DOI: 10.5061/dryad.6fh81vd
title: Data from: Characterizing and comparing phylogenetic trait data from their normalized Laplacian spectrum

description: 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 non-parametric framework for
 characterising and comparing patterns of phenotypic evolution. Here we
 build on a recently introduced approach for using the phylogenetic
 spectral density profile to compare and characterize patterns of
 phylogenetic diversification, in order to provide a framework for
 non-parametric analysis of phylogenetic trait data. We show how to
 construct the spectral density profile of trait data on a phylogenetic
 tree from the normalized graph Laplacian. We demonstrate on simulated data
 the utility of the spectral density profile to successfully cluster
 phylogenetic trait data into meaningful groups and to characterise the
 phenotypic patterning within those groups. We furthermore demonstrate how
 the spectral density profile is a powerful tool for visualising 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 datasets: a comprehensive dataset of traits
 involved in song, plumage and resource-use in tanagers, and a
 high-dimensional dataset 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.
description: Figure_Supplemental_1Measuring the effect of phylogenetic signal on splitter values.} (A) Boxplot of the splitter values for 100 randomized datasets (white) obtained for each of the ten datasets with two monophyletic clusters. Splitter values for the initial BM datasets with two clusters are shown in purple. Boxplot of 100 datasets simulated under a simple BM process with no clusters on a single tree (coral) is shown for comparison. (B) Boxplot of Blomberg’s $K$ for each randomized dataset (white); values for the initial BM datasets with two clusters are shown in purple. Boxplot of 100 datasets simulated under a simple BM process with no clusters on a single tree (coral) is shown for comparison.Figure_Supplemental_2Measuring the effect of erroneous trait data on spectral density profile summary statistics.} Spectral density profile summary statistics for data simulated under a BM process (coral) with introduced error for $10\%$ of tips with a sampling variance equal to one, two, and three times the standard error of the simulated BM data; and with a sampling variance equal to one times the standard error for $10, 20, 30, 100\%$ of tips. Spectral density profile summary statistics for data simulated on the same tree under an ACDC process ($\beta=1.5$) is also shown (cornflowerblue).Figure_Supplemental_3Clustering phylogenetic trait data using the spectral density profile of the nMGL on a non-ultrametric tree.} Hierarchical clustering of spectral density profiles and three-dimensional plotting of spectral density profile summary statistics for phylogenetic trait data simulated under AC (cornflower blue), BM (coral), and DC (sea green) models of trait evolution on a single (A) constant-rate, (C) increasing-rate, and (D) decreasing-rate birth-death tree without pruning extinct lineages. Tree is shown in inset. Asterisks denote bootstrap probabilities $&gt;0.95$ at the split. (B) Silhouette widths for profiles comprising each trait model cluster simulated on the ultrametric or non-ultrametric tree (see Fig. 5A).Figure_Supplemental_4Effect of tree size on the nMGL. (A) Scatterplots and OLS regression slopes for spectral density profile summary statistics for trait data simulated under DC (sea green), BM (coral), and AC (cornflower blue) models on constant-rate birth-death trees with different numbers of tips. (B) Phylogenetic trait space for trait models simulated under AC, BM, and DC models on trees with different numbers of tips.