The Tree of Blobs of a Species Network: Identifiability under the Coalescent

TL;DR

This paper introduces a theoretical framework for identifying the tree of blobs in species networks using gene quartet data, advancing the understanding of species network inference under the coalescent model.

Contribution

It establishes an identifiability theorem for the tree of blobs, linking network features to gene quartet distributions, and proposes a basis for a practical inference algorithm.

Findings

Most features of the unrooted tree of blobs are identifiable from gene quartet topologies.

A new combinatorial inference rule is developed for the model.

Theoretical results suggest a practical inference algorithm.

Abstract

Inference of species networks from genomic data under the Network Multispecies Coalescent Model is currently severely limited by heavy computational demands. It also remains unclear how complicated networks can be for consistent inference to be possible. As a step toward inferring a general species network, this work considers its tree of blobs, in which non-cut edges are contracted to nodes, so only tree-like relationships between the taxa are shown. An identifiability theorem, that most features of the unrooted tree of blobs can be determined from the distribution of gene quartet topologies, is established. This depends upon an analysis of gene quartet concordance factors under the model, together with a new combinatorial inference rule. The arguments for this theoretical result suggest a practical algorithm for tree of blobs inference, to be fully developed in a subsequent work.