A General Framework for Branch Length Estimation in Ancestral Recombination Graphs

Inference of Ancestral Recombination Graphs (ARGs) is of central interest in the analysis of genomic variation. ARGs can be specified in terms of topologies and coalescence times. The coalescence times are usually estimated using an informative prior derived from coalescent theory, but this may generate biased estimates and can also complicate downstream inferences based on ARGs. Here we introduce, POLEGON, a novel approach for estimating branch lengths for ARGs which uses an uninformative prior. Using extensive simulations, we show that this method provides improved estimates of coalescence times and lead to more accurate inferences of effective population sizes under a wide range of demographic assumptions (population expansion, bottleneck, split, etc). It also improves other downstream inferences including estimates of mutation rates. We apply the method to data from the 1000 Genomes Project to investigate population size histories and differential mutation signatures across populations. We also estimate coalescence times in the HLA region, and show that they exceed 30 million years in multiple segments. Significance StatementModel misspecification is a common challenge in population genetic inference, as oversimplified mathematical models often fail to capture complex evolutionary processes. Here we introduce a novel framework for branch length estimation in whole-genome genealogies, which enables accurate inference using non-informative priors and subsequent posterior calibration, rather than relying on heavily parametrized models. This flexible approach has been validated in various simulation settings. When applied to real genomic data, it enables robust inference of demography, mutation rates, and transspecies polymorphisms.