Inferring Migration Networks with Time-Lagged F2 Statistics

Major demographic events, such as population bottlenecks, founder effects, range expansions, and admixture events, have left lasting imprints on human genetic diversity. Ancient DNA (aDNA) sequencing now makes it increasingly possible to observe these signals across time, opening new avenues to address long-standing questions in human demographic history. Yet, deciphering this genetic archive of demographic history is challenging due to high levels of noise, and the complex ways in which demographic processes shape genetic variation. Here, leveraging the linear time evolution of the expectation of neutral allele frequencies, we develop a method to uncover systematic patterns of gene flow from metapopulation time-series data. We show that directional migration rates can be inferred via linear regression on time-dependent genetic dissimilarity between populations, quantified by an extended F2 statistic evaluated between successive time points. Despite small sample sizes, the method reliably infers migration rates from simulated data by integrating information across multiple time slices. Applied to aDNA sampled from the last 6000 years, we recover signals of well-documented migrations and infer an ancient pan-European migration network. While complementing existing tools that estimate static ancestry proportions, our framework tracks how ancestry is dynamically redistributed through time.