Data from: A comment on the use of stochastic character maps to estimate evolutionary rate variation in a continuously valued trait
Revell, Liam J. (2012), Data from: A comment on the use of stochastic character maps to estimate evolutionary rate variation in a continuously valued trait, Dryad, Dataset, https://doi.org/10.5061/dryad.8mj66m5c
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 use the approach of Neilsen (2002) 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 been mapped” (O’Meara et al., 2006, p. 931). Indeed, this has become common practice for this and other closely related methods. Here, I examine this practice. In particular, I show that evolutionary rates estimated this way (i.e., by using maximum likelihood [ML] to fit a multirate model on each stochastically mapped tree; and then averaging across trees) are systematically biased to be more similar to each other than are the underlying generating parameters. My analysis also reveals that this effect is dependent on the rate of evolution for the discrete trait. Specifically, if the rate of evolution for the discrete character is low then the difference between the true history and any stochastically mapped 1 history is generally small. This results in evolutionary rates for the continuous trait that are estimated with little bias. Conversely, if the rate of evolution for the discrete character is very high, then the true and hypothesized character histories are often extremely dissimilar, evolutionary rate estimates are biased to be more similar to each other than their underlying generating values, and we lose power to distinguish evolutionary rates on the tree.