数百个部落中。世代是离散的和不重叠的，迁移是不可约的和非周期性的，所有成对重组率都是正的，选择可能会因种群而异。它被证明，在没有选择的情况下，所有的轨迹收敛到一个流形上的全球连锁平衡举行和等位基因频率是相同的整个demes的几何速度。各种限制的情况下，其中一个或多个的三个进化力量，选择，迁移和重组，是弱相对于其他。有两个特别有趣。如果迁移和重组相对于选择是强的，那么动态可以被认为是所谓的弱选择极限的扰动，这是一个简单的动态系统，用于适当平均的等位基因频率。在此弱选择极限的非简并性假设下，全动力学的每个平衡点都是弱选择极限平衡点的扰动，并且具有相同的稳定性。两个系统中的平衡数是相同的，在完整（扰动）系统中的平衡是准连锁平衡，并且在整个种群中等位基因频率之间的差异很小。如果迁移相对于重组是弱的，并且上位性也是弱的，则每个平衡都是相应的无迁移系统的平衡的扰动，具有相同的稳定性，并且处于准连锁平衡。在这两种情况下，每个轨迹都收敛到一个平衡点，因此不会发生循环或复杂的动态。
The dynamics and equilibrium structure of a deterministic population-genetic model of migration and selection acting on multiple multiallelic loci is studied. A large population of diploid individuals is distributed over finitely many demes connected by migration. Generations are discrete and nonoverlapping, migration is irreducible and aperiodic, all pairwise recombination rates are positive, and selection may vary across demes. It is proved that, in the absence of selection, all trajectories converge at a geometric rate to a manifold on which global linkage equilibrium holds and allele frequencies are identical across demes. Various limiting cases are derived in which one or more of the three evolutionary forces, selection, migration, and recombination, are weak relative to the others. Two are particularly interesting. If migration and recombination are strong relative to selection, the dynamics can be conceived as a perturbation of the so-called weak-selection limit, a simple dynamical system for suitably averaged allele frequencies. Under nondegeneracy assumptions on this weak-selection limit which are generic, every equilibrium of the full dynamics is a perturbation of an equilibrium of the weak-selection limit and has the same stability properties. The number of equilibria is the same in both systems, equilibria in the full (perturbed) system are in quasi-linkage equilibrium, and differences among allele frequencies across demes are small. If migration is weak relative to recombination and epistasis is also weak, then every equilibrium is a perturbation of an equilibrium of the corresponding system without migration, has the same stability properties, and is in quasi-linkage equilibrium. In both cases, every trajectory converges to an equilibrium, thus no cycling or complicated dynamics can occur.