A practical approximation algorithm for solving massive instances of hybridization number for binary and nonbinary trees

TL;DR

This paper introduces new algorithms that efficiently approximate solutions for the complex problem of determining reticulation events in large phylogenetic trees, significantly outperforming existing methods in speed and scalability.

Contribution

The authors present CycleKiller, NonbinaryCycleKiller, and TerminusEst, innovative algorithms that handle large, complex instances of the hybridization number problem with high accuracy and efficiency.

Findings

Algorithms run quickly on large instances

Solutions are very close to optimal

TerminusEst is the fastest exact method for nonbinary trees

Abstract

Reticulate events play an important role in determining evolutionary relationships. The problem of computing the minimum number of such events to explain discordance between two phylogenetic trees is a hard computational problem. Even for binary trees, exact solvers struggle to solve instances with reticulation number larger than 40-50. Here we present CycleKiller and NonbinaryCycleKiller, the first methods to produce solutions verifiably close to optimality for instances with hundreds or even thousands of reticulations. Using simulations, we demonstrate that these algorithms run quickly for large and difficult instances, producing solutions that are very close to optimality. As a spin-off from our simulations we also present TerminusEst, which is the fastest exact method currently available that can handle nonbinary trees: this is used to measure the accuracy of the NonbinaryCycleKiller algorithm. All three methods are based on extensions of previous theoretical work and are publicly available. We also apply our methods to real data.