Bayesian Selection of Relaxed-Clock Models: Distinguishing between Independent and Autocorrelated Rates

In Bayesian molecular-clock dating of species divergences, rate models are used to construct the prior on the molecular evolutionary rates for branches in the phylogeny, with independent and autocorrelated rate models being commonly used. The two classes of models, however, can result in markedly different divergence time estimates for the same data set, and thus selecting the best rate model appears important for obtaining reliable inferences of divergence times. However, the properties of Bayesian rate model selection are not well understood, in particular when the number of sequence partitions analyzed increases and when age calibrations (such as fossil calibrations) are misspecified. Furthermore, Bayesian rate model selection is computationally expensive as it requires the calculation of marginal likelihoods by Markov Chain Monte Carlo sampling, and therefore, methods that can speed up the model selection procedure without compromising its accuracy are desirable. In this study, we use a combination of computer simulations and real data analysis to investigate the statistical behavior of Bayesian rate model selection and we also explore approximations of the likelihood to improve computational efficiency in large phylogenomic data sets. Our simulations demonstrate that the posterior probability for the correct rate model converges to one as more molecular sequence partitions are analyzed and when no calibrations are used, as expected due to asymptotic Bayesian model selection theory. Furthermore, we also show the model selection procedure is robust to slight misspecification of calibrations, and reliable inference of the correct rate model is possible in this case. However, we show that when calibrations are seriously misspecified, calculated model probabilities are completely wrong and may converge to one for the wrong rate model. Finally, we demonstrate that approximating the phylogenetic likelihood under an arcsine branch-length transform can dramatically reduce the computational cost of rate model selection without compromising accuracy. We test the approximate procedure on two large phylogenies of primates (372 species) and flowering plants (644 species), replicating results obtained on smaller data sets using exact likelihood. Our findings and methodology can assist users in selecting the optimal rate model for estimating times and rates along the Tree of Life.