The SNPR neighbourhood of tree-child networks

Klawitter, Jonathan

doi:10.7155/jgaa.00472

Cited by 6 publications

(6 citation statements)

References 24 publications

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“…In particular, each vertex in a rooted phylogenetic network whose in-degree is at least two represents a reticulation event and is referred to as a reticulation. In comparison to tree space, the space of phylogenetic networks is significantly larger and searching this space remains poorly understood although the above-mentioned rearrangement operations on phylogenetic trees have been generalised to rooted (and unrooted) phylogenetic networks [BLS17, FHMW18, GvIJ + 17, HLMW16, HMW16, JJE + 18, Kla18].…”

Section: Introductionmentioning

confidence: 99%

On the Subnet Prune and Regraft Distance

Klawitter

Linz

2019

Electron. J. Combin.

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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.

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Section: Introductionmentioning

confidence: 99%

On the Subnet Prune and Regraft Distance

Klawitter

Linz

2019

Electron. J. Combin.

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“…The size of the neighbourhood is important for local search heuristics, as it gives the number of networks that need to be considered at each step. For networks, the only rearrangement move neighbourhood that has been studied is that of the SNPR move (Klawitter, 2017).…”

Section: Phylogenetic Network Spacesmentioning

confidence: 99%

“…For a lower bound for the tail move neighbourhood size we turn to Proposition 4.1 from a paper by Klawitter (Klawitter (2017)) about SNPR neighbourhoods. Because SNPR moves are tail moves together with vertical moves, the sizes of SNPR neighbourhoods and tail move neighbourhoods can easily be compared.…”

Section: Diameter Boundsmentioning

confidence: 99%

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

Janssen¹

2018

Preprint

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Head moves are a type of rearrangement moves for phylogenetic networks. They have mostly been studied as part of more encompassing types of moves, such as rSPR moves. Here, we study head moves as a type of moves on themselves. We show that the tiers (k > 0) of phylogenetic network space are connected by local head moves. Then we show tail moves and head moves are closely related: sequences of tail moves can be converted to sequences of head moves and vice versa, changing the length by at most a constant factor. Because the tiers of network space are connected by rSPR moves, this gives a second proof of the connectivity of these tiers. Furthermore, we show that these tiers have small diameter by reproving the connectivity a third time. As the head move neighbourhood is in general small, this makes head moves a good candidate for local search heuristics. Finally we prove that finding the shortest sequence of head moves between two networks is NP-hard.

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“…In other words, can every phylogenetic network of a space of networks (e.g., all semi-directed phylogenetic networks on a fixed leaf set) be reached from any other phylogenetic network in the space by applying a sequence of these rearrangement operations such that the resulting network after each operation is also in the space? This question has been analyzed for various spaces of unrooted and rooted phylogenetic trees (e.g., [1,6,14]), unrooted phylogenetic networks (e.g., [16,17,10,21]) and rooted phylogenetic networks (e.g., [7,9,11,20,22,23]), and several rearrangement moves to traverse these spaces have been introduced. However, these results do not immediately carry over to spaces of semi-directed phylogenetic networks.…”

Section: Introductionmentioning

confidence: 99%

Exploring spaces of semi-directed phylogenetic networks

Linz¹,

Wicke²

2023

Preprint

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Semi-directed phylogenetic networks have recently emerged as a class of phylogenetic networks sitting between rooted (directed) and unrooted (undirected) phylogenetic networks as they contain both directed as well as undirected edges. While the spaces of rooted phylogenetic networks and unrooted phylogenetic networks have been analyzed in recent years and various rearrangement moves to traverse these spaces have been introduced, the results do not immediately carry over to semi-directed phylogenetic networks. Here, we propose a simple rearrangement move for semi-directed phylogenetic networks, called cut edge transfer (CET), and show that the space of semi-directed level-1 networks with precisely k reticulations is connected under CET. This level-1 space is currently the predominantly used search space for most algorithms that reconstruct semi-directed phylogenetic networks. Hence, every semi-directed level-1 network with a fixed number of reticulations and leaf set can be reached from any other such network by a sequence of CETs. By introducing two additional moves, CET + and CET − , that allow for the addition or deletion of reticulations, we then establish connectedness for the space of all semi-directed phylogenetic networks on a fixed leaf set. As a byproduct of our results for semi-directed phylogenetic networks, we also show that the space of rooted level-1 networks with a fixed number of reticulations and leaf set is connected under CET, when translated into the rooted setting.

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The SNPR neighbourhood of tree-child networks

Cited by 6 publications

References 24 publications

On the Subnet Prune and Regraft Distance

On the Subnet Prune and Regraft Distance

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

Exploring spaces of semi-directed phylogenetic networks

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