Journal of Classification

, Volume 36, Issue 2, pp 200–231 | Cite as

Hierarchies from Lowest Stable Ancestors in Nonbinary Phylogenetic Networks

  • Katharina T. Huber
  • Vincent Moulton
  • Taoyang WuEmail author
Open Access


The reconstruction of the evolutionary history of a set of species is an important problem in classification and phylogenetics. Phylogenetic networks are a generalization of evolutionary trees that are used to represent histories for species that have undergone reticulate evolution, an important evolutionary force for many organisms (e.g. plants or viruses). In this paper, we present a novel approach to understanding the structure of networks that are not necessarily binary. More specifically, we define the concept of a closed set and show that the collection of closed sets of a network forms a hierarchy, and that this hierarchy can be deduced from either the subtrees or subnetworks on all 3-subsets. This allows us to also show that closed sets generalize the concept of the SN-sets of a binary network, sets which have proven very useful in elucidating the structure of binary networks. We also characterize the minimal closed sets (under set inclusion) for a special class of networks (2-terminal networks). Taken together, we anticipate that our results should be useful for the development of new phylogenetic network reconstruction algorithms.


Phylogenetic network Hierarchy Lower Stable Ancestor Nonbinary network 


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© The Author(s) 2018

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  • Katharina T. Huber
    • 1
  • Vincent Moulton
    • 1
  • Taoyang Wu
    • 1
    Email author
  1. 1.School of Computing SciencesUniversity of East AngliaNorwichUK

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