Identifiability of Level-1 Species Networks from Gene Tree Quartets

TL;DR

This paper investigates the ability to identify features of level-1 species networks from gene tree quartets under the network multispecies coalescent model, revealing limitations in identifiability related to 3-cycles.

Contribution

It provides new theoretical results on which aspects of level-1 networks can be uniquely identified from quartet concordance factors, especially highlighting issues with 3-cycle features.

Findings

Identifiability of certain network features is possible under the model.

3-cycles in networks pose challenges for identifiability.

Some topological and numerical parameters are not identifiable due to network structure.

Abstract

When hybridization or other forms of lateral gene transfer have occurred, evolutionary relationships of species are better represented by phylogenetic networks than by trees. While inference of such networks remains challenging, several recently proposed methods are based on quartet concordance factors -- the probabilities that a tree relating a gene sampled from the species displays the possible 4-taxon relationships. Building on earlier results, we investigate what level-1 network features are identifiable from concordance factors under the network multispecies coalescent model. We obtain results on both topological features of the network, and numerical parameters, uncovering a number of failures of identifiability related to 3-cycles in the network.