Bayesian Inference of Evolutionary Histories under Time-Dependent Substitution Rates

Abstract Many factors complicate the estimation of time scales for phylogenetic histories, requiring increasingly complex evolutionary models and inference procedures. The widespread application of molecular clock dating has led to the insight that evolutionary rate estimates may vary with the time frame of measurement. This is particularly well established for rapidly evolving viruses that can accumulate sequence divergence over years or even months. However, this rapid evolution stands at odds with a relatively high degree of conservation of viruses or endogenous virus elements over much longer time scales. Building on recent insights into time-dependent evolutionary rates, we develop a formal and flexible Bayesian statistical inference approach that accommodates rate variation through time. We evaluate the novel molecular clock model on a foamy virus cospeciation history and a lentivirus evolutionary history and compare the performance to other molecular clock models. For both virus examples, we estimate a similarly strong time-dependent effect that implies rates varying over four orders of magnitude. The application of an analogous codon substitution model does not implicate long-term purifying selection as the cause of this effect. However, selection does appear to affect divergence time estimates for the less deep evolutionary history of the Ebolavirus genus. Finally, we explore the application of our approach on woolly mammoth ancient DNA data, which shows a much weaker, but still important, time-dependent rate effect that has a noticeable impact on node age estimates. Future developments aimed at incorporating more complex evolutionary processes will further add to the broad applicability of our approach.