# On the accuracy of ancestral sequence reconstruction for ultrametric trees with parsimony

## TL;DR

This paper proves that for ultrametric trees and the Jukes-Cantor model, Fitch's parsimony method using all terminal taxa is at least as accurate as using any subset, confirming a conjecture for four-state data.

## Contribution

It confirms a conjecture that using all terminal taxa with Fitch's method yields optimal accuracy for ancestral sequence reconstruction under the Jukes-Cantor model on ultrametric trees.

## Key findings

- Fitch's method with all taxa is at least as accurate as any subset.
- The conjecture is confirmed for four-state models, relevant to DNA/RNA.
- Results extend previous two-state data findings to more realistic biological models.

## Abstract

We examine a mathematical question concerning the reconstruction accuracy of the Fitch algorithm for reconstructing the ancestral sequence of the most recent common ancestor given a phylogenetic tree and sequence data for all taxa under consideration. In particular, for the symmetric 4-state substitution model which is also known as Jukes-Cantor model, we answer affirmatively a conjecture of Li, Steel and Zhang which states that for any ultrametric phylogenetic tree and a symmetric model, the Fitch parsimony method using all terminal taxa is more accurate, or at least as accurate, for ancestral state reconstruction than using any particular terminal taxon or any particular pair of taxa. This conjecture had so far only been answered for two-state data by Fischer and Thatte. Here, we focus on answering the biologically more relevant case with four states, which corresponds to ancestral sequence reconstruction from DNA or RNA data.