Consistency of the QNet algorithm for generating planar split graphs from weighted quartets

S Gruenewald, V Moulton, A Spillner

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10 Citations (Scopus)


Phylogenetic networks are a generalization of evolutionary or phylogenetic trees that allow the representation of conflicting signals or alternative evolutionary histories in a single diagram. Recently the Quartet-Net or “QNet” method was introduced, a method for computing a special kind of phylogenetic network called a split network from a collection of weighted quartet trees (i.e. phylogenetic trees with 4 leaves). This can be viewed as a quartet analogue of the distance-based Neighbor-Net (NNet) method for constructing outer-labeled planar split networks. In this paper, we prove that QNet is a consistent method, that is, we prove that if QNet is applied to a collection of weighted quartets arising from a circular split weight function, then it will return precisely this function. This key property of QNet not only ensures that it is guaranteed to produce a tree if the input corresponds to a tree, and an outer-labeled planar split network if the input corresponds to such a network, but also provides the main guiding principle for the design of the method.
Original languageEnglish
Pages (from-to)2325-2334
Number of pages10
JournalDiscrete Applied Mathematics
Issue number10
Publication statusPublished - 28 May 2009

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