Mixture Models for Dating with Confidence

Robust estimation of divergence times is commonly performed using Bayesian inference with relaxed clock models. The specific choice of relaxed clock model and tree prior model can impact divergence time estimates, thus necessitating model selection among alternative models. The common approach is to select a model based on Bayes factors estimated via computational demanding approaches such as stepping stone sampling. Here we explore an alternative approach: mixture models that analytically integrate over all candidate models. Our mixture model approach only requires one Markov chain Monte Carlo analysis to both estimate the parameters of interest (e.g., the time-calibrated phylogeny) and to compute model posterior probabilities. We demonstrate the application of our mixture model approach using three relaxed clock models (uncorrelated exponential, uncorrelated lognormal and independent gamma rates) combined with three tree prior models (constant-rates pure birth process, constant-rate birth-death process and piecewise-constant birth-death process) and mitochondrial genome dataset of Crocodylia. We calibrate the phylogeny using well-defined fossil node calibrations. Our results show that Bayes factors estimated using stepping stone sampling are unreliable due to noise in repeated analyses while our analytical mixture model approach shows higher precision and robustness. Thus, divergence time estimates under our mixture model are comparably robust as previous relaxed clock approaches but model selection is significantly faster and avoids marginal likelihood estimation. Finally, our time-calibrated phylogeny of Crocodylia presents a robust benchmark for further studies in the group.