  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.
