Population divergence time estimation using individual lineage label switching.

Divergence time estimation from multilocus genetic data has become common in population genetics and phylogenetics. We present a new Bayesian inference method that treats the divergence time as a random variable. The divergence time is calculated from an assembly of splitting events on individual lineages in a genealogy. The time for such a splitting event is drawn from a hazard function of the truncated normal distribution. This allows easy integration into the standard coalescence framework used in programs such as Migrate. We explore the accuracy of the new inference method with simulated population splittings over a wide range of divergence time values and with a reanalysis of a dataset of 5 populations consisting of 3 present-day populations (Africans, Europeans, Asian) and 2 archaic samples (Altai and Ust'Isthim). Evaluations of simple divergence models without subsequent geneflow show high accuracy, whereas the accuracy of the results of isolation with migration models depends on the magnitude of the immigration rate. High immigration rates lead to a time of the most recent common ancestor of the sample that, looking backward in time, predates the divergence time. Even with many independent loci, accurate estimation of the divergence time with high immigration rates becomes problematic. Our comparison to other software tools reveals that our lineage-switching method, implemented in Migrate, is comparable to IMa2p. The software Migrate can run large numbers of sequence loci (>1,000) on computer clusters in parallel.

A continuous method for gene flow.

Most modern population genetics inference methods are based on the coalescence framework. Methods that allow estimating parameters of structured populations commonly insert migration events into the genealogies. For these methods the calculation of the coalescence probability density of a genealogy requires a product over all time periods between events. Data sets that contain populations with high rates of gene flow among them require an enormous number of calculations. A new method, transition probability-structured coalescence (TPSC), replaces the discrete migration events with probability statements. Because the speed of calculation is independent of the amount of gene flow, this method allows calculating the coalescence densities efficiently. The current implementation of TPSC uses an approximation simplifying the interaction among lineages. Simulations and coverage comparisons of TPSC vs. MIGRATE show that TPSC allows estimation of high migration rates more precisely, but because of the approximation the estimation of low migration rates is biased. The implementation of TPSC into programs that calculate quantities on phylogenetic tree structures is straightforward, so the TPSC approach will facilitate more general inferences in many computer programs.

Unified framework to evaluate panmixia and migration direction among multiple sampling locations.

For many biological investigations, groups of individuals are genetically sampled from several geographic locations. These sampling locations often do not reflect the genetic population structure. We describe a framework using marginal likelihoods to compare and order structured population models, such as testing whether the sampling locations belong to the same randomly mating population or comparing unidirectional and multidirectional gene flow models. In the context of inferences employing Markov chain Monte Carlo methods, the accuracy of the marginal likelihoods depends heavily on the approximation method used to calculate the marginal likelihood. Two methods, modified thermodynamic integration and a stabilized harmonic mean estimator, are compared. With finite Markov chain Monte Carlo run lengths, the harmonic mean estimator may not be consistent. Thermodynamic integration, in contrast, delivers considerably better estimates of the marginal likelihood. The choice of prior distributions does not influence the order and choice of the better models when the marginal likelihood is estimated using thermodynamic integration, whereas with the harmonic mean estimator the influence of the prior is pronounced and the order of the models changes. The approximation of marginal likelihood using thermodynamic integration in MIGRATE allows the evaluation of complex population genetic models, not only of whether sampling locations belong to a single panmictic population, but also of competing complex structured population models.