Orchard Networks are Trees with Additional Horizontal Arcs
Leo van Iersel (TU Delft - Electrical Engineering, Mathematics and Computer Science)
Remie Janssen (TU Delft - Electrical Engineering, Mathematics and Computer Science)
Mark Jones (TU Delft - Electrical Engineering, Mathematics and Computer Science)
Yukihiro Murakami (TU Delft - Electrical Engineering, Mathematics and Computer Science)
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Abstract
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)).
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