Modeling Protein Evolution via Generative Inference From Monte Carlo Chains to Population Genetics

Generative models derived from large protein sequence alignments define complex fitness landscapes, but their utility for accurately modeling non-equilibrium evolutionary dynamics remains unclear. In this work, we perform a rigorous comparative analysis of three simulation schemes, designed to mimic evolution in silico by local sampling of the probability distribution defined by a generative model. We compare standard independent Markov Chain Monte Carlo, Monte Carlo on a phylogenetic tree, and a population genetics dynamics, benchmarking their outputs against deep sequencing data from four distinct in vitro evolution experiments. We find that standard Monte Carlo fails to reproduce the correct phylogenetic structure and generates unrealistic, gradual mutational sweeps. Performing Monte Carlo on a tree inferred from data improves phylogenetic fidelity and historical accuracy. The population genetics scheme successfully captures phylogenetic correlations, mutational abundances, and selective sweeps as emergent properties, without the need to infer additional information from data. However, the latter choice come at the price of not sampling the proper generative model distribution at long times. Our findings highlight the crucial role of phylogenetic correlations and finite-population effects in shaping evolutionary trajectories on fitness landscapes. These models therefore provide powerful tools for predicting complex adaptive paths and for reliably extrapolating evolutionary dynamics beyond current experimental limitations.