The current consensus is that chordates are monophyletic, meaning that the Chordata include all and only the descendants of a single common ancestor, which is itself a chordate, and that craniates' nearest relatives are cephalochordates.t has also proved difficult to produce a detailed classification within the living chordates. Attempts to produce evolutionary  family trees  give results that differ from traditional classes because several of those classes are not monophyletic. As a result, vertebrate classification is in a state of flux.