Data from: A method for analysis of phenotypic change for phenotypes described by high-dimensional data

The analysis of phenotypic change is important for several evolutionary
biology disciplines, including phenotypic plasticity, evolutionary
developmental biology, morphological evolution, physiological evolution,
evolutionary ecology and behavioral evolution. It is common for
researchers in these disciplines to work with multivariate phenotypic
data. When phenotypic variables exceed the number of research
subjects—data called ‘high-dimensional data’—researchers are confronted
with analytical challenges. Parametric tests that require high observation
to variable ratios present a paradox for researchers, as eliminating
variables potentially reduces effect sizes for comparative analyses, yet
test statistics require more observations than variables. This problem is
exacerbated with data that describe ‘multidimensional’ phenotypes, whereby
a description of phenotype requires high-dimensional data. For example,
landmark-based geometric morphometric data use the Cartesian coordinates
of (potentially) many anatomical landmarks to describe organismal shape.
Collectively such shape variables describe organism shape, although the
analysis of each variable, independently, offers little benefit for
addressing biological questions. Here we present a nonparametric method of
evaluating effect size that is not constrained by the number of phenotypic
variables, and motivate its use with example analyses of phenotypic change
using geometric morphometric data. Our examples contrast different
characterizations of body shape for a desert fish species, associated with
measuring and comparing sexual dimorphism between two populations. We
demonstrate that using more phenotypic variables can increase effect
sizes, and allow for stronger inferences.