Abstract
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, which are generalisations of phylogenetic trees that can model reticulated evolutionary relationships. 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.
Highlights
Phylogenetic trees and networks are leaf-labelled graphs that are used to visualise and study the evolutionary history of taxa like species, genes, or languages
We 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
We investigated basic properties of spaces of unrooted phylogenetic networks and their metrics under the rearrangement operations NNI, PR, and TBR
Summary
Phylogenetic trees and networks are leaf-labelled graphs that are used to visualise and study the evolutionary history of taxa like species, genes, or languages. Bordewich et al [BLS17] introduced SNPR (subnet prune and regraft), a generalisation of SPR that includes vertical moves, which add or remove an edge They proved connectedness under SNPR for the space of rooted phylogenetic networks and for special classes of phylogenetic networks including tree-based networks. This includes the translation of the results from Bordewich et al [BLS17] and Klawitter and Linz [KL19] on the SNPR-distance of rooted phylogenetic networks to the TBR-distance of unrooted phylogenetic networks. We show that computing the PR-distance is NP-hard
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