Watanabe Junya
Department of Earth Sciences, University of Cambridge, Cambridge, United Kingdom.
J Evol Biol. 2024 Dec 2;37(12):1576-1590. doi: 10.1093/jeb/voae049.
Quantitative genetic theory on multivariate character evolution predicts that a population's response to directional selection is biased towards the major axis of the genetic covariance matrix G-the so-called genetic line of least resistance. Inferences on the genetic constraints in this sense have traditionally been made by measuring the angle of deviation of evolutionary trajectories from the major axis or, more recently, by calculating the amount of genetic variance-the Hansen-Houle evolvability-available along the trajectories. However, there have not been clear practical guidelines on how these quantities can be interpreted, especially in a high-dimensional space. This study summarizes pertinent distribution theories for relevant quantities, pointing out that they can be written as ratios of quadratic forms in evolutionary trajectory vectors by taking G as a parameter. For example, a beta distribution with appropriate parameters can be used as a null distribution for the squared cosine of the angle of deviation from a major axis or subspace. More general cases can be handled with the probability distribution of ratios of quadratic forms in normal variables. Apart from its use in hypothesis testing, this latter approach could potentially be used as a heuristic tool for looking into various selection scenarios, like directional and/or correlated selection, as parameterized with the mean and covariance of selection gradients.
多变量性状进化的定量遗传理论预测，种群对定向选择的响应偏向于遗传协方差矩阵G的主轴——即所谓的遗传最小阻力线。传统上，从这个意义上对遗传限制的推断是通过测量进化轨迹与主轴的偏离角度来进行的，或者最近是通过计算沿轨迹可用的遗传方差量——汉森-霍尔可进化性来进行的。然而，对于如何解释这些量，尤其是在高维空间中，还没有明确的实用指南。本研究总结了相关量的相关分布理论，指出通过将G作为参数，它们可以写成进化轨迹向量中二次型的比率。例如，具有适当参数的贝塔分布可以用作与主轴或子空间偏离角度的平方余弦的零分布。更一般的情况可以用正态变量中二次型比率的概率分布来处理。除了用于假设检验外，后一种方法还可能用作一种启发式工具，用于研究各种选择场景，如定向和/或相关选择，这些选择场景是用选择梯度的均值和协方差进行参数化的。
