Signature-Informed Selection Detection: A Novel Method for Multi-Locus Wright-Fisher Models with Recombination

In this manuscript, we present an innovative Bayesian framework tailored for the inference of the selection coefficients in multi-locus Wright-Fisher models. Utilizing a signature kernel score, our approach offers an innovative solution for approximating likelihoods by extracting informative signatures from the trajectories of haplotype frequencies. Moreover, within the framework of a generalized Bayesian posterior, we derive the scoring rule posterior, which we then pair with a Population Monte Carlo (PMC) algorithm to obtain posterior samples for selection coefficients. This powerful combination enables us to infer selection dynamics efficiently even in complex high-dimensional and temporal data settings. We show that our method works well through extensive tests on both simulated and real-world data. Notably, our approach effectively detects selection not just in univariate, but also in multivariate Wright-Fisher models, including 2-locus and 3-locus models with recombination. Our proposed novel technique contributes to a better understanding of complex evolutionary dynamics.