  We consider the problem of inferring an ancestral state from observations at
the leaves of a tree, assuming the state evolves along the tree according to a
two-state symmetric Markov process. We establish a general branching rate
condition under which maximum parsimony, a common reconstruction method
requiring only the knowledge of the tree, succeeds better than random guessing
uniformly in the depth of the tree. We thereby generalize previous results of
(Zhang et al., 2010) and (Gascuel and Steel, 2010). Our results apply to both
deterministic and i.i.d. edge weights.
