A likelihood-based framework for demographic inference from genealogical trees

The demographic history of a population underlies patterns of genetic variation and is encoded in the gene-genealogical trees of the sampled haplotypes. Here we propose a demographic inference framework called the genealogical likelihood (gLike). Our method uses a graph-based structure to summarize the relationships among all lineages in a gene-genealogical tree with all possible trajectories of population memberships through time and derives the full likelihood across trees under a parameterized demographic model. We show through simulations and empirical applications that for populations that have experienced multiple admixtures, gLike can accurately estimate dozens of demographic parameters, including ancestral population sizes, admixture timing and admixture proportions, and it outperforms conventional demographic inference methods using the site frequency spectrum. Taken together, our proposed gLike framework harnesses underused genealogical information to offer high sensitivity and accuracy in inferring complex demographies for humans and other species.