Characterizing and Comparing Phylogenetic Trait Data from Their Normalized Laplacian Spectrum

The dissection of the mode and tempo of phenotypic evolution is integral to our understanding of global biodiversity. Our ability to infer patterns of phenotypes across phylogenetic clades is essential to how we infer the macroevolutionary processes governing those patterns. Many methods are already available for fitting models of phenotypic evolution to data. However, there is currently no comprehensive nonparametric framework for characterizing and comparing patterns of phenotypic evolution. Here, we build on a recently introduced approach for using the phylogenetic spectral density profile (SDP) to compare and characterize patterns of phylogenetic diversification, in order to provide a framework for nonparametric analysis of phylogenetic trait data. We show how to construct the SDP of trait data on a phylogenetic tree from the normalized graph Laplacian. We demonstrate on simulated data the utility of the SDP to successfully cluster phylogenetic trait data into meaningful groups and to characterize the phenotypic patterning within those groups. We furthermore demonstrate how the SDP is a powerful tool for visualizing phenotypic space across traits and for assessing whether distinct trait evolution models are distinguishable on a given empirical phylogeny. We illustrate the approach in two empirical data sets: a comprehensive data set of traits involved in song, plumage, and resource-use in tanagers, and a high-dimensional data set of endocranial landmarks in New World monkeys. Considering the proliferation of morphometric and molecular data collected across the tree of life, we expect this approach will benefit big data analyses requiring a comprehensive and intuitive framework.