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Systematic Biology 2008 57(4):540-543; doi:10.1080/10635150802203880
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© 2008 Society of Systematic Biologists

Perfectly Misleading Distances from Ternary Characters

Hans-Jürgen Bandelt1 and Mareike Fischer2

1 Department of Mathematics, University of Hamburg Bundesstr. 55, 20146 Hamburg, Germany; E-mail: bandelt{at}math.uni-hamburg.de
2 Biomathematics Research Centre, University of Canterbury Private Bag 4800, Christchurch, New Zealand; E-mail: mfi28{at}student.canterbury.ac.nz

Edited by Paul Lewis


  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).

Keywords: Disconcordant trees; noninformative ternary characters; perfect phylogeny; ultrametric

Received November 7, 2007; Revised January 15, 2008; Accepted April 2, 2008
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