Data from: There is more than one way to skin a G matrix

Because of its importance in directing evolutionary trajectories there has been considerable interest in comparing variation among genetic variance-covariance ( G) matrices. Numerous statistical approaches have been suggested but no general analysis of the relationship among these methods has previously been published. In this paper we used data from a half-sib experiment and simulations to explore the results of applying eight tests (T method, modified Mantel test, Bartlett’s test, Flury hierarchy, Jackknife-MANOVA, Jackknife-eigenvalue test, random skewers, selection skewers). Whereas a randomization approach produced acceptable estimates those from a bootstrap were typically unacceptable and we recommend randomization as the preferred method. All methods except the Jackknife-eigenvalue test gave similar results although a fine scale analysis suggested that the former group can be subdivided into two or possibly three groups, hierarchical tests, skewers, and the rest (Jackknife-MANOVA, Modified Mantel, T method, probably Bartlett’s). An advantage of the jackknife methods is that they permit tests of association with other factors, such as in this case, temperature and sex. We recommend applying all the tests described in this paper, with the exception of the T method, and provide R functions for this purpose.

鉴于遗传方差-协方差（G）矩阵在调控进化轨迹中的重要意义，学界对比较不同遗传方差-协方差矩阵间的差异产生了浓厚兴趣。目前已提出诸多统计方法用于此类比较，但此前尚无针对这些方法间关联的系统性分析成果发表。本文基于半同胞实验数据与模拟数据，探究了八种检验方法的应用结果，包括T检验法、修正Mantel检验、Bartlett检验、Flury层级检验、刀切法多元方差分析（Jackknife-MANOVA）、刀切法特征值检验、随机斜向检验（random skewers）以及选择斜向检验（selection skewers）。研究发现，随机化方法可生成可接受的估计结果，而自举法（bootstrap）的估计结果通常不符合要求，因此我们推荐优先使用随机化方法。除刀切法特征值检验外，其余七种方法均得到了相似的结果；而精细化分析显示，该组方法可进一步划分为2或3个子类：层级检验类、斜向检验类，以及剩余方法（刀切法多元方差分析、修正Mantel检验、T检验法，以及Bartlett检验）。刀切法类方法的优势在于，其允许检验与其他因素的关联，例如本研究中的温度与性别因素。我们推荐使用本文所述的全部检验方法（T检验法除外），并为此提供了对应的R语言函数。