Impossibility results on stability of phylogenetic consensus methods

TL;DR

This paper demonstrates fundamental incompatibilities between certain stability criteria and basic properties of phylogenetic consensus methods, using theoretical analysis and computational tools.

Contribution

It proves that extension stability and associative stability cannot be simultaneously satisfied with basic regularity properties in phylogenetic consensus methods.

Findings

Incompatibility of extension stability with regularity properties.

Incompatibility of associative stability with regularity properties.

Use of computational tools to establish theoretical results.

Abstract

We answer two questions raised by Bryant, Francis and Steel in their work on consensus methods in phylogenetics. Consensus methods apply to every practical instance where it is desired to aggregate a set of given phylogenetic trees (say, gene evolution trees) into a resulting, "consensus" tree (say, a species tree). Various stability criteria have been explored in this context, seeking to model desirable consistency properties of consensus methods as the experimental data are updated (e.g., more taxa, or more trees, are mapped). However, such stability conditions can be incompatible with some basic regularity properties that are widely accepted to be essential in any meaningful consensus method. Here, we prove that such an incompatibility does arise in the case of extension stability on binary trees and in the case of associative stability. Our methods combine general theoretical considerations with the use of computer programs tailored to the given stability requirements.