Turelli M
Genetics. 1985 Sep;111(1):165-95. doi: 10.1093/genetics/111.1.165.
Previous mathematical analyses of mutation-selection balance for metric traits assume that selection acts on the relevant loci only through the character(s) under study. Thus, they implicitly assume that all of the relevant mutation and selection parameters are estimable. A more realistic analysis must recognize that many of the pleiotropic effects of loci contributing variation to a given character are not known. To explore the consequences of these hidden effects, I analyze models of two pleiotropically connected polygenic traits, denoted P1 and P2. The actual equilibrium genetic variance for P1, based on complete knowledge of all mutation and selection parameters for both P1 and P2, can be compared to a prediction based solely on observations of P1. This extrapolation mimics empirically obtainable predictions because of the inevitability of unknown pleiotropic effects. The mutation parameters relevant to P1 are assumed to be known, but selection intensity is estimated from the within-generation reduction of phenotypic variance for P1. The extrapolated prediction is obtained by substituting these parameters into formulas based on single-character analyses. Approximate analytical and numerical results show that the level of agreement between these univariate extrapolations and the actual equilibrium variance depends critically on both the genetic model assumed and the relative magnitudes of the mutation and selection parameters. Unless per locus mutation rates are extremely high, i.e., generally greater than 10(-4), the widely used gaussian approximation for genetic effects at individual loci is not applicable. Nevertheless, the gaussian approximations predict that the true and extrapolated equilibria are in reasonable agreement, i.e., within a factor of two, over a wide range of parameter values. In contrast, an alternative approximation that applies for moderate and low per locus mutation rates predicts that the extrapolation will generally overestimate the true equilibrium variance unless there is little selection associated with hidden effects. The tendency to overestimate is understandable because selection acts on all of the pleiotropic manifestations of a new mutation, but equilibrium covariances among the characters affected may not reveal all of this selection. This casts doubt on the proposal that much of the additive polygenic variance observed in natural populations can be explained by mutation-selection balance. It also indicates the difficulty of critically evaluating this hypothesis.
先前针对度量性状的突变 - 选择平衡进行的数学分析假定，选择仅通过所研究的性状对相关基因座起作用。因此，它们隐含地假定所有相关的突变和选择参数都是可估计的。更现实的分析必须认识到，许多对给定性状产生变异的基因座的多效性效应是未知的。为了探究这些隐藏效应的后果，我分析了两个多基因性状（分别记为P1和P2）通过多效性相连的模型。基于对P1和P2所有突变和选择参数的完全了解，P1的实际平衡遗传方差可以与仅基于P1观测值的预测值进行比较。由于未知多效性效应的不可避免性，这种外推法模拟了根据经验可获得的预测。假定与P1相关的突变参数是已知的，但选择强度是根据P1表型方差在代内的减少来估计的。通过将这些参数代入基于单性状分析的公式中，得到外推预测值。近似的解析和数值结果表明，这些单变量外推值与实际平衡方差之间的一致程度关键取决于所假定的遗传模型以及突变和选择参数的相对大小。除非每个基因座的突变率极高，即通常大于10^(-4)，否则广泛使用的关于单个基因座遗传效应的高斯近似是不适用的。然而，高斯近似预测，在广泛的参数值范围内，真实平衡和外推平衡是合理一致的，即相差不超过两倍。相比之下，一种适用于中等和低每个基因座突变率的替代近似预测，除非与隐藏效应相关的选择很少，否则外推通常会高估真实平衡方差。高估的趋势是可以理解的，因为选择作用于新突变的所有多效性表现，但受影响性状之间的平衡协方差可能无法揭示所有这些选择。这对自然种群中观察到的许多加性多基因方差可由突变 - 选择平衡来解释这一观点提出了质疑。它还表明了严格评估这一假设的困难。
