Phylogenetic consensus networks: Computing a consensus of 1-nested phylogenetic networks

TL;DR

This paper introduces an efficient algorithm to compute a consensus of 1-nested phylogenetic networks, extending traditional consensus trees to more complex evolutionary models involving species crossing.

Contribution

It presents a novel method for computing consensus networks of 1-nested phylogenetic networks using an encoding approach, with proven polynomial-time complexity.

Findings

Algorithm computes consensus in O(t|X|^2+|X|^3) time.

Extends consensus methods from trees to 1-nested networks.

Recovers the majority rule consensus tree when applied to phylogenetic trees.

Abstract

An important and well-studied problem in phylogenetics is to compute a \emph{consensus tree} so as to summarize the common features within a collection of rooted phylogenetic trees, all whose leaf-sets are bijectively labeled by the same set~(X) of species. More recently, however, it has become of interest to find a consensus for a collection of more general, rooted directed acyclic graphs all of whose sink-sets are bijectively labeled by~(X), so called rooted \emph{phylogenetic networks}. These networks are used to analyse the evolution of species that cross with one another, such as plants and viruses. In this paper, we introduce an algorithm for computing a consensus for a collection of so-called 1-\emph{nested} phylogenetic networks. Our approach builds on a previous result by Rosell\'o et al. that describes an encoding for any 1-nested phylogenetic network in terms of a collection of ordered pairs of subsets of (X).More specifically, we characterize those collections of ordered pairs that arise as the encoding of some 1-nested phylogenetic network, and then use this characterization to compute a \emph{consensus network} for a collection of~$t$ 1-nested networks in $O(t|X|^2+|X|^3)$ time. Applying our algorithm to a collection of phylogenetic trees yields the well-known majority rule consensus tree. Our approach leads to several new directions for futurework, and we expect that it should provide a useful new tool to help understand complex evolutionary scenarios.