Orchard Networks are Trees with Additional Horizontal Arcs

Leo van Iersel, Remie Janssen, Mark Jones, Yukihiro Murakami*

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

6 Citations (Scopus)
38 Downloads (Pure)


Phylogenetic networks are used in biology to represent evolutionary histories. The class of orchard phylogenetic networks was recently introduced for their computational benefits, without any biological justification. Here, we show that orchard networks can be interpreted as trees with additional horizontal arcs. Therefore, they are closely related to tree-based networks, where the difference is that in tree-based networks the additional arcs do not need to be horizontal. Then, we use this new characterization to show that the space of orchard networks on n leaves with k reticulations is connected under the rNNI rearrangement move with diameter O(kn+ nlog (n)).

Original languageEnglish
Article number76
Number of pages21
JournalBulletin of Mathematical Biology
Issue number8
Publication statusPublished - 2022


  • Connectedness
  • Orchard networks
  • Phylogenetic networks
  • Rearrangement moves


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