D together. As a consequence, if the "true tree" is a tree of this type, the more data we collect (i.e. the more characters we study), the more the evidence will support the wrong tree. Of course, except in mathematical simulations, we never know what the "true tree" is. Thus, unless we are able to devise a model that is guaranteed to accurately recover the "true tree," any other optimality criterion or weighting scheme could also, in principle, be statistically inconsistent. The bottom line is, that while statistical inconsistency is an interesting theoretical issue, it is empirically a purely metaphysical concern, outside the realm of empirical testing. Any method could be inconsistent, and there is no way to know for certain whether it is, or not. It is for this reason that many systematists characterize their phylogenetic results as hypotheses of relationship. Another complication with maximum parsimony, and other optimaltiy-criterion based phylogenetic methods, is that finding the shortest tree is an NP-hard problem. The only currently available, efficient way of obtaining a solution, given an arbitrarily large set of taxa, is by using heuristic methods which do not guarantee that the shortest tree will be recovered. These methods employ hill-climbing algorithms to progressively approach the best tree. However, it has been shown that there can be "tree islands" of suboptimal solutions, and the analysis can become trapped in these local optima. Thus, complex, flexible heuristics are required to ensure that tree space has been adequately explored. Several heuristics are available, including nearest neighbor interchange (NNI), tree bisection reconnection (TBR), and the parsimony ratchet. Criticism It has been asserted that a major problem, especially for paleontology, is that maximum parsimony assumes that the only way two species can share the same nucleotide at the same position is if they are genetically related. This asserts that phylogenetic applications of parsimony assume that all similarity is homologous (other interpretations, such as the assertion that two organisms might not be related at all, are nonsensical). This is emphatically not the case: as with any form of character-based phylogeny estimation, parsimony is used to test the homologous nature of similarities by finding the phylogenetic tree which best accounts for all of the similarities. It is often stated that parsimony is not relevant to phylogenetic inference because "evolution is not parsimonious." In most cases, there is no explicit alternative proposed; if no alternative is available, any