Robust phylogenetic regression

Abstract

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.

Keywords: Brownian motion; gene expression; linear regression; phylogenetics; quantitative traits; trait evolution.