Data from: A method for assessing phylogenetic least squares models for shape and other high-dimensional multivariate data

Studies of evolutionary correlations commonly utilize phylogenetic regression (i.e., independent contrasts and phylogenetic generalized least squares) to assess trait covariation in a phylogenetic context. However, while this approach is appropriate for evaluating trends in one or a few traits, it is incapable of assessing patterns in highly-multivariate data, as the large number of variables relative to sample size prohibits parametric test statistics from being computed. This poses serious limitations for comparative biologists, who must either simplify how they quantify phenotypic traits, or alter the biological hypotheses they wish to examine. In this article, I propose a new statistical procedure for performing ANOVA and regression models in a phylogenetic context that can accommodate high-dimensional datasets. The approach is derived from the statistical equivalency between parametric methods utilizing covariance matrices and methods based on distance matrices. Using simulations under Brownian motion, I show that the method displays appropriate Type I error rates and statistical power, whereas standard parametric procedures have decreasing power as data dimensionality increases. As such, the new procedure provides a useful means of assessing trait covariation across a set of taxa related by a phylogeny, enabling macroevolutionary biologists to test hypotheses of adaptation and phenotypic change in high-dimensional datasets.进化相关性研究通常借助系统发育回归（phylogenetic regression）——包括独立对比法（independent contrasts）与系统发育广义最小二乘法（phylogenetic generalized least squares）——在系统发育框架内评估性状协变关系。然而，该方法虽适用于单个性状或少数性状的趋势分析，却无法处理高维多元数据的模式解析：相较于样本量，变量数目过多会导致无法计算参数检验统计量。这给比较生物学家造成了严重局限，他们要么不得不简化表型性状的量化方案，要么调整原本拟检验的生物学假说。 本文提出一种全新的统计流程，可在系统发育框架下开展方差分析（ANOVA）与回归建模，且能够兼容高维数据集。该方法的理论基础为基于协方差矩阵的参数方法与基于距离矩阵的方法之间的统计等价性。通过布朗运动模型下的模拟实验，本文证实该方法可维持稳定的一类错误率与统计效力；而标准参数方法的统计效力则随数据维度升高持续降低。综上，该新方法为评估系统发育关联类群间的性状协变关系提供了实用手段，使宏观进化生物学家能够在高维数据集下检验适应性进化与表型变化相关假说。