title: Perfectly misleading distances from ternary characters.
abstract: D. Huson and M. Steel showed that for any two binary phylogenetic trees on the same set of n taxa, there exists a sequence of multistate characters that is homoplasy-free only on the first tree but perfectly additive only on the second one. The original construction of such a sequence required n - 1 character states and it remained an open question whether a sequence using fewer character states can always be found. In the present note we will answer this question by showing that three character states suffice to construct such misleading sequences--even if we insist that they conform to an ultrametric (i.e., fit a molecular clock).
authors.affiliation: Department of Mathematics, University of Hamburg, Hamburg, Germany. bandelt@math.uni-hamburg.de
authors.forename: Hans-Jürgen
authors.initials: HJ
authors.lastname: Bandelt
authors.forename: Mareike
authors.initials: M
authors.lastname: Fischer
mesh_terms: D002965:Classification / Q000379:methods*; D003627:Data Interpretation, Statistical; D008957:Models, Genetic; D010802:Phylogeny