Maximum Parsimony on Subsets of Taxa

TL;DR

This paper explores the accuracy of Fitch's maximum parsimony algorithm in reconstructing ancestral states, revealing that using subsets of taxa can sometimes improve accuracy and confirming a conjecture under specific models.

Contribution

It demonstrates that applying maximum parsimony to subsets of taxa can outperform using all taxa and proves a conjecture relating single-taxon accuracy to overall reconstruction reliability under a molecular clock.

Findings

Subset analysis can improve ancestral state reconstruction accuracy.

Ignoring closer taxa can sometimes enhance reliability.

Under a molecular clock, single-taxon accuracy bounds overall method performance.

Abstract

In this paper we investigate mathematical questions concerning the reliability (reconstruction accuracy) of Fitch's maximum parsimony algorithm for reconstructing the ancestral state given a phylogenetic tree and a character. In particular, we consider the question whether the maximum parsimony method applied to a subset of taxa can reconstruct the ancestral state of the root more accurately than when applied to all taxa, and we give an example showing that this indeed is possible. A surprising feature of our example is that ignoring a taxon closer to the root improves the reliability of the method. On the other hand, in the case of the two-state symmetric substitution model, we answer affirmatively a conjecture of Li, Steel and Zhang which states that under a molecular clock the probability that the state at a single taxon is a correct guess of the ancestral state is a lower bound on the reconstruction accuracy of Fitch's method applied to all taxa.