Species Trees Forcing Parsimony to Fail

Abstract

To the known fact that Parsimony method sometimes fails on the problem of inferring species trees from gene trees, here we proved that no mater of what topology the true 9-taxon and greater species tree is the only thing one needs to break down Parsimony is to have in this species tree three consecutive inner edges not going through the root but perhaps ending on it with lengths T1, T2, T3 of some proportions. Obviously, the probability to meet these lengths is growing in general with the size of species tree. Therefore, Parsimony may be applied only when the described lengths of edges cannot be met in the tree.