Lost in space? Generalising subtree prune and regraft to spaces of phylogenetic networks

Bordewich, Magnus; Linz, Simone; Semple, Charles

doi:10.1016/j.jtbi.2017.03.032

Cited by 30 publications

(71 citation statements)

References 29 publications

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“…Additionally, a desirable feature can be to restrict the search space to only tree-child networks. As shown in [8] the SNPR operation guarantees connectedness of networks within layers under this restriction.…”

Section: Methods Summarymentioning

confidence: 99%

“…Our local search method is based on the SNPR edit operation introduced by Bordewich et al [8]. SNPR is an extension of the classical subtree prune and regraft (SPR) edit operation on trees.…”

Section: Exploring the Snpr-neighborhoodmentioning

confidence: 99%

“…Recently Bordewich et al [8] addressed this issue by introducing an edit operation on networks, subnet prune and regraft (SNPR), that generalizes the classical rSPR edit operation defined on trees. Further, Bordewich et al proved that the general space of networks is connected under this operation and that layers of networks with a fixed number of reticulations are connected under SNPR when restricting the networks to several well-studied subclasses; i.e., tree-based, reticulation-visible, and tree-child networks.…”

Section: Introductionmentioning

confidence: 99%

“…These lineages are generally the major detectable genetic clades of endemically circulating viruses, and routine surveillance such as that conducted by the USDA Influenza A Virus in Swine Surveillance system can be expected to sample both the putative parental strains and the child strains [52,3]. Moreover, as shown by Bordewich et al [8] the second mode guarantees connectedness of layers of candidate networks under SNPR. We call our proposed method for inference of hybridization and reassortment networks RF-Net.…”

Section: Introductionmentioning

confidence: 99%

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Robinson-Foulds Reticulation Networks

Markin

Anderson

Vadali

et al. 2019

Preprint

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Phylogenetic (hybridization) networks allow investigation of evolutionary species histories that involve complex phylogenetic events other than speciation, such as reassortment in virus evolution or introgressive hybridization in invertebrates and mammals. Reticulation networks can be inferred by solving the reticulation network problem, typically known as the hybridization network problem. Given a collection of phylogenetic input trees, this problem seeks a minimum reticulation network with the smallest number of reticulation vertices into which the input trees can be embedded exactly. Unfortunately, this problem is limited in practice, since minimum reticulation networks can be easily obfuscated by even small topological errors that typically occur in input trees inferred from biological data. We adapt the reticulation network problem to address erroneous input trees using the classic Robinson-Foulds distance. The RF embedding cost allows trees to be embedded into reticulation networks inexactly, but up to a measurable error. The adapted problem, called the Robinson-Foulds reticulation network (RF-Network) problem is, as we show and like many other problems applied in molecular biology, NP-hard. To address this, we employ local search strategies that have been successfully applied in other NP-hard phylogenetic problems. Our local search method benefits from recent theoretical advancements in this area. Further, we introduce inpractice effective algorithms for the computational challenges involved in our local search approach. Using simulations we experimentally validate the ability of our method, RF-Net, to reconstruct correct phylogenetic networks in the presence of error in input data. Finally, we demonstrate how RF-networks can help identify reassortment in influenza A viruses, and provide insight into the evolutionary history of these viruses. RF-Net was able to estimate a large and credible reassortment network with 164 taxa.

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Section: Methods Summarymentioning

confidence: 99%

Section: Exploring the Snpr-neighborhoodmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Robinson-Foulds Reticulation Networks

Markin

Anderson

Vadali

et al. 2019

Preprint

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“…Roughly speaking, these are networks that have a spanning tree that is the subdivision of a phylogenetic tree on the same taxa [FS15,FHM18]. Furthermore, Bordewich et al [BLS17] gave several bounds on the SNPR-distance of two phylogenetic networks. Further bounds and a characterisation of the SNPR-distance of a tree and a network were recently proven by Klawitter and Linz [KL19].…”

Section: Introductionmentioning

confidence: 99%

Rearrangement operations on unrooted phylogenetic networks

Janssen¹,

Klawitter²

2019

tag

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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.

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The Space of Equidistant Phylogenetic Cactuses

Huber¹,

Moulton²,

Owen³

et al. 2023

Ann. Comb.

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An equidistantX-cactus is a type of rooted, arc-weighted, directed acyclic graph with leaf set X, that is used in biology to represent the evolutionary history of a set $$X$$ X of species. In this paper, we introduce and investigate the space of equidistant X-cactuses. This space contains, as a subset, the space of ultrametric trees on X that was introduced by Gavryushkin and Drummond. We show that equidistant-cactus space is a CAT(0)-metric space which implies, for example, that there are unique geodesic paths between points. As a key step to proving this, we present a combinatorial result concerning ranked rooted X-cactuses. In particular, we show that such graphs can be encoded in terms of a pairwise compatibility condition arising from a poset of collections of pairs of subsets of $$X$$ X that satisfy certain set-theoretic properties. As a corollary, we also obtain an encoding of ranked, rooted X-trees in terms of partitions of X, which provides an alternative proof that the space of ultrametric trees on X is CAT(0). We expect that our results will provide the basis for novel ways to perform statistical analyses on collections of equidistant X-cactuses, as well as new directions for defining and understanding spaces of more general, arc-weighted phylogenetic networks.

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Lost in space? Generalising subtree prune and regraft to spaces of phylogenetic networks

Cited by 30 publications

References 29 publications

Robinson-Foulds Reticulation Networks

Robinson-Foulds Reticulation Networks

Rearrangement operations on unrooted phylogenetic networks

The Space of Equidistant Phylogenetic Cactuses

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