Can we 'future-proof' consensus trees?

TL;DR

This paper investigates whether consensus methods in phylogenetics can be designed to be 'future-proof', ensuring consistent results when new data or trees are added, and finds that such methods are generally impossible.

Contribution

The paper formalizes the concept of 'future-proof' consensus methods in phylogenetics and proves a no-go theorem showing their non-existence in general, with some specific exceptions.

Findings

Some consensus methods are 'future-proof' for specific input types.

A general 'future-proof' consensus method does not exist.

Adding trees rather than taxa yields mixed results.

Abstract

Consensus methods are widely used for combining phylogenetic trees into a single estimate of the evolutionary tree for a group of species. As more taxa are added, the new source trees may begin to tell a different evolutionary story when restricted to the original set of taxa. However, if the new trees, restricted to the original set of taxa, were to agree exactly with the earlier trees, then we might hope that their consensus would either agree with or resolve the original consensus tree. In this paper, we ask under what conditions consensus methods exist that are 'future proof' in this sense. While we show that some methods (e.g. Adams consensus) have this property for specific types of input, we also establish a rather surprising `no-go' theorem: there is no 'reasonable' consensus method that satisfies the future-proofing property in general. We then investigate a second notion of 'future proofing' for consensus methods, in which trees (rather than taxa) are added, and establish some positive and negative results. We end with some questions for future work.