Data from: Ancestral state reconstruction, rate heterogeneity, and the evolution of reptile viviparity

Virtually all models for reconstructing ancestral states for discrete characters make the crucial assumption that the trait of interest evolves at a uniform rate across the entire tree. Although methods for identifying evolutionary rate shifts in continuous characters have attracted recent attention (e.g. Eastman et al., 2011, Stack et al., 2011), such methods for discrete characters have only very recently been developed (Beaulieu et al., 2013, Beaulieu and O'Meara 2014) and have yet to be widely used. However, ancestral state reconstructions of discrete characters are being performed on increasingly large phylogenies, where it is likely that evolutionary rates will vary greatly between different clades (Beaulieu and O'Meara 2014). Here, we show how failure to account for such variable evolutionary rates can cause highly anomalous (and likely incorrect) results, while three methods that accommodate rate variability yield the opposite, more plausible, and more robust reconstructions. The random local clock method, implemented in BEAST, estimates the position and magnitude of rate changes on the tree, split BiSSE estimates separate rate parameters for pre-specified clades, and the hidden rates model partitions each character state into a number of rate categories. The importance of accounting for rate heterogeneity in ancestral state reconstruction is highlighted empirically with a new analysis of the evolution of viviparity in squamate reptiles. Additionally, simulations show the inadequacy of traditional models when characters evolve with both asymmetry (different rates of change between states within a character) and heterotachy (different rates of character evolution across different clades).