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

  • Authors:

  • S. Grünewald;V. Moulton;A. Spillner

  • Affiliations:

  • CAS-MPG Partner Institute for Computational Biology, Shanghai Institutes for Biological Sciences, Chinese Academy of Sciences, 320 Yue Yang Rd, Shanghai 200031, PR China and MPI for Mathematics in ...;School of Computing Sciences, University of East Anglia, Norwich, NR4 7TJ, UK;School of Computing Sciences, University of East Anglia, Norwich, NR4 7TJ, UK

  • Venue:
  • Discrete Applied Mathematics
  • Year:
  • 2009

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Abstract

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.