Estimating divergence times from DNA sequences.

The patterns of genetic variation within and among individuals and populations can be used to make inferences about the evolutionary forces that generated those patterns. Numerous population genetic approaches have been developed in order to infer evolutionary history. Here, we present the "Two-Two (TT)" and the "Two-Two-outgroup (TTo)" methods; two closely related approaches for estimating divergence time based in coalescent theory. They rely on sequence data from two haploid genomes (or a single diploid individual) from each of two populations. Under a simple population-divergence model, we derive the probabilities of the possible sample configurations. These probabilities form a set of equations that can be solved to obtain estimates of the model parameters, including population split times, directly from the sequence data. This transparent and computationally efficient approach to infer population divergence time makes it possible to estimate time scaled in generations (assuming a mutation rate), and not as a compound parameter of genetic drift. Using simulations under a range of demographic scenarios, we show that the method is relatively robust to migration and that the TTo method can alleviate biases that can appear from drastic ancestral population size changes. We illustrate the utility of the approaches with some examples, including estimating split times for pairs of human populations as well as providing further evidence for the complex relationship among Neandertals and Denisovans and their ancestors.