On the Subnet Prune and Regraft Distance

Abstract

Phylogenetic networks are rooted directed acyclic graphs that represent evolutionary relationships between species whose past includes reticulation events such as hybridisation and horizontal gene transfer. To search the space of phylogenetic networks, the popular tree rearrangement operation rooted subtree prune and regraft (rSPR) was recently generalised to phylogenetic networks. This new operation -called subnet prune and regraft (SNPR) -induces a metric on the space of all phylogenetic networks as well as on several widely-used network classes. In this paper, we investigate several problems that arise in the context of computing the SNPR-distance. For a phylogenetic tree T and a phylogenetic network N , we show how this distance can be computed by considering the set of trees that are embedded in N and then use this result to characterise the SNPR-distance between T and N in terms of agreement forests. Furthermore, we analyse properties of shortest SNPR-sequences between two phylogenetic networks N and N , and answer the question whether or not any of the classes of tree-child, reticulation-visible, or tree-based networks isometrically embeds into the class of all phylogenetic networks under SNPR.

Rearrangement operations on unrooted phylogenetic networks

“…However, for higher tiers, we have not been able to prove that shortest TBR-sequences never traverse higher tiers. To answer this question we may need to utilise agreement graphs such as frequently used for phylogenetic trees [AS01, BS05] and, more recently, also for rooted phylogenetic networks [KL19,Kla19]. Concerning NNI and PR we gave counterexamples to prove that higher tiers are not isometric subgraphs of uN n .…”

“…The following theorem is the unrooted analogous of Theorem 7 by Klawitter and Linz [KL19] and their proof can be applied straightforward by swapping SNPR and rooted networks with TBR and unrooted networks, and by using Lemmas 5.5 and 5.10 and Theorem 6.1.…”

Parameterized Algorithms in Bioinformatics: An Overview

“…Furthermore, all three agreement forest variants are fixed-parameter tractable for the treewidth of the display graph of the input trees [213] (see corresponding results for unrooted TREE CONSISTENCY [149,150]). The rSPR distance has been generalized to a distance measure for phylogenetic networks called SNPR and its computation is fixed-parameter tractable [214] parameterized by the distance. Variations of the discussed distance measures include: (1) the uSPR distance, which does not have an agreement-forest formulation, is NP-hard to decide [215], admits a kernel with 76k 2 taxa [216] (in a preprint, Whidden and Matsen [217] claimed an improvement to 28k taxa), and can be calculated in O * ((28k)!…”

Heading in the right direction? Using head moves to traverse phylogenetic network space

“…For phylogenetic networks, however, not much is known about such distances for a given pair of networks. Recently, Klawitter and Linz (2018) introduced an agreement forest analogue for networks, which bounds such distances but does not give the exact distance.…”

“…Such questions have been answered for other moves (Bordewich et al, 2017) Lastly, in this paper we have studied the problem of computing the head move distance between two networks. For tail moves, rSPR moves (Janssen et al, 2018) and for SNPR moves (Klawitter and Linz, 2018), it was already known that computing the distance between two networks is NP-hard. For the first two of these, we additionally know that computation of distances is hard for each tier.…”