Supplemental data from: Exploring phylogenetic signal in multivariate phenotypes by maximizing Blomberg’s K

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 two 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 Kmult, especially if phylogenetic
signal is low or concentrated in a few trait dimensions. In two 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.

鉴于生命之树具备层级结构，亲缘关系较近的物种通常比远缘物种更具形态相似性，这一模式被定义为系统发育信号（phylogenetic signal）。目前已有诸多单变量统计量被提出，用于量化单一表型性状的系统发育信号，但针对现代生物学中广泛应用的多变量数据的系统发育信号研究，仍存在较大挑战。为此，本文提出一种全新方法，用于探究多变量表型中的系统发育信号。该方法将原始数据分解为以布卢姆伯格K值（Blomberg's K）衡量的、具备最大（或最小）系统发育信号的线性组合。这些系统发育组分（或称K组分）的载荷向量可开展生物学阐释，而基于组分得分绘制的散点图可作为数据的低维排序工具，能够最大（或最小）程度保留原始数据的系统发育信号。本文同时阐述了该方法的代数与统计性质，并提出了两个用于衡量多变量数据系统发育信号的全新汇总统计量：K_A与K_G。模拟研究结果显示，相较于此前提出的统计量K_mult，K_A与K_G具备更高的统计功效，尤其当系统发育信号较弱，或仅集中于少数性状维度时。在两项针对脊椎动物颅骨形态的实证应用（鳄形类与狒狒亚科类群）中，本研究发现具有统计显著性的系统发育信号集中于少数性状维度。系统发育信号在多变量表型的各维度间存在显著异质性这一发现，对当前多变量数据系统发育信号的极大似然分析方法具有重要的理论启示与应用价值。