Data from: A generalized K statistic for estimating phylogenetic signal from shape and other high-dimensional multivariate data

Phylogenetic signal is the tendency for closely related species to display
similar trait values due to their common ancestry. Several methods have
been developed for quantifying phylogenetic signal in univariate traits
and for sets of traits treated simultaneously, and the statistical
properties of these approaches have been extensively studied. However,
methods for assessing phylogenetic signal in high-dimensional multivariate
traits like shape are less well developed, and their statistical
performance is not well characterized. In this article, I describe a
generalization of the K statistic of Blomberg et al. (2003) that is useful
for quantifying and evaluating phylogenetic signal in highly-dimensional
multivariate data. The method (Kmult) is found from the equivalency
between statistical methods based on covariance matrices and those based
on distance matrices. Using computer simulations based on Brownian motion,
I demonstrate that the expected value of Kmult remains at 1.0 as trait
variation among species is increased or decreased, and as the number of
trait dimensions is increased. By contrast, estimates of phylogenetic
signal found with a squared-change parsimony procedure for multivariate
data change with increasing trait variation among species and with
increasing numbers of trait dimensions, confounding biological
interpretations. I also evaluate the statistical performance of hypothesis
testing procedures based on Kmult and find that the method displays
appropriate Type I error and high statistical power for detecting
phylogenetic signal in high-dimensional data. Statistical properties of
Kmult were consistent for simulations using bifurcating and random
phylogenies, for simulations using different numbers of species, for
simulations that varied the number of trait dimensions, and for different
underlying models of trait covariance structure. Overall these findings
demonstrate that Kmult provides a useful means of evaluating phylogenetic
signal in high-dimensional multivariate traits. Finally, I illustrate the
utility of the new approach by evaluating the strength of phylogenetic
signal for head shape in a lineage of Plethodon salamanders.