Accurate model selection of relaxed molecular clocks in bayesian phylogenetics

Abstract

Recent implementations of path sampling (PS) and stepping-stone sampling (SS) have been shown to outperform the harmonic mean estimator (HME) and a posterior simulation-based analog of Akaike's information criterion through Markov chain Monte Carlo (AICM), in bayesian model selection of demographic and molecular clock models. Almost simultaneously, a bayesian model averaging approach was developed that avoids conditioning on a single model but averages over a set of relaxed clock models. This approach returns estimates of the posterior probability of each clock model through which one can estimate the Bayes factor in favor of the maximum a posteriori (MAP) clock model; however, this Bayes factor estimate may suffer when the posterior probability of the MAP model approaches 1. Here, we compare these two recent developments with the HME, stabilized/smoothed HME (sHME), and AICM, using both synthetic and empirical data. Our comparison shows reassuringly that MAP identification and its Bayes factor provide similar performance to PS and SS and that these approaches considerably outperform HME, sHME, and AICM in selecting the correct underlying clock model. We also illustrate the importance of using proper priors on a large set of empirical data sets.

Fig. 1.

Results for the analysis of a large set of mammalian genes: (A) model selection results for the analysis of 872 genes using improper priors using the different estimators; (B) model selection results for the analysis of 961 genes using proper priors; (C) comparison of the log Bayes factor estimates for a common set of 872 genes for the MAP and sHME (gray) and for the MAP and SS (black), assuming improper priors; and (D) comparison of the log Bayes factor estimates for a common set of 961 genes for the MAP and sHME (gray) and for the MAP and SS (black), assuming proper priors.