The Structure of Level-k Phylogenetic Networks

Gambette, Philippe; Berry, Vincent; Paul, Christophe

doi:10.1007/978-3-642-02441-2_26

Cited by 22 publications

(37 citation statements)

References 33 publications

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“…We begin by showing that trinets can be used to recover this decomposition of binary phylogenetic networks. Note that similar results have been proven for triplets in [19] and for quartets in unrooted phylogenetics networks [11]. Theorem 1.…”

Section: Decomposition Theorems For Trinetssupporting

confidence: 68%

“…However, a new technique would have to be developed for k ≥ 4 since, for such k, there exist level-k networks that have no crucial trinets. Another difficulty is that the number of generators for level-k networks grows very rapidly (the number of level-k generators is at least 2 k−1 [11]) making a similar case analysis impossible in general. To prove that tree-child networks are encoded by trinets, we heavily depended on special properties of such networks, and we have not been able to find a way to extend our proof to even slightly more general networks (e.g.…”

Section: Discussionmentioning

confidence: 99%

“…Such a network is called binary if all vertices have indegree and outdegree at most two and all vertices with indegree two have outdegree one. In addition, a binary network is called level -k [11,12,13,14,18,19] if each biconnected component has at most k indegree-2 vertices, and it is called tree-child [6,8,21,29] if each non-leaf vertex has at least one child which has indegree 1. Note that a rooted phylogenetic tree is a network, but that networks are more general since they can represent evolutionary events where species combine rather than speciate.…”

Section: Introductionmentioning

confidence: 99%

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Trinets encode tree-child and level-2 phylogenetic networks

Iersel

Moulton

2013

J. Math. Biol.

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Abstract. Phylogenetic networks generalize evolutionary trees, and are commonly used to represent evolutionary histories of species that undergo reticulate evolutionary processes such as hybridization, recombination and lateral gene transfer. Recently, there has been great interest in trying to develop methods to construct rooted phylogenetic networks from triplets, that is rooted trees on three species. However, although triplets determine or encode rooted phylogenetic trees, they do not in general encode rooted phylogenetic networks, which is a potential issue for any such method. Motivated by this fact, Huber and Moulton recently introduced trinets as a natural extension of rooted triplets to networks. In particular, they showed that level-1 phylogenetic networks are encoded by their trinets, and also conjectured that all "recoverable" rooted phylogenetic networks are encoded by their trinets. Here we prove that recoverable binary level-2 networks and binary tree-child networks are also encoded by their trinets. To do this we prove two decomposition theorems based on trinets which hold for all recoverable binary rooted phylogenetic networks. Our results provide some additional evidence in support of the conjecture that trinets encode all recoverable rooted phylogenetic networks, and could also lead to new approaches to construct phylogenetic networks from trinets.

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Section: Decomposition Theorems For Trinetssupporting

confidence: 68%

Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Trinets encode tree-child and level-2 phylogenetic networks

Iersel

Moulton

2013

J. Math. Biol.

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“…However, N is a less parsimonious representation of those 4 systems which cannot be encoded by any of the 4 systems of interest in this paper, we follow van Iersel et al (2009b) and require that every block in a level-1 network which is not a cut-arc contains at least 4 vertices. For k = 1, 2, it was shown in van Iersel et al (2009a) (see also Jansson and Sung 2006 for the case k = 1) that level-k networks can be built up by chaining together structurally very simple level-k networks called simple level-k networks (see also Gambette et al 2009 for more on this). More precisely, a level-k network N , k ≥ 0, is called simple if every cut-arc of N is a trivial cut-arc.…”

Section: Basic Terminology and Results Concerning Level-1 Networkmentioning

confidence: 97%

On encodings of phylogenetic networks of bounded level

Gambette

Huber

2011

J. Math. Biol.

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Phylogenetic networks have now joined phylogenetic trees in the center of phylogenetics research. Like phylogenetic trees, such networks canonically induce collections of phylogenetic trees, clusters, and triplets, respectively. Thus it is not surprising that many network approaches aim to reconstruct a phylogenetic network from such collections. Related to the well-studied perfect phylogeny problem, the following question is of fundamental importance in this context: When does one of the above collections encode (i.e. uniquely describe) the network that induces it? For the large class of level-1 (phylogenetic) networks we characterize those level-1 networks for which an encoding in terms of one (or equivalently all) of the above collections exists. In addition, we show that three known distance measures for comparing phylogenetic networks are in fact metrics on the resulting subclass and give the diameter for two of them. Finally, we investigate the related concept of indistinguishability and also show that many properties enjoyed by level-1 networks are not satisfied by networks of higher level.

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“…The LST operations that we define generalize and extend the nearest-neighbor interchange (NNI) operations on phylogenetic trees (Robinson, 1971;Moore et al, 1973), whose properties are well-studied and which are commonly used in computer programs that search for optimal trees in tree space (Swofford et al, 1996). We will mainly concentrate on properties of LST operations when they are applied to unrooted and rooted level-1 networks (Jansson et al, 2006;Gambette et al, 2009), a well understood class of phylogenetic networks that are almost tree-like, and which have been used to, for example, represent the evolution of viruses (Huber et al, 2011).…”

Section: Introductionmentioning

confidence: 99%

Spaces of phylogenetic networks from generalized nearest-neighbor interchange operations

et al. 2015

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Phylogenetic networks are a generalization of evolutionary or phylogenetic trees that are used to represent the evolution of species which have undergone reticulate evolution. In this paper we consider spaces of such networks defined by some novel local operations that we introduce for converting one phylogenetic network into another. These operations are modeled on the well-studied nearest-neighbor interchange (NNI) operations on phylogenetic trees, and lead to natural generalizations of the tree spaces that have been previously associated to such operations. We present several results on spaces of some relatively simple networks, called level-1 networks, including the size of the neighborhood of a fixed network, and bounds on the diameter of the metric defined by taking the smallest number of operations required to convert one network into another. We expect that our results will be useful in the development of methods for systematically searching for optimal phylogenetic networks using, for example, likelihood and Bayesian approaches.

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The Structure of Level-k Phylogenetic Networks

Cited by 22 publications

References 33 publications

Trinets encode tree-child and level-2 phylogenetic networks

Trinets encode tree-child and level-2 phylogenetic networks

On encodings of phylogenetic networks of bounded level

Spaces of phylogenetic networks from generalized nearest-neighbor interchange operations

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