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A Bayesian coalescent-based method has recently been proposed to delimit species using multilocus genetic sequence data. Posterior probabilities of different species delimitation models are calculated using reversible-jump Markov chain Monte Carlo algorithms. The method accounts for species phylogenies and coalescent events in both extant and extinct species and accommodates lineage sorting and uncertainties in the gene trees. Although the method is theoretically appealing, its utility in practical data analysis is yet to be rigorously examined. In particular, the analysis may be sensitive to priors on ancestral population sizes and on species divergence times and to gene flow between species. Here we conduct a computer simulation to evaluate the statistical performance of the method, such as the false negatives (the error of lumping multiple species into one) and false positives (the error of splitting one species into several). We found that the correct species model was inferred with high posterior probability with only one or two loci when 5 or 10 sequences were sampled from each population, or with 50 loci when only one sequence was sampled. We also simulated data allowing migration under a two-species model, a mainland-island model and a stepping-stone model to assess the impact of gene flow (hybridization or introgression). The behavior of the method was diametrically different depending on the migration rate. Low rates at < 0.1 migrants per generation had virtually no effect, so that the method, while assuming no hybridization between species, identified distinct species despite small amounts of gene flow. This behavior appears to be consistent with biologists' practice. In contrast, higher migration rates at ≥ 10 migrants per generation caused the method to infer one species. At intermediate levels of migration, the method is indecisive. Our results suggest that Bayesian analysis under the multispecies coalescent model may provide important insights into population divergences, and may be useful for generating hypotheses of species delimitation, to be assessed with independent information from anatomical, behavioral, and ecological data.

Motivation: Cancer is well known to be the end result of somatic mutations that disrupt normal cell division. The number of such mutations that have to be accumulated in a cell before cancer develops depends on the type of cancer. The waiting time T(m) until the appearance of m mutations in a cell is thus an important quantity in population genetics models of carcinogenesis. Such models are often difficult to analyze theoretically because of the complex interactions of mutation, drift and selection. They are also computationally expensive to simulate because of the large number of cells and the low mutation rate., Results: We develop an efficient algorithm for simulating the waiting time T(m) until m mutations under a population genetics model of cancer development. We use an exact algorithm to simulate evolution of small cell populations and coarse-grained τ-leaping approximation to handle large populations. We compared our hybrid simulation algorithm with the exact algorithm in small populations and with available asymptotic results for large populations. The comparison suggested that our algorithm is accurate and computationally efficient. We used the algorithm to study the waiting time for up to 20 mutations under a Moran model with variable population sizes. Our new algorithm may be useful for studying realistic models of carcinogenesis, which incorporates variable mutation rates and fitness effects.