Beyond Level-1: Fast Inference of Generic Semi-directed Phylogenetic Networks

Hybridization, introgression, and lateral gene transfer shape genomes across the diversity of life, but our ability to reconstruct these histories has been constrained by a methodological bottleneck: nearly all network inference methods are restricted to level-1 topologies, leaving more complex reticulate histories methodologically inaccessible. Here, we extend the widely used SNaQ method to scalably infer arbitrary binary, metric, semi-directed phylogenetic networks. Computational improvements yield substantial speedups in marginal composite likelihood evaluation, enabling genome-scale network inference under this framework for the first time. We systematically evaluate inference accuracy across networks of varying complexity, including cases where the true history falls outside the inferred search space, and find that SNaQ reliably recovers complex reticulate histories under diverse conditions, and still recovers meaningful information about hybridization events even when the full topology is not correctly inferred. Applied to the phylogeny of Xiphophorus (Poeciliidae), the method reveals a richer history of hybridization than level-1 approaches could capture, with network models that fit the data significantly better than previously inferred topologies. By enabling scalable inference beyond level-1 networks, our work facilitates the reconstruction of far richer reticulate histories from genomic data, bringing phylogenetic analysis closer to capturing the full network of life.