  In this paper we investigate mathematical questions concerning the
reliability (reconstruction accuracy) of Fitch's maximum parsimony algorithm
for reconstructing the ancestral state given a phylogenetic tree and a
character. In particular, we consider the question whether the maximum
parsimony method applied to a subset of taxa can reconstruct the ancestral
state of the root more accurately than when applied to all taxa, and we give an
example showing that this indeed is possible. A surprising feature of our
example is that ignoring a taxon closer to the root improves the reliability of
the method. On the other hand, in the case of the two-state symmetric
substitution model, we answer affirmatively a conjecture of Li, Steel and Zhang
which states that under a molecular clock the probability that the state at a
single taxon is a correct guess of the ancestral state is a lower bound on the
reconstruction accuracy of Fitch's method applied to all taxa.
