Robust regression and posterior predictive simulation increase power to detect early bursts of trait evolution.

A central prediction of much theory on adaptive radiations is that traits should evolve rapidly during the early stages of a clade's history and subsequently slowdown in rate as niches become saturated--a so-called "Early Burst." Although a common pattern in the fossil record, evidence for early bursts of trait evolution in phylogenetic comparative data has been equivocal at best. We show here that this may not necessarily be due to the absence of this pattern in nature. Rather, commonly used methods to infer its presence perform poorly when when the strength of the burst--the rate at which phenotypic evolution declines--is small, and when some morphological convergence is present within the clade. We present two modifications to existing comparative methods that allow greater power to detect early bursts in simulated datasets. First, we develop posterior predictive simulation approaches and show that they outperform maximum likelihood approaches at identifying early bursts at moderate strength. Second, we use a robust regression procedure that allows for the identification and down-weighting of convergent taxa, leading to moderate increases in method performance. We demonstrate the utility and power of these approach by investigating the evolution of body size in cetaceans. Model fitting using maximum likelihood is equivocal with regards the mode of cetacean body size evolution. However, posterior predictive simulation combined with a robust node height test return low support for Brownian motion or rate shift models, but not the early burst model. While the jury is still out on whether early bursts are actually common in nature, our approach will hopefully facilitate more robust testing of this hypothesis. We advocate the adoption of similar posterior predictive approaches to improve the fit and to assess the adequacy of macroevolutionary models in general.