Critical threshold for ancestral reconstruction by maximum parsimony on general phylogenies

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 [GS10, ZSYL10]. Our results apply to both deterministic and i.i.d. edge weights. ∗