title: Distances that perfectly mislead.
abstract: Given a collection of discrete characters (e.g., aligned DNA sites, gene adjacencies), a common measure of distance between taxa is the proportion of characters for which taxa have different character states. Tree reconstruction based on these (uncorrected) distances can be statistically inconsistent and can lead to trees different from those obtained using character-based methods such as maximum likelihood or maximum parsimony. However, in these cases the distance data often reveal their unreliability by some deviation from additivity, as indicated by conflicting support for more than one tree. We describe two results that show how uncorrected (and miscorrected) distance data can be simultaneously perfectly additive and misleading. First, multistate character data can be perfectly compatible and define one tree, and yet the uncorrected distances derived from these characters are perfectly treelike (and obey a molecular clock), only for a completely different tree. Second, under a Markov model of character evolution a similar phenomenon can occur; not only is there statistical inconsistency using uncorrected distances, but there is no evidence of this inconsistency because the distances look perfectly treelike (this does not occur in the classic two-parameter Felsenstein zone). We characterize precisely when uncorrected distances are additive on the true (and on a false) tree for four taxa. We also extend this result to a more general setting that applies to distances corrected according to an incorrect model.
authors.affiliation: Center for Bioinformatics, Tübingen University, Tuebingen, Germany. huson@informatik.uni-tuebingen.de
authors.forename: Daniel H
authors.initials: DH
authors.lastname: Huson
authors.forename: Mike
authors.initials: M
authors.lastname: Steel
mesh_terms: D002965:Classification / Q000379:methods*; D003627:Data Interpretation, Statistical; D019143:Evolution, Molecular; D008390:Markov Chains; D008957:Models, Genetic; D010802:Phylogeny