Uprooted phylogenetic networks

Philippe Gambette, Katharina T. Huber (Lead Author), Guillaume E. Scholz

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)
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The need for structures capable of accommodating complex evolutionary signals such as those found in, for example, wheat has fueled research into phylogenetic networks. Such structures generalize the standard model of a phylogenetic tree by also allowing for cycles and have been introduced in rooted and unrooted form. In contrast to phylogenetic trees or their unrooted versions, rooted phylogenetic networks are notoriously difficult to understand. To help alleviate this, recent work on them has also centered on their “uprooted” versions. By focusing on such graphs and the combinatorial concept of a split system which underpins an unrooted phylogenetic network, we show that not only can a so-called (uprooted) 1-nested network N be obtained from the Buneman graph (sometimes also called a median network) associated with the split system  Σ(N)Σ(N)  induced on the set of leaves of N but also that that graph is, in a well-defined sense, optimal. Along the way, we establish the 1-nested analogue of the fundamental “splits equivalence theorem” for phylogenetic trees and characterize maximal circular split systems.
Original languageEnglish
Pages (from-to)2022–2048
Number of pages27
JournalBulletin of Mathematical Biology
Issue number9
Early online date31 Jul 2017
Publication statusPublished - Sep 2017


  • phylogenetic network
  • Buneman graph
  • circular split system
  • closure
  • median network
  • PC-trees

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