A likelihood-based framework for demographic inference from genealogical trees.

The demographic history of a population drives the pattern of genetic variation and is encoded in the gene-genealogical trees of the sampled alleles. However, existing methods to infer demographic history from genetic data tend to use relatively low-dimensional summaries of the genealogy, such as allele frequency spectra. As a step toward capturing more of the information encoded in the genome-wide sequence of genealogical trees, here we propose a novel framework called the genealogical likelihood (gLike), which derives the full likelihood of a genealogical tree under any hypothesized demographic history. Employing a graph-based structure, gLike summarizes across independent trees the relationships among all lineages in a tree with all possible trajectories of population memberships through time and efficiently computes the exact marginal probability under a parameterized demographic model. Through extensive simulations and empirical applications on populations that have experienced multiple admixtures, we showed that gLike can accurately estimate dozens of demographic parameters when the true genealogy is known, including ancestral population sizes, admixture timing, and admixture proportions. Moreover, when using genealogical trees inferred from genetic data, we showed that gLike outperformed conventional demographic inference methods that leverage only the allele-frequency spectrum and yielded parameter estimates that align with established historical knowledge of the past demographic histories for populations like Latino Americans and Native Hawaiians. Furthermore, our framework can trace ancestral histories by analyzing a sample from the admixed population without proxies for its source populations, removing the need to sample ancestral populations that may no longer exist. Taken together, our proposed gLike framework harnesses underutilized genealogical information to offer exceptional sensitivity and accuracy in inferring complex demographies for humans and other species, particularly as estimation of genome-wide genealogies improves.