饲养员的方程,Δz^=Gβ,让我们了解遗传学(遗传协方差矩阵,G)和线性选择梯度β的向量相互作用以生成进化轨迹。使用相对适合度的性状值多元回归估算β,彻底改变了我们在实验室和野生种群中研究选择的方式。然而,多重共线性,或预测因子的相关性,会导致β元素之间非常高的方差和协方差,对参数估计的解释构成了挑战。这在大数据时代尤其重要,其中预测因子的数量可能接近或超过观察值的数量。多共线预测因子的一种常见方法是丢弃其中的一些,从而失去可能从这些特征中获得的任何信息。使用模拟,我们展示了如何,一方面,多重共线性会导致对选择的不准确估计,and,另一方面,从分析中去除相关表型如何提供对选择目标的误导。我们证明了正则化回归,这对β的各个元素的大小施加了数据验证的约束,在存在多重共线性和有限数据的情况下,可以对多元选择的总强度和方向产生更准确的估计,当多重共线性较低时,成本往往很小。在对三个已发表的案例研究的重新分析中,我们还比较了标准和正则化的回归估计的选择,表明正则化回归可以改善独立数据中的适应度预测。我们的结果表明,正则化回归是一种有价值的工具,可以用作传统最小二乘选择估计的重要补充。在某些情况下,它的使用可以改善对个体健康的预测,并改进了多元选择的总强度和方向的估计。
The breeder\'s equation, Δ z ¯ = G β , allows us to understand how genetics (the genetic covariance matrix, G) and the vector of linear selection gradients β interact to generate evolutionary trajectories. Estimation of β using multiple regression of trait values on relative fitness revolutionized the way we study selection in laboratory and wild populations. However,
multicollinearity, or correlation of predictors, can lead to very high variances of and covariances between elements of β, posing a challenge for the interpretation of the parameter estimates. This is particularly relevant in the era of big data, where the number of predictors may approach or exceed the number of observations. A common approach to multicollinear predictors is to discard some of them, thereby losing any information that might be gained from those traits. Using simulations, we show how, on the one hand,
multicollinearity can result in inaccurate estimates of selection, and, on the other, how the removal of correlated phenotypes from the analyses can provide a misguided view of the targets of selection. We show that regularized regression, which places data-validated constraints on the magnitudes of individual elements of β, can produce more accurate estimates of the total strength and direction of multivariate selection in the presence of
multicollinearity and limited data, and often has little cost when
multicollinearity is low. We also compare standard and regularized regression estimates of selection in a reanalysis of three published case studies, showing that regularized regression can improve fitness predictions in independent data. Our results suggest that regularized regression is a valuable tool that can be used as an important complement to traditional least-squares estimates of selection. In some cases, its use can lead to improved predictions of individual fitness, and improved estimates of the total strength and direction of multivariate selection.