Data from: Comparative analysis of principal components can be misleading

Most existing methods for modeling trait evolution are univariate, although researchers are often interested in investigating evolutionary patterns and processes across multiple traits. Principal components analysis (PCA) is commonly used to reduce the dimensionality of multivariate data so that univariate trait models can be fit to individual principal components. The problem with using standard PCA on phylogenetically structured data has been previously pointed out yet it continues to be widely used in the literature. Here we demonstrate precisely how using standard PCA can mislead inferences: The first few principal components of traits evolved under constant-rate multivariate Brownian motion will appear to have evolved via an “early burst” process. A phylogenetic PCA (pPCA) has been proprosed to alleviate these issues. However, when the true model of trait evolution deviates from the model assumed in the calculation of the pPCA axes, we find that the use of pPCA suffers from similar artifacts as standard PCA. We show that data sets with high effective dimensionality are particularly likely to lead to erroneous inferences. Ultimately, all of the problems we report stem from the same underlying issue—by considering only the first few principal components as univariate traits, we are effectively examining a biased sample of a multivariate pattern. These results highlight the need for truly multivariate phylogenetic comparative methods. As these methods are still being developed, we discuss potential alternative strategies for using and interpreting models fit to univariate axes of multivariate data.

当前绝大多数用于性状演化建模的方法均为单变量方法，尽管研究者往往希望同时探究多性状维度下的演化模式与过程。主成分分析（Principal Components Analysis, PCA）是目前常用的降维手段，可实现多变量数据的维度缩减，从而使单变量性状模型能够适配至各个主成分。此前已有研究指出，对系统发育结构化数据使用标准主成分分析存在缺陷，但该方法仍在相关文献中被广泛应用。本研究精准阐明了标准主成分分析如何误导统计推断：在恒定速率多变量布朗运动模型下演化的性状，其前若干主成分会表现出“早爆发”演化过程的特征。系统发育主成分分析（phylogenetic PCA, pPCA）正是为缓解此类问题而提出的方法。然而，当真实的性状演化模型与pPCA轴计算时所假定的模型不符时，我们发现pPCA的使用同样会出现与标准主成分分析类似的偏差问题。本研究表明，有效维度较高的数据集尤其容易产生错误的统计推断。归根结底，本研究所揭示的所有问题均源于同一核心矛盾：仅将前若干主成分视为单变量性状进行分析时，我们实际上是在对多变量模式的有偏样本进行研究。上述结果凸显了开发真正意义上的多变量系统发育比较方法的必要性。鉴于此类方法仍处于开发阶段，我们还针对多变量数据的单变量轴适配模型的使用与解读，探讨了若干可行的替代策略。