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. One of the most important developments has been the application of likelihood-based methods to fit alternative models for trait evolution in a phylogenetic tree with branch lengths proportional to time. An important example of this type of method is O’Meara et al.’s (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. 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, in which the instantaneous variance of the Brownian random diffusion process has different values in different parts of the phylogeny. The authors suggest that to test a hypothesis that the state of a discrete character influenced the rate of a continuous character, one could u...