New FPT algorithms for finding the temporal hybridization number for sets of phylogenetic trees

TL;DR

This paper introduces fixed-parameter tractable algorithms for constructing minimal temporal hybridization networks from phylogenetic trees, with practical implementation and experimental validation.

Contribution

It presents new FPT algorithms for the temporal hybridization problem, including for nonbinary trees, and introduces the concept of temporal distance to measure network proximity.

Findings

Algorithms run efficiently for small hybridization numbers

Implementation demonstrates practical applicability

Experimental results validate theoretical performance

Abstract

We study the problem of finding a temporal hybridization network for a set of phylogenetic trees that minimizes the number of reticulations. First, we introduce an FPT algorithm for this problem on an arbitrary set of $m$ binary trees with $n$ leaves each with a running time of $O(5^k\cdot n\cdot m)$, where $k$ is the minimum temporal hybridization number. We also present the concept of temporal distance, which is a measure for how close a tree-child network is to being temporal. Then we introduce an algorithm for computing a tree-child network with temporal distance at most $d$ and at most $k$ reticulations in $O((8k)^d5^ k\cdot n\cdot m)$ time. Lastly, we introduce a $O(6^kk!\cdot k\cdot n^2)$ time algorithm for computing a minimum temporal hybridization network for a set of two nonbinary trees. We also provide an implementation of all algorithms and an experimental analysis on their performance.