On the number of binary characters needed to recover a phylogeny using maximum parsimony.

We give an explicit construction to solve a conjecture of Mike Steel and David Penny that any phylogeny involving N taxa can be recovered unambiguously using on the order of log N binary characters and the method of maximum parsimony. Biologically, this means that homoplasy need not be a deterrent to parsimony methods. Some patterns of homoplasy are phylogenetically informative and can exponentially reduce the amount of data needed to resolve a phylogeny.