Journal of Mathematical Biology

, Volume 72, Issue 3, pp 699–725 | Cite as

Spaces of phylogenetic networks from generalized nearest-neighbor interchange operations

  • Katharina T. Huber
  • Simone Linz
  • Vincent Moulton
  • Taoyang Wu


Phylogenetic networks are a generalization of evolutionary or phylogenetic trees that are used to represent the evolution of species which have undergone reticulate evolution. In this paper we consider spaces of such networks defined by some novel local operations that we introduce for converting one phylogenetic network into another. These operations are modeled on the well-studied nearest-neighbor interchange operations on phylogenetic trees, and lead to natural generalizations of the tree spaces that have been previously associated to such operations. We present several results on spaces of some relatively simple networks, called level-1 networks, including the size of the neighborhood of a fixed network, and bounds on the diameter of the metric defined by taking the smallest number of operations required to convert one network into another. We expect that our results will be useful in the development of methods for systematically searching for optimal phylogenetic networks using, for example, likelihood and Bayesian approaches.


Phylogenetic networks Spaces of phylogenetic trees Phylogenetic tree metrics Nearest-neighbor interchange (NNI) 

Mathematics Subject Classification

05C90 92D15 



The authors thank the organizers of the workshop “Utilizing Genealogical Phylogenetic Networks in Evolutionary Biology: Touching the Data” at the Lorentz Center (the Netherlands) where the ideas for this paper were first discussed. We also thank the anonymous referee for very careful reading and helpful suggestions on the first version of this manuscript.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Katharina T. Huber
    • 1
  • Simone Linz
    • 2
  • Vincent Moulton
    • 1
  • Taoyang Wu
    • 1
  1. 1.School of Computing SciencesUniversity of East AngliaNorwichUK
  2. 2.Department of Computer ScienceUniversity of AucklandAucklandNew Zealand

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