Explaining and identifying variation in rates of evolution among lineages has long been a focus for evolutionary biologists (e.g., Darwin 1859; Simpson 1953; Gingerich 1983; Eldredge and Stanley 1984; Estes and Arnold 2007). Simpson (1944, 1953) coined a set of terms for the very purpose of distinguishing exceptional rates of evolution in particular lineages (i.e., tachytely, bradtely, horotely). Current approaches require that shifts in the evolutionary process are identified a priori (e.g., Butler and King 2004; O'Meara et al. 2006; Revell and Collar 2009). What these and related methods (Harmon et al. 2003; Freckleton and Jetz 2009) lack is the acknowledgment and accommodation of uncertainty in the evolutionary processes that give rise to trait values observed in extant taxa (but see Revell et al., in revision). The quality of inference is bounded by the quality of the models that we apply in the comparative framework: even the best among a set of inadequate models is still inadequate. Relaxing the assumption of static points in the tree where rates have shifted should diminish bias in branchwise estimates of evolutionary rates. Most ideal would be methods that limit influence of a priori expectations, while fairly comparing fit among the largest possible set of models and allowing robust inference of rate variation.

Drawing on recent progress in modeling molecular evolution (e.g., Huelsenbeck et al. 2004; Pagel and Meade 2008; Drummond and Suchard 2010), we model trait evolution by allowing phylogenetically localized shifts in the rate of a random-walk process of trait change. In a novel Bayesian approach, here referred to as auteur, we allow the data to directly inform uncertainty in the estimated evolutionary process. auteur (Accommodating Uncertainty in Trait Evolution Using R) samples across a broad set of possible trait evolution scenarios, considering models differing in number and topological position of local rate shifts.

We model trait evolution as a Brownian-motion process, which describes a broad set of neutral and nonneutral models of phenotypic evolution (Felsenstein 1973), and may be a reasonably adequate approximation of the evolutionary process in some lineages (Harmon et al. 2010). Under the modeled random-walk process, the trajectory of trait evolution (magnitude and directionality) is independent of the current state of the character. Whereas the expected value at the end of a random walk is simply the starting value, variance in traits accumulates in proportion to both the extent of independent evolution in lineages and the evolutionary rate of the character (see Felsenstein 1973; O'Meara et al. 2006; Revell et al. 2008). We thus expect little trait variance between sister species who have just diverged, especially for a slowly evolving trait. Its mathematical tractability makes Brownian motion an ideal framework in which to develop the model-fitting approach described here.

auteur applies a Bayesian approach to modeling rate heterogeneity on a phylogenetic tree using reversible-jump Markov Chain Monte Carlo (Metropolis et al. 1953; Hastings 1970). This reversible-jump approach is implemented to assess fit of models of differing complexity, which in this context is the number of rate shifts in the tree (Green 1995; Huelsenbeck et al. 2004; Drummond and Suchard 2010). We construct a Markov chain such that, upon convergence, distinct Brownian-motion models are sampled according to their posterior probability (Bartolucci et al. 2006). Of main interest, and inherently tied to the set of sampled models, are the marginalized distributions of relative rates for each branch in the tree.