Calibrating a molecular clock from phylogeographic data: moments and likelihood estimators.

We present moments and likelihood methods that estimate a DNA substitution rate from a group of closely related sister species pairs separated at an assumed time, and we test these methods with simulations. The methods also estimate ancestral population size and can test whether there is a significant difference among the ancestral population sizes of the sister species pairs. Estimates presented in the literature often ignore the ancestral coalescent prior to speciation and therefore should be biased upward. The simulations show that both methods yield accurate estimates given sample sizes of five or more species pairs and that better likelihood estimates are obtained if there is no significant difference among ancestral population sizes. The model presented here indicates that the larger than expected variation found in multitaxa datasets can be explained by variation in the ancestral coalescence and the Poisson mutation process. In this context, observed variation can often be accounted for by variation in ancestral population sizes rather than invoking variation in other parameters, such as divergence time or mutation rate. The methods are applied to data from two groups of species pairs (sea urchins and Alpheus snapping shrimp) that are thought to have separated by the rise of Panama three million years ago.