Analyzing the Accuracy of the Fitch Method for Reconstructing Ancestral States on Ultrametric Phylogenies

TL;DR

This paper investigates the accuracy of the Fitch method for ancestral state reconstruction on ultrametric phylogenies, providing recurrence formulas and analyzing convergence and bounds for root state accuracy.

Contribution

It introduces recurrence formulas to assess Fitch method accuracy and analyzes convergence and bounds in ultrametric trees, advancing understanding of ancestral reconstruction reliability.

Findings

Fitch method accuracy converges in complete binary trees as size increases.

A lower bound on root state reconstruction accuracy in ultrametric trees is established.

Recurrence formulas facilitate analysis of ancestral state reconstruction methods.

Abstract

Recurrence formulas are presented for studying the accuracy of the Fitch method for reconstructing the ancestral states in a given phylogenetic tree. As their applications, we analyze the convergence of the accuracy of reconstructing the root state in a complete binary tree of $2^n$ as $n$ goes to infinity and also give a lower bound on the accuracy of reconstructing the root state in an ultrametric tree.