Due to the hierarchical structure of the tree of life, closely related species often resemble each other more than distantly related species; a pattern termed phylogenetic signal. Numerous univariate statistics have been proposed as measures of phylogenetic signal for single phenotypic traits, but the study of phylogenetic signal for multivariate data, as is common in modern biology, remains challenging. Here, we introduce a new method to explore phylogenetic signal in multivariate phenotypes. Our approach decomposes the data into linear combinations with maximal (or minimal) phylogenetic signal, as measured by Blomberg’s K. The loading vectors of these phylogenetic components or K-components can be biologically interpreted, and scatterplots of the scores can be used as a low-dimensional ordination of the data that maximally (or minimally) preserves phylogenetic signal. We present algebraic and statistical properties, along with 2 new summary statistics, KA and KG, of phylogenetic signal in multivariate data. Simulation studies showed that KA and KG have higher statistical power than the previously suggested statistic Km⁢u⁢l⁢t, especially if phylogenetic signal is low or concentrated in a few trait dimensions. In 2 empirical applications to vertebrate cranial shape (crocodyliforms and papionins), we found statistically significant phylogenetic signal concentrated in a few trait dimensions. The finding that phylogenetic signal can be highly variable across the dimensions of multivariate phenotypes has important implications for current maximum likelihood approaches to phylogenetic signal in multivariate data.

中文翻译：

---

通过最大化 Blomberg 的 K 来探索多变量表型中的系统发育信号


由于生命之树的等级结构，密切相关的物种通常比远亲物种更相似;一种称为系统发育信号的模式。许多单变量统计已被提议作为单一表型特征的系统发育信号的度量，但现代生物学中常见的多变量数据系统发育信号的研究仍然具有挑战性。在这里，我们介绍了一种探索多变量表型中的系统发育信号的新方法。我们的方法将数据分解为具有最大（或最小）系统发育信号的线性组合，由 Blomberg 的 K 测量。这些系统发育成分或 K 成分的加载向量可以进行生物学解释，并且分数的散点图可以用作数据的低维排序，从而最大（或最小）地保留系统发育信号。我们提出了多变量数据中系统发育信号的代数和统计特性，以及 2 个新的汇总统计数据 KA 和 KG。模拟研究表明，KA 和 KG 比先前建议的统计量 Kmult 具有更高的统计功效，特别是当系统发育信号较低或集中在几个性状维度时。在脊椎动物颅骨形状 （鳄形目和 papionins） 的 2 个实证应用中，我们发现具有统计学意义的系统发育信号集中在几个性状维度中。系统发育信号在多变量表型的维度上可以高度可变的发现对当前多变量数据中系统发育信号的最大似然方法具有重要意义。