Encoding and Constructing 1-Nested Phylogenetic Networks with Trinets

TL;DR

This paper introduces a novel method for encoding and constructing 1-nested phylogenetic networks using trinets, which uniquely determine the network and can be efficiently reconstructed from dense trinet data.

Contribution

It demonstrates that trinets encode 1-nested networks and provides an efficient algorithm for reconstructing such networks from dense trinet sets.

Findings

Trinets uniquely encode 1-nested phylogenetic networks.

An efficient algorithm decides if a dense trinet set can be displayed by a 1-nested network.

The approach opens new directions for constructing and comparing phylogenetic networks.

Abstract

Phylogenetic networks are a generalization of phylogenetic trees that are used in biology to represent reticulate or non-treelike evolution. Recently, several algorithms have been developed which aim to construct phylogenetic networks from biological data using {\em triplets}, i.e. binary phylogenetic trees on 3-element subsets of a given set of species. However, a fundamental problem with this approach is that the triplets displayed by a phylogenetic network do not necessary uniquely determine or {\em encode} the network. Here we propose an alternative approach to encoding and constructing phylogenetic networks, which uses phylogenetic networks on 3-element subsets of a set, or {\em trinets}, rather than triplets. More specifically, we show that for a special, well-studied type of phylogenetic network called a 1-nested network, the trinets displayed by a 1-nested network always encode the network. We also present an efficient algorithm for deciding whether a {\em dense} set of trinets (i.e. one that contains a trinet on every 3-element subset of a set) can be displayed by a 1-nested network or not and, if so, constructs that network. In addition, we discuss some potential new directions that this new approach opens up for constructing and comparing phylogenetic networks.