Bayesian inference of admixture graphs on Native American and Arctic populations

Admixture graphs are mathematical structures that describe the ancestry of populations in terms of divergence and merging (admixing) of ancestral populations as a graph. An admixture graph consists of a graph topology, branch lengths, and admixture proportions. The branch lengths and admixture proportions can be estimated using numerous numerical optimization methods, but inferring the topology involves a combinatorial search for which no polynomial algorithm is known. In this paper, we present a reversible jump MCMC algorithm for sampling high-probability admixture graphs and show that this approach works well both as a heuristic search for a single best-fitting graph and for summarizing shared features extracted from posterior samples of graphs. We apply the method to 11 Native American and Siberian populations and exploit the shared structure of high-probability graphs to address the relationship between Saqqaq, Inuit, Koryaks, and Athabascans. Our analyses show that the Saqqaq is not a good proxy for the previously identified gene flow from Arctic people into the Na-Dene speaking Athabascans. Author Summary One way of summarizing historical relationships between genetic samples is by constructing an admixture graph. An admixture graph describes the demographic history of a set of populations as a directed acyclic graph representing population splits and mergers. The inference of admixture graphs is currently done via greedy search algorithms that may fail to find the global optimum. We here improve on these approaches by developing a novel MCMC sampling method, AdmixtureBayes , that can sample from the posterior distribution of admixture graphs. This enables an efficient search of the entire state space as well as the ability to report a level of confidence in the sampled graphs. We apply AdmixtureBayes to a set of Native American and Arctic genomes to reconstruct the demographic history of these populations and report posterior probabilities of specific admixture events. While some previous studies have identified the ancient Saqqaq culture as a source of introgression into Athabascans, we instead find that it is the Siberian Koryak population, not the Saqqaq, that serves as the best proxy for gene flow into Athabascans.