Sufficient condition for root reconstruction by parsimony on binary trees with general weights

We consider the problem of inferring an ancestral state from observations at leaves a tree, assuming evolves along tree according to two-state symmetric Markov process. establish general branching rate condition under which maximum parsimony, common reconstruction method requiring only knowledge topology (but not substitution rates or other parameters), succeeds better than random guessing uniformly in depth tree. thereby generalize previous results [13, 37]. Our apply both deterministic and i.i.d. edge weights.