Relative efficiencies of simple and complex substitution models in estimating divergence times in phylogenomics

Abstract

The conventional wisdom in molecular evolution is to apply parameter-rich models of nucleotide and amino acid substitutions for estimating divergence times. However, the actual extent of the difference between time estimates produced by highly complex models compared to those from simple models is yet to be quantified for contemporary datasets that frequently contain sequences from many species and genes. In a reanalysis of many large multispecies alignments from diverse groups of taxa using the same tree topologies and calibrations, we found that the use of the simplest models can produce divergence time estimates and credibility intervals similar to those obtained from the complex models applied in the original studies. This result is surprising because the use of simple models underestimates sequence divergence for all the datasets analyzed. We find three fundamental reasons for the observed robustness of time estimates to model complexity in many practical datasets. First, the estimates of branch lengths and node-to-tip distances under the simplest model show an approximately linear relationship with those produced by using the most complex models applied, especially for datasets with many sequences. Second, relaxed clock methods automatically adjust rates on branches that experience considerable underestimation of sequence divergences, resulting in time estimates that are similar to those from complex models. And, third, the inclusion of even a few good calibrations in an analysis can reduce the difference in time estimates from simple and complex models. The robustness of time estimates to models complexity in these empirical data analyses is encouraging, because all phylogenomics studies use statistical models that are oversimplified descriptions of actual evolutionary substitution processes.