Ultrafast learning of 4-node hybridization cycles in phylogenetic networks using algebraic invariants

TL;DR

This paper introduces a fast, algebraic invariant-based method for reconstructing 4-node hybridization cycles in phylogenetic networks, significantly improving speed over existing approaches while maintaining accuracy.

Contribution

It is the first to define phylogenetic invariants on concordance factors for level-1 networks, enabling optimization-free inference under the multispecies coalescent model.

Findings

Method is at least 10 times faster than existing network methods.

Accurately reconstructs phylogenetic networks in simulated scenarios.

Successfully applied to the Canis genus data.

Abstract

Motivation: The abundance of gene flow in the Tree of Life challenges the notion that evolution can be represented with a fully bifurcating process, as this process cannot capture important biological realities like hybridization, introgression, or horizontal gene transfer. Coalescent-based network methods are increasingly popular, yet not scalable for big data, because they need to perform a heuristic search in the space of networks as well as numerical optimization that can be NP-hard. Results: Here, we introduce a novel method to reconstruct phylogenetic networks based on algebraic invariants. While there is a long tradition of using algebraic invariants in phylogenetics, our work is the first to define phylogenetic invariants on concordance factors (frequencies of 4-taxon splits in the input gene trees) to identify level-1 phylogenetic networks under the multispecies coalescent model. Our novel inference methodology is optimization-free as it only requires the evaluation of polynomial equations, and as such, it bypasses the traversal of network space, yielding a computational speed at least 10 times faster than the fastest-to-date network methods. We illustrate the accuracy and speed of our new method on a variety of simulated scenarios as well as in the estimation of a phylogenetic network for the genus Canis. Availability and Implementation: We implement our novel theory on an open-source publicly available Julia package PhyloDiamond.jl available at https://github.com/solislemuslab/PhyloDiamond.jl with broad applicability within the evolutionary biology community. Contact: solislemus@wisc.edu