On the Comparison of LGT networks and Tree-based Networks

Phylogenetic networks are widespread representations of evolutionary histories for taxa that undergo hybridization or Lateral-Gene Transfer (LGT) events. There are now many tools to reconstruct such networks, but no clearly established metric to compare them. Such metrics are needed, for example, to evaluate predictions against a simulated ground truth. Despite years of effort in developing metrics, known dissimilarity measures either do not distinguish all pairs of different networks, or are extremely difficult to compute. Since it appears challenging, if not impossible, to create the ideal metric for all classes of networks, it may be relevant to design them for specialized applications. In this article, we introduce a metric on LGT networks, which consist of trees with additional arcs that represent lateral gene transfer events. Our metric is based on edit operations, namely the addition/removal of transfer arcs, and the contraction/expansion of arcs of the base tree, allowing it to connect the space of all LGT networks. We show that it is linear-time computable if the order of transfers along a branch is unconstrained but NP-hard otherwise, in which case we provide a fixed-parameter tractable (FPT) algorithm in the level. We implemented our algorithms and demonstrate their applicability on three numerical experiments. Full online versionhttps://www.biorxiv.org/content/10.1101/2025.11.20.689557