Data from: EMMLi: a maximum likelihood approach to the analysis of modularity

Identification of phenotypic modules, semiautonomous sets of highly
correlated traits, can be accomplished through exploratory (e.g., cluster
analysis) or confirmatory approaches (e.g., RV coefficient analysis).
Although statistically more robust, confirmatory approaches are generally
unable to compare across different model structures. For example, RV
coefficient analysis finds support for both two- and six-module models for
the therian mammalian skull. Here, we present a maximum likelihood
approach that takes into account model parameterization. We compare model
log-likelihoods of trait correlation matrices using the finite-sample
corrected Akaike Information Criterion, allowing for comparison of
hypotheses across different model structures. Simulations varying model
complexity and within- and between-module contrast demonstrate that this
method correctly identifies model structure and parameters across a wide
range of conditions. We further analyzed a dataset of 3-D data, consisting
of 61 landmarks from 181 macaque (Macaca fuscata) skulls, distributed
among five age categories, testing 31 models, including no modularity
among the landmarks and various partitions of two, three, six, and eight
modules. Our results clearly support a complex six-module model, with
separate within- and intermodule correlations. Furthermore, this model was
selected for all five age categories, demonstrating that this complex
pattern of integration in the macaque skull appears early and is highly
conserved throughout postnatal ontogeny. Subsampling analyses demonstrate
that this method is robust to relatively low sample sizes, as is commonly
encountered in rare or extinct taxa. This new approach allows for the
direct comparison of models with different parameterizations, providing an
important tool for the analysis of modularity across diverse systems.