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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 shown 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. 

Abstract Understanding phenotypic disparity across the tree of life requires identifying where and when evolutionary rates change on phylogeny. A primary methodological challenge in macroevolution is therefore to develop methods for accurate inference of among-lineage variation in rates of phenotypic evolution. Here, we describe a method for inferring among-lineage evolutionary rate heterogeneity in both continuous and discrete traits. The method assumes that the present-day distribution of a trait is shaped by a variable-rate process arising from a mixture of constant-rate processes and uses a single-pass tree traversal algorithm to estimate branch-specific evolutionary rates. By employing dynamic programming optimization techniques and approximate maximum likelihood estimators where appropriate, our method permits rapid exploration of the tempo and mode of phenotypic evolution. Simulations indicate that the method reconstructs rates of trait evolution with high accuracy. Application of the method to data sets on squamate reptile reproduction and turtle body size recovers patterns of rate heterogeneity identified by previous studies but with computational costs reduced by many orders of magnitude. Our results expand the set of tools available for detecting macroevolutionary rate heterogeneity and point to the utility of fast, approximate methods for studying large-scale biodiversity dynamics. [Brownian motion; continuous characters; discrete characters; macroevolution; Markov process; rate heterogeneity.]