Data from: Comparing G: multivariate analysis of genetic variation in multiple populations

The additive genetic variance–covariance matrix (G) summarizes the multivariate genetic relationships among a set of traits. The geometry of G describes the distribution of multivariate genetic variance, and generates genetic constraints that bias the direction of evolution. Determining if and how the multivariate genetic variance evolves has been limited by a number of analytical challenges in comparing G-matrices. Current methods for the comparison of G typically share several drawbacks: metrics that lack a direct relationship to evolutionary theory, the inability to be applied in conjunction with complex experimental designs, difficulties with determining statistical confidence in inferred differences and an inherently pair-wise focus. Here, we present a cohesive and general analytical framework for the comparative analysis of G that addresses these issues, and that incorporates and extends current methods with a strong geometrical basis. We describe the application of random skewers, common subspace analysis, the 4th-order genetic covariance tensor and the decomposition of the multivariate breeders equation, all within a Bayesian framework. We illustrate these methods using data from an artificial selection experiment on eight traits in Drosophila serrata, where a multi-generational pedigree was available to estimate G in each of six populations. One method, the tensor, elegantly captures all of the variation in genetic variance among populations, and allows the identification of the trait combinations that differ most in genetic variance. The tensor approach is likely to be the most generally applicable method to the comparison of G-matrices from any sampling or experimental design.

加性遗传方差-协方差矩阵（additive genetic variance–covariance matrix，简称G矩阵）概括了一组性状间的多变量遗传关联。G矩阵的几何结构刻画了多变量遗传方差的分布格局，并产生了可偏向进化方向的遗传约束。学界此前欲明确多变量遗传方差是否演化以及如何演化，却长期受制于G矩阵比较过程中的诸多分析难题。当前主流的G矩阵比较方法存在诸多共性缺陷：其评价指标与进化理论缺乏直接关联，无法适配复杂实验设计，难以对推断出的差异给出统计置信度检验，且本质上仅支持成对比较。为此，我们提出了一套统一通用的G矩阵比较分析框架，可有效解决上述局限，并对现有具备坚实几何基础的方法进行了整合与拓展。我们详细阐述了贝叶斯（Bayesian）框架下的随机skewers法、公共子空间分析法、四阶遗传协方差张量法以及多变量育种方程分解法的应用流程。我们以棘胫果蝇（Drosophila serrata）8个性状的人工选择实验数据为例，演示了这些方法的应用——该研究拥有多代系谱信息，可用于估算6个种群各自的G矩阵。其中，四阶遗传协方差张量法能够精准捕捉种群间遗传方差的全部变异，并可识别出遗传方差差异最显著的性状组合。该张量法有望成为适配任意抽样或实验设计的G矩阵比较通用方法。