Defining binary phylogenetic trees using parsimony

TL;DR

This paper proves that for large enough leaf counts, phylogenetic trees are uniquely determined by characters with a fixed parsimony score, supporting the validity of maximum parsimony in evolutionary tree reconstruction when changes are few.

Contribution

It establishes that each phylogenetic tree with sufficiently many leaves is uniquely identified by characters with a specific parsimony score, advancing understanding of maximum parsimony's effectiveness.

Findings

Phylogenetic trees are uniquely defined by character sets with fixed parsimony scores.

The result holds for trees with at least 20 times the fixed score in leaves.

Supports the use of maximum parsimony when data changes are rare.

Abstract

Phylogenetic (i.e. leaf-labeled) trees play a fundamental role in evolutionary research. A typical problem is to reconstruct such trees from data like DNA alignments (whose columns are often referred to as characters), and a simple optimization criterion for such reconstructions is maximum parsimony. It is generally assumed that this criterion works well for data in which state changes are rare. In the present manuscript, we prove that each phylogenetic tree $T$ with $n\geq 20 k$ leaves is uniquely defined by the set $A_k(T)$, which consists of all characters with parsimony score $k$ on $T$. This can be considered as a promising first step towards showing that maximum parsimony as a tree reconstruction criterion is justified when the number of changes in the data is relatively small.