Evaluation of Bayesian Models of Substitution Rate Evolution—Parental Guidance versus Mutual Independence

We have evaluated the performance of two classes of probabilistic models for substitution rate variation over phylogenetic trees. In the first class, branch rates are considered to be independent and identically distributed (i.i.d.) stochastic variables. Three versions with respect to the underlying distribution (Gamma, Inverse Gaussian, and LogNormal) are considered. The i.i.d. models are compared with the autocorrelated (AC) model, where rates of adjacent nodes in the tree are AC, so that a node rate is LogNormal distributed around the rate of the parent node. The performance of different models is evaluated using three empirical data sets. For all data sets, it was clear that all tested models extracted substantial knowledge from data when posterior divergence time distributions were compared with the prior distributions and, furthermore, that they clearly outperformed a molecular clock. Moreover, the descriptive power of the i.i.d. models, as evaluated by Bayes factors, was either equal to or clearly better than that of the AC model. The latter effect increased with extended taxon sampling. Likewise, under none of the models could we find compelling evidence, in any of the data sets, for rate correlation between adjacent branches/nodes. These findings challenge previous suggestions of universality of autocorrelation in sequence evolution. We also performed an additional comparison with a divergence time prior including calibration information from fossil evidence. Adding fossil information to the prior had negligible effect on Bayes factors and mainly affected the width of the posterior distribution of the divergence times, whereas the relative position of the mean divergence times were largely unaffected.