Coalescence and Translation: A Language Model for Population Genetics

Probabilistic models such as the sequentially Markovian coalescent (SMC) have long provided a powerful framework for population genetic inference, enabling reconstruction of demographic history and ancestral relationships from genomic data. However, these methods are inherently specialized, relying on predefined assumptions and/or limited scalability. Recent advances in simulation and deep learning provide an alternative approach: learning directly to generalize from synthetic genetic data to infer specific hidden evolutionary processes. Here we reframe the inference of coalescence times as a problem of translation between two biological languages: the sparse, observable patterns of mutation along the genome and the unobservable ancestral recombination graph (ARG) that gave rise to them. Inspired by large language models, we develop cxt, a decoder-only transformer that autoregressively predicts coalescent events conditioned on local mutational context. We show that cxt performs on par with state-of-the-art MCMC-based likelihood models across a broad range of demographic scenarios, including both in-distribution and out-of-distribution settings. Trained on simulations spanning the stdpopsim catalog, the model generalizes robustly and enables efficient inference at scale, producing over a million coalescence predictions in minutes. In addition cxt produces a well calibrated approximate posterior distribution of its predictions, enabling principled uncertainty quantification. Our work moves towards a foundation model for population genetics, bridging deep learning and coalescent theory to enable flexible, scalable inference of genealogical history from genomic data.