Reconstructing population histories from single nucleotide polymorphism data

Population genetics encompasses a strong theoretical and applied research tradition on the multiple demographic processes that shape genetic variation present within a species. When several distinct populations exist in the current generation, it is often natural to consider the pattern of their divergence from a single ancestral population in terms of a binary tree structure. Inference about such population histories based on molecular data has been an intensive research topic in the recent years. The most common approach uses coalescent theory to model genealogies of individuals sampled from the current populations. Such methods are able to compare several different evolutionary scenarios and to estimate demographic parameters. However, their major limitation is the enormous computational complexity associated with the indirect modeling of the demographies, which limits the application to small data sets. Here, we propose a novel Bayesian method for inferring population histories from unlinked single nucleotide polymorphisms, which is applicable also to data sets harboring large numbers of individuals from distinct populations. We use an approximation to the neutral Wright-Fisher diffusion to model random fluctuations in allele frequencies. The population histories are modeled as binary rooted trees that represent the historical order of divergence of the different populations. A combination of analytical, numerical, and Monte Carlo integration techniques are utilized for the inferences. A particularly important feature of our approach is that it provides intuitive measures of statistical uncertainty related with the estimates computed, which may be entirely lacking for the alternative methods in this context. The potential of our approach is illustrated by analyses of both simulated and real data sets.