Spaces of phylogenetic networks from generalized nearest-neighbor interchange operations

Huber, Katharina T.; Linz, Simone; Moulton, Vincent; Wu, Taoyang

doi:10.1007/s00285-015-0899-7

Cited by 22 publications

(38 citation statements)

References 35 publications

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“…As such, a phylogenetic reconstruction method often uses nearest neighbor interchanges (NNIs) or other rearrangement operations to search for an optimal tree or network [8,9]. Recently, different variants of NNI have been proposed for RPNs [10,11,12,13,14,15,16].…”

Section: Introductionmentioning

confidence: 99%

Generating normal networks via leaf insertion and nearest neighbor interchange

Zhang

2019

BMC Bioinformatics

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BackgroundGalled trees are studied as a recombination model in theoretical population genetics. This class of phylogenetic networks has been generalized to tree-child networks and other network classes by relaxing a structural condition imposed on galled trees. Although these networks are simple, their topological structures have yet to be fully understood.ResultsIt is well-known that all phylogenetic trees on n taxa can be generated by the insertion of the n-th taxa to each edge of all the phylogenetic trees on n−1 taxa. We prove that all tree-child (resp. normal) networks with k reticulate nodes on n taxa can be uniquely generated via three operations from all the tree-child (resp. normal) networks with k−1 or k reticulate nodes on n−1 taxa. Applying this result to counting rooted phylogenetic networks, we show that there are exactly binary phylogenetic networks with one reticulate node on n taxa.ConclusionsThe work makes two contributions to understand normal networks. One is a generalization of an enumeration procedure for phylogenetic trees into one for normal networks. Another is simple formulas for counting normal networks and phylogenetic networks that have only one reticulate node.

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Section: Introductionmentioning

confidence: 99%

Generating normal networks via leaf insertion and nearest neighbor interchange

Zhang

2019

BMC Bioinformatics

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“…Additionally, for unrooted phylogenetic networks, two operations have recently been developed that generalise the NNI operation from trees to networks (Huber et al, 2016a,b). While the first operation (Huber et al, 2016a) induces a metric on a relatively simple class of phylogenetic networks that do not have any overlapping cycles, the operation presented in (Huber et al, 2016b) draws its inspiration from the cubic graph literature and can be used to transform any unrooted phylogenetic network into any other such network.…”

Section: Introductionmentioning

confidence: 99%

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

Bordewich

Linz

Semple

2017

Journal of Theoretical Biology

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Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. AbstractOver the last fifteen years, phylogenetic networks have become a popular tool to analyse relationships between species whose past includes reticulation events such as hybridisation or horizontal gene transfer. However, the space of phylogenetic networks is significantly larger than that of phylogenetic trees, and how to analyse and search this enlarged space remains a poorly understood problem. Inspired by the widely-used rooted subtree prune and regraft (rSPR) operation on rooted phylogenetic trees, we propose a new operation-called subnet prune and regraft (SNPR)-that induces a metric on the space of all rooted phylogenetic networks on a fixed set of leaves. We show that the spaces of several popular classes of rooted phylogenetic networks (e.g. tree child, reticulation visible, and tree based) are connected under SNPR and that connectedness remains for the subclasses of these networks with a fixed number of reticulations. Lastly, we bound the distance between two rooted phylogenetic networks under the SNPR operation, show that it is computationally hard to compute this distance exactly, and analyse how the SNPR-distance between two such networks relates to the rSPR-distance between rooted phylogenetic trees that are embedded in these networks.

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“…Moreover, they showed that the corresponding diameter of T C n is linear in n. NNI. The Nearest Neighbour Interchange (NNI) operation was defined on (unrooted) phylogenetic trees [20], but has recently been generalised to unrooted and rooted phylogenetic networks by Huber et al [13,14]. We define the NNI operation here only for tree-child networks, because we will only use it as a tool to count special sets of SNPR operations.…”

Section: Suboperationsmentioning

confidence: 99%

The SNPR neighbourhood of tree-child networks

Klawitter¹

2018

JGAA

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Network rearrangement operations like SNPR (SubNet Prune and Regraft), a recent generalisation of rSPR (rooted Subtree Prune and Regraft), induce a metric on phylogenetic networks. To search the space of these networks one important property of these metrics is the sizes of the neighbourhoods, that is, the number of networks reachable by exactly one operation from a given network. In this paper, we present exact expressions for the SNPR neighbourhood of tree-child networks, which depend on both the size and the topology of a network. We furthermore give upper and lower bounds for the minimum and maximum size of such a neighbourhood.

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Spaces of phylogenetic networks from generalized nearest-neighbor interchange operations

Cited by 22 publications

References 35 publications

Generating normal networks via leaf insertion and nearest neighbor interchange

Generating normal networks via leaf insertion and nearest neighbor interchange

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

The SNPR neighbourhood of tree-child networks

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