Orchard Networks are Trees with Additional Horizontal Arcs

Abstract

AbstractPhylogenetic 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 additionalhorizontalarcs. 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 nleaves with kreticulations is connected under the rNNI rearrangement move with diameter$$O(kn+n\log (n))$$O(kn+nlog(n)).