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. However, this assumption is unlikely to hold in many situations, particularly as ancestral state reconstructions are being performed on increasingly large phylogenies. 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. 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). 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, which reveal a predominance of forward (oviparous-viviparous) transitions and very few reversals.