Non-hereditary maximum parsimony trees

TL;DR

This paper examines the hereditary properties of Maximum Parsimony trees in phylogenetics, proving the conjecture for some cases and providing counterexamples, and extends findings to Maximum Likelihood methods under certain models.

Contribution

It proves the conjecture for binary alignments on five taxa, constructs counterexamples, and generalizes results to Maximum Likelihood methods.

Findings

Maximum Parsimony trees are not always hereditary.

Counterexamples show non-hereditary maximum parsimony trees.

Results extend to Maximum Likelihood under specific models.

Abstract

In this paper, we investigate a conjecture by von Haeseler concerning the Maximum Parsimony method for phylogenetic estimation, which was published by the Newton Institute in Cambridge on a list of open phylogenetic problems in 2007. This conjecture deals with the question whether Maximum Parsimony trees are hereditary. The conjecture suggests that a Maximum Parsimony tree for a particular (DNA) alignment necessarily has subtrees of all possible sizes which are most parsimonious for the corresponding subalignments. We answer the conjecture affirmatively for binary alignments on five taxa but also show how to construct examples for which Maximum Parsimony trees are not hereditary. Apart from showing that a most parsimonious tree cannot generally be reduced to a most parsimonious tree on fewer taxa, we also show that compatible most parsimonious quartets do not have to provide a most parsimonious supertree. Last, we show that our results can be generalized to Maximum Likelihood for certain nucleotide substitution models.