Rearrangement operations on unrooted phylogenetic networks

Remie Janssen, Jonathan Klawitter

Research output: Contribution to journalArticleScientificpeer-review

2 Citations (Scopus)
24 Downloads (Pure)


Rearrangement operations transform a phylogenetic tree into another one and hence induce a metric on the space of phylogenetic trees. Popular operations for unrooted phylogenetic trees are NNI (nearest neighbour interchange), SPR (subtree prune and regraft), and TBR (tree bisection and reconnection). Recently, these operations have been extended to unrooted phylogenetic networks-generalisations of phylogenetic trees that can model reticulated evolutionary relationships-where they are called NNI, PR, and TBR moves. Here, we study global and local properties of spaces of phylogenetic networks under these three operations. In particular, we prove connectedness and asymptotic bounds on the diameters of spaces of different classes of phylogenetic networks, including tree-based and level-k networks. We also examine the behaviour of shortest TBR-sequence between two phylogenetic networks in a class, and whether the TBR-distance changes if intermediate networks from other classes are allowed: for example, the space of phylogenetic trees is an isometric subgraph of the space of phylogenetic networks under TBR. Lastly, we show that computing the TBR-distance and the PR-distance of two phylogenetic networks is NP-hard.

Original languageEnglish
Article number060206
Pages (from-to)1-31
Number of pages31
JournalTheory and Applications of Graphs
Issue number2
Publication statusPublished - 15 Dec 2019


  • Phylogenetic network
  • Rearrangement


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