Analyzing the Fitch Method for Reconstructing Ancestral States on Ultrametric Phylogenetic Trees

Abstract

The accuracy of the Fitch method for reconstructing ancestral states on ultrametric phylogenetic trees is studied. Two recurrence relations for computing the accuracy are given here. Using these relations, we analyze the convergence of the accuracy of the Fitch method for reconstructing the root state on a complete binary tree of 2 n leaves as n goes to infinity, present a closed-form formula for the accuracy on ultrametric comb trees, and provide a lower bound on the accuracy on arbitrary ultrametric phylogenetic trees. © 2010 Society for Mathematical Biology.