DOI: 10.5061/dryad.xpnvx0kn1
title: Supplementary Materials include results of simulation experiments to investigate the impact of phylogenetic regression with model violations.

description: Modern comparative biology owes much to phylogenetic regression. At its
 conception, this technique sparked a revolution that armed biologists with
 phylogenetic comparative methods (PCMs) for disentangling evolutionary
 correlations from those arising from hierarchical phylogenetic
 relationships. Over the past few decades, the phylogenetic regression
 framework has become a paradigm of modern comparative biology that has
 been widely embraced as a remedy for shared ancestry. However, recent
 evidence has sown doubt over the efficacy of phylogenetic regression, and
 PCMs more generally, with the suggestion that many of these methods fail
 to provide an adequate defense against unreplicated evolution—the primary
 justification for using them in the first place. Importantly, some of the
 most compelling examples of biological innovation in nature result from
 abrupt lineage-specific evolutionary shifts, which current regression
 models are largely ill-equipped to deal with. Here we explore a solution
 to this problem by applying robust linear regression to comparative trait
 data. We formally introduce robust phylogenetic regression to the PCM
 toolkit with linear estimators that are less sensitive to model violations
 than the standard least-squares estimator, while still retaining high
 power to detect true trait associations. Our analyses also highlight an
 ingenuity of the original algorithm for phylogenetic regression based on
 independent contrasts, whereby robust estimators are particularly
 effective. Collectively, we find that robust estimators hold promise for
 improving tests of trait associations and offer a path forward in
 scenarios where classical approaches may fail. Our study joins recent
 arguments for increased vigilance against unreplicated evolution and a
 better understanding of evolutionary model performance in challenging–yet
 biologically important–settings.
description: # Supplementary Material and figures showing results of simulation
 experiments and phylogenetic case studies
 [https://doi.org/10.5061/dryad.xpnvx0kn1](https://doi.org/10.5061/dryad.xpnvx0kn1) Supplementary Figures include results of simulation experiments to investigate the impact of phylogenetic regression with mismatched trees. ## Supplementary Details associated with manuscript "Robust Phylogenetic Regression" Supplementary Materials include results of simulation experiments to investigate the impact of phylogenetic regression with model violations.  # Brief Description of Supplementary Figures (see documents for further information) SUPPLEMENTARY FIGURE 1. Diagnostic plots depicting studentized residuals as a function of leverage for the L2 estimator applied to the example datasets shown in Figure 2 with PIC (a) and PGLS (b) regression. SUPPLEMENTARY FIGURE 2. Histograms illustrating distributions of RPKM values across species (rows) and tissues (columns) for male (left column within tissue) and female (right column within tissue) from the Brawand et al. (2011) dataset.   SUPPLEMENTARY FIGURE 3. Investigating the impacts of evolutionary model violations for uncorrelated traits simulated under a shift model with variance . SUPPLEMENTARY FIGURE 4. Investigating the impacts of evolutionary model violations for uncorrelated traits simulated under a shift model with variance . SUPPLEMENTARY FIGURE 5. Investigating the impacts of the degree of true trait association for correlated traits simulated with true trait covariance . SUPPLEMENTARY FIGURE 6. Investigating the impacts of the degree of true trait association for correlated traits simulated with true trait covariance . SUPPLEMENTARY FIGURE 7. Phylogenetic regression in complex settings that include the joint scenario of a shift  and nonzero trait covariance  with  = 256 species. SUPPLEMENTARY FIGURE 8. Exploring robust regression for predicting female expression as a function of male expression in three tissues from nine species. SUPPLEMENTARY FIGURE 9. Alluvial plots showing relative fractions of genes with significant (*P *≤ 0.05) and non-significant (*P *&gt; 0.05) correlated expression in female and male brain, heart, and kidney tissues from nine species. SUPPLEMENTARY FIGURE 10. Applying robust phylogenetic regression to muscle fiber data from 22 lizard species. ##