Turelli Michael, Barton N H
Section of Evolution and Ecology and Center for Population Biology, University of California, Davis 95616, USA.
Genetics. 2004 Feb;166(2):1053-79. doi: 10.1534/genetics.166.2.1053.
We investigate three alternative selection-based scenarios proposed to maintain polygenic variation: pleiotropic balancing selection, G x E interactions (with spatial or temporal variation in allelic effects), and sex-dependent allelic effects. Each analysis assumes an additive polygenic trait with n diallelic loci under stabilizing selection. We allow loci to have different effects and consider equilibria at which the population mean departs from the stabilizing-selection optimum. Under weak selection, each model produces essentially identical, approximate allele-frequency dynamics. Variation is maintained under pleiotropic balancing selection only at loci for which the strength of balancing selection exceeds the effective strength of stabilizing selection. In addition, for all models, polymorphism requires that the population mean be close enough to the optimum that directional selection does not overwhelm balancing selection. This balance allows many simultaneously stable equilibria, and we explore their properties numerically. Both spatial and temporal G x E can maintain variation at loci for which the coefficient of variation (across environments) of the effect of a substitution exceeds a critical value greater than one. The critical value depends on the correlation between substitution effects at different loci. For large positive correlations (e.g., rho(ij)2>3/4), even extreme fluctuations in allelic effects cannot maintain variation. Surprisingly, this constraint on correlations implies that sex-dependent allelic effects cannot maintain polygenic variation. We present numerical results that support our analytical approximations and discuss our results in connection to relevant data and alternative variance-maintaining mechanisms.
多效性平衡选择、基因与环境相互作用（等位基因效应存在空间或时间变异）以及性别依赖的等位基因效应。每项分析均假设一个加性多基因性状，在稳定选择下有n个双等位基因位点。我们允许位点具有不同的效应，并考虑群体均值偏离稳定选择最优值时的平衡状态。在弱选择下，每个模型都会产生基本相同的近似等位基因频率动态。只有在平衡选择强度超过稳定选择有效强度的位点上，多效性平衡选择才能维持变异。此外，对于所有模型而言，多态性要求群体均值足够接近最优值，以使定向选择不会压倒平衡选择。这种平衡允许存在许多同时稳定的平衡状态，我们通过数值方法探究了它们的性质。空间和时间上的基因与环境相互作用都能在替代效应的变异系数（跨环境）超过一个大于1的临界值的位点上维持变异。该临界值取决于不同位点上替代效应之间的相关性。对于较大的正相关性（例如，rho(ij)2>3/4），即使等位基因效应出现极端波动也无法维持变异。令人惊讶的是，这种对相关性的限制意味着性别依赖的等位基因效应无法维持多基因变异。我们给出了支持我们分析近似结果的数值结果，并结合相关数据和其他维持方差的机制讨论了我们的结果。
