Perfectly misleading distances from ternary characters |
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Authors: | Bandelt Hans-Jürgen Fischer Mareike |
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Institution: | Department of Mathematics, University of Hamburg, Hamburg, Germany. bandelt@math.uni-hamburg.de |
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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). |
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