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.
Figure_Supplemental_1
Measuring 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_2
Measuring 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_3
Clustering 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 $>0.95$ 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_4
Effect 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.
