Exploiting Low Scanwidth to Resolve Soft Polytomies

TL;DR

This paper introduces an algorithm for the Soft Tree Containment problem in phylogenetic networks, exploiting low scanwidth to improve computational efficiency in modeling reticulate evolution.

Contribution

It presents a novel algorithm that solves Soft Tree Containment efficiently by leveraging the low scanwidth property of practical phylogenetic networks.

Findings

Algorithm runs in fixed-parameter tractable time based on scanwidth and degrees.

Low scanwidth networks are common in practice, making the approach applicable.

Provides a new perspective on handling uncertainty in phylogenetic network analysis.

Abstract

Phylogenetic networks allow modeling reticulate evolution, capturing events such as hybridization and horizontal gene transfer. A fundamental computational problem in this context is the Tree Containment problem, which asks whether a given phylogenetic network is compatible with a given phylogenetic tree. However, the classical statement of the problem is not robust to poorly supported branches in biological data, possibly leading to false negatives. In an effort to address this, a relaxed version that accounts for uncertainty, called Soft Tree Containment, has been introduced by Bentert, Mal\'ik, and Weller [SWAT'18]. We present an algorithm that solves Soft Tree Containment in $2^{O(\Delta_T \cdot k \cdot \log(k))} \cdot n^{O(1)}$ time, where $k = \operatorname{sw}(\Gamma) + \Delta_N$, with $\Delta_T$ and $\Delta_N$ denoting the maximum out-degrees in the tree and the network, respectively, and $\operatorname{sw}(\Gamma)$ denoting the "scanwidth" [Berry, Scornavacca, and Weller, SOFSEM'20] of a given tree extension of the network, while $n$ is the input size. Our approach leverages the fact that phylogenetic networks encountered in practice often exhibit low scanwidth, making the problem more tractable.