A comment on the use of stochastic character maps to estimate evolutionary rate variation in a continuously valued trait.

Phylogenetic comparative biology has progressed considerably in recent years (e.g., Butler and King 2004; Rabosky 2006; Bokma 2008; Alfaro et al. 2009; Stadler 2011; Slater et al. 2012). One of the most important developments has been the application of likelihood-based methods to fit alternative models for trait evolution in a phylogenetic treewith branch lengths proportional to time (e.g., Butler andKing2004;O’Meara et al. 2006; Thomas et al. 2006; Revell and Collar 2009; Beaulieu et al. 2012). An important example of this type of method is O’Meara et al. (2006) “noncensored” test for variation in the evolutionary rate for a continuously valued character trait through time or across the branches of a phylogenetic tree (also see Thomas et al. 2006 for a closely related approach). According to this method, we first hypothesize evolutionary rate regimes on the tree (called “painting” in Butler and King 2004); and then we fit an evolutionary model, specifically the popular Brownian model (Cavalli-Sforza and Edwards 1967; Felsenstein 1973, 1985), in which the instantaneous variance of the Brownian random diffusion process has different values in different parts of the phylogeny (O’Meara et al. 2006). In their original article, O’Meara et al. (2006) did not focus specifically on how to hypothesize evolutionary regimes on the tree. The authors did, however, suggest that to test the hypothesis that a discrete character state had influenced the rate of a continuous character, one could use the approach of (Nielsen 2002; Huelsenbeck et al. 2003; Bollback 2006) to first stochastically map the discretely valued trait, and then “test to see whether the portions of the tree with one state for the discrete character have a different rate of evolution for the continuous character than portions of the tree to which the other discrete state has beenmapped” (O’Meara et al. 2006, p. 931). Indeed, this has become common practice for this and other closely related methods (e.g., Collar et al. 2009, 2010; Revell and Collar 2009; Martin and Wainwright 2011; Price et al. 2011). Normally, then, the set of evolutionary rate estimates from the stochastically mapped trees are averaged across all the trees in the sample. This is presented as a method of obtaining rate estimates that “integrate over uncertainty in...ancestral states” (Collar et al. 2010, p. 1035). Figure 1 illustrates this analysis pipeline. a)