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Phylogenetic Diversity Over an Abelian Group
Andreas Dress1 and Mike Steel2
1Department for Combinatorics and Geometry, CAS-MPG Partner Institute for Computational Biology, Shanghai Institutes for Biological Sciences, Chinese Academy of Sciences, Shanghai 200031, P.R. China
dress@mis.mpg.de
2Allan Wilson Centre for Molecular Ecology and Evolution, University of Canterbury, Christchurch, New Zealand
m.steel@math.canterbury.ac.nz
Annals of Combinatorics 11 (2) p.143-160 June, 2007
AMS Subject Classification: 05C05, 92D15
Abstract:
There is a natural way to associate to any tree T with leaf set X, and with edges weighted by elements from an abelian group G, a map from the power set of X into G―simply add the elements on the edges that connect the leaves in that subset. This map has been wellstudied in the case where G has no elements of order 2 (particularly when G is the additive group of real numbers) and, for this setting, subsets of leaves of size two play a crucial role. However, the existence and uniqueness results in that setting do not extend to arbitrary abelian groups. We study this more general problem here, and by working instead with both, pairs and triples of leaves, we obtain analogous existence and uniqueness results. Some particular results for elementary abelian 2-groups are also described.
Keywords: X-trees, split systems, abelian groups, group-valued distances, phylogenetic diversity

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