The Limits of Bayesian Estimates of Divergence Times in Measurably Evolving Populations.

Bayesian inference of divergence times for extant species using molecular data is an unconventional statistical problem: divergence times and molecular rates are confounded, and only their product, the molecular branch length, is statistically identifiable. Priors on times and rates are needed to break this identifiability problem, imposing a lower bound on the uncertainty attainable under infinite data. With infinite data, uncertainty in node ages increases proportionally with their mean age, such that older nodes have higher uncertainty than younger nodes. If extinct taxa with known sampling times are present (ie "heterochronous" data), times and rates become identifiable and uncertainties go to zero with infinite data. However, in real heterochronous datasets (such as viruses and bacteria), alignments tend to be small and how uncertainty scales with data size has not been explored. Here, we conducted extensive simulations and analyses of empirical data to develop the infinite-sites theory for heterochronous data. Contrary to expectations, we find that uncertainty in ages of internal nodes scales positively with the distance to their closest tip with known age (ie calibration age), not their absolute age. Estimation uncertainty decreases with calibration age more slowly in datasets with more site patterns, although overall uncertainty is lower in such datasets. Our framework establishes the minimum uncertainty attainable with perfect calibrations and effectively infinite sequence data. In a vast majority of cases, viral outbreak data are not sufficiently informative to display infinite-sites behavior, and estimates of evolutionary timescales will depend on dataset size, information content, and model complexity.