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

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.