A Practical Fixed-Parameter Algorithm for Constructing Tree-Child Networks from Multiple Binary Trees

Abstract

We present the first fixed-parameter algorithm for constructing a tree-child phylogenetic network that displays an arbitrary number of binary input trees and has the minimum number of reticulations among all such networks. The algorithm uses the recently introduced framework of cherry picking sequences and runs in O((8k) k poly(n, t)) time, where n is the number of leaves of every tree, t is the number of trees, and k is the reticulation number of the constructed network. Moreover, we provide an efficient parallel implementation of the algorithm and show that it can deal with up to 100 input trees on a standard desktop computer, thereby providing a major improvement over previous phylogenetic network construction methods.

A fast and scalable method for inferring phylogenetic networks from trees by aligning lineage taxon strings

“…We compared ALTS with two heuristic network inference programs: PRINs ( Mirzaei and Wu 2015 ), which infers an arbitrary phylogenetic network, and van Iersel et al’s method ( van Iersel et al 2022 ), which infers a tree–child network. We first ran the three methods on 50 sets of trees on 20 and 30 taxa, each containing 10 trees.…”

“…Here, we focus on computing phylogenetic networks that display a given set of gene trees ( Wu 2010 ; Albrecht et al 2012 ; Whidden et al 2013 ; Elworth et al 2019 ; van Iersel et al 2022 ). In this approach, trees are first inferred from biomolecular sequences and then used to reconstruct a phylogenetic network with the smallest hybridization number (HN) that displays all the trees (see Elworth et al 2019 ), where the HN is defined as the sum over all the reticulate nodes of the indegree of each reticulate node minus 1.…”

Can Multiple Phylogenetic Trees Be Displayed in a Tree-Child Network Simultaneously?

“…The proof of Theorem 4.1 can be generalized to prove the existence of a tree-child network that co-display multiple trees in which each reticulate node is of indegree 2 or more. The minimum reticulate number of the tree-child networks that co-display a set of multiple trees is called their tree-child hybridization number [24].…”

“…Another interesting algorithmic question is developing fast approaches for constructing parsimonious non-binary tree-child networks for co-displaying a given set of trees. For this problem, we are only aware of one existing approach [24], which appears to be slow for large data.…”

“…In addition, the problem of determining whether or not a tree is displayed in a phylogenetic network is NP-complete [18] in general but becomes linear time solvable for tree-child networks [12,25] and so is whether or not a phylogenetic network is displayed in another [17]. A parametric algorithm has also been developed for determining whether a set of multiple trees can be display in a tree-child network simultaneously [24]. As an exponential-time algorithm, it may become slow for large data.…”