Not all phylogenetic networks are leaf-reconstructible

TL;DR

This paper disproves a conjecture in phylogenetics by providing counterexamples showing that not all unrooted phylogenetic networks with at least four leaves can be uniquely reconstructed from their leaf-deleted subnetworks, even in binary cases.

Contribution

The authors demonstrate that the conjecture claiming all such networks are reconstructible from leaf-deleted subnetworks is false, providing explicit counterexamples for networks with four or more leaves.

Findings

Counterexamples exist for all networks with at least four leaves.

The conjecture fails even for binary phylogenetic networks.

Reconstruction from leaf-deleted subnetworks is not always possible.

Abstract

Unrooted phylogenetic networks are graphs used to represent evolutionary relationships. Accurately reconstructing such networks is of great relevance for evolutionary biology. It has recently been conjectured that all phylogenetic networks with at least five leaves can be uniquely reconstructed from their subnetworks obtained by deleting a single leaf and suppressing degree-2 vertices. Here, we show that this conjecture is false, by presenting a counter example for each possible number of leaves that is at least~4. Moreover, we show that the conjecture is still false when restricted to binary networks.