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39
Evolutionary Phylogenetic Networks: Models and Issues
"... Abstract Phylogenetic networks are special graphs that generalize phylogenetic trees to allow for modeling of nontreelike evolutionary histories. The ability to sequence multiple genetic markers from a set of organisms and the conflicting evolutionary signals that these markers provide in many case ..."
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Abstract Phylogenetic networks are special graphs that generalize phylogenetic trees to allow for modeling of nontreelike evolutionary histories. The ability to sequence multiple genetic markers from a set of organisms and the conflicting evolutionary signals that these markers provide in many cases, have propelled research and interest in phylogenetic networks to the forefront in computational phylogenetics. Nonetheless, the term ‘phylogenetic network ’ has been generically used to refer to a class of models whose core shared property is tree generalization. Several excellent surveys of the different flavors of phylogenetic networks and methods for their reconstruction have been written recently. However, unlike these surveys, this chapter focuses specifically on one type of phylogenetic networks, namely evolutionary phylogenetic networks, which explicitly model reticulate evolutionary events. Further, this chapter focuses less on surveying existing tools, and addresses in more detail issues that are central to the accurate reconstruction of phylogenetic networks. 1
Properties of normal phylogenetic networks
, 2009
"... Abstract. A phylogenetic network is a rooted acyclic digraph with vertices corresponding to taxa. Let X denote a set of vertices containing the root, the leaves, and all vertices of outdegree 1. Regard X as the set of vertices on which measurements such as DNA can be made. A vertex is called normal ..."
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Abstract. A phylogenetic network is a rooted acyclic digraph with vertices corresponding to taxa. Let X denote a set of vertices containing the root, the leaves, and all vertices of outdegree 1. Regard X as the set of vertices on which measurements such as DNA can be made. A vertex is called normal if it has one parent, and hybrid if it has more than one parent. The network is called normal if it has no redundant arcs and also from every vertex there is a directed path to a member of X such that all vertices after the first are normal. This paper studies properties of normal networks. Under a simple model of inheritance that allows homoplasies only at hybrid vertices, there is essentially unique determination of the genomes at all vertices by the genomes at members of X if and only if the network is normal. This model is a limiting case of more standard models of inheritance when the substitution rate is sufficiently low. Various mathematical properties of normal networks are described. These properties include that the number of vertices grows at most quadratically with the number of leaves and that the number of hybrid vertices grows at most linearly with the number of leaves. Key words: normal network; hybrid; recombination; speciation; genome; ancestral reconstruction. 1
A Metric on the Space of Reduced Phylogenetic Networks
"... Phylogenetic networks are leaflabeled, rooted, acyclic, directed graphs, that are used to model reticulate evolutionary histories. Several measures for quantifying the topological dissimilarity between two phylogenetic networks have been devised, each of which was proven to be a metric on certain r ..."
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Phylogenetic networks are leaflabeled, rooted, acyclic, directed graphs, that are used to model reticulate evolutionary histories. Several measures for quantifying the topological dissimilarity between two phylogenetic networks have been devised, each of which was proven to be a metric on certain restricted classes of phylogenetic networks. A biologicallymotivated class of phylogenetic networks, namely reduced phylogenetic networks, was recently introduced. None of the existing measures is a metric on the space of reduced phylogenetic networks. In this paper, we provide a metric on the space of reduced phylogenetic networks that is computable in time polynomial in the size of the networks.
On Nakhleh's metric for reduced phylogenetic networks
 IEEE/ACM Transactions on Computational Biology and Bioinformatics
, 2009
"... Abstract—We prove that Nakhleh’s metric for reduced phylogenetic networks is also a metric on the classes of treechild phylogenetic networks, semibinary treesibling time consistent phylogenetic networks, and multilabeled phylogenetic trees. We also prove that it separates distinguishable phylogene ..."
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Abstract—We prove that Nakhleh’s metric for reduced phylogenetic networks is also a metric on the classes of treechild phylogenetic networks, semibinary treesibling time consistent phylogenetic networks, and multilabeled phylogenetic trees. We also prove that it separates distinguishable phylogenetic networks. In this way, it becomes the strongest dissimilarity measure for phylogenetic networks available so far. Furthermore, we propose a generalization of that metric that separates arbitrary phylogenetic networks. Index Terms—Biology and genetics, graph algorithms, network problems. Ç 1
A practical algorithm for reconstructing level1 phylogenetic networks
 IEEE/ACM Transactions on Computational Biology and Bioinformatics
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Reconstruction of certain phylogenetic networks from the genomes at their leaves
 Journal of Theoretical Biology
, 2008
"... This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal noncommercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or sel ..."
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Cited by 6 (3 self)
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This article appeared in a journal published by Elsevier. The attached copy is furnished to the author for internal noncommercial research and education use, including for instruction at the authors institution and sharing with colleagues. Other uses, including reproduction and distribution, or selling or licensing copies, or posting to personal, institutional or third party websites are prohibited. In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier’s archiving and manuscript policies are encouraged to visit:
Regular networks are determined by their trees
, 2009
"... Abstract. A rooted acyclic digraph N with labelled leaves displays a tree T when there exists a way to select a unique parent of each hybrid vertex resulting in the tree T. Let Tr(N) denote the set of all trees displayed by the network N. In general, there may be many other networks M such that Tr(M ..."
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Abstract. A rooted acyclic digraph N with labelled leaves displays a tree T when there exists a way to select a unique parent of each hybrid vertex resulting in the tree T. Let Tr(N) denote the set of all trees displayed by the network N. In general, there may be many other networks M such that Tr(M) = Tr(N). A network is regular if it is isomorphic with its cover digraph. This paper shows that if N is regular, there is a procedure to reconstruct N given Tr(N). Hence if N and M are regular networks and Tr(N) = Tr(M), it follows that N = M, proving that a regular network is uniquely determined by its displayed trees. 1
Locating a tree in a phylogenetic network in quadratic time
 In: Przytycka T., editor. Research in Computational Molecular Biology, LectureNotes inComputer Science
, 2015
"... Abstract. A fundamental problem in the study of phylogenetic networks is to determine whether or not a given phylogenetic network contains a given phylogenetic tree. We develop a quadratictime algorithm for this problem for binary nearlystable phylogenetic networks. We also show that the number ..."
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Abstract. A fundamental problem in the study of phylogenetic networks is to determine whether or not a given phylogenetic network contains a given phylogenetic tree. We develop a quadratictime algorithm for this problem for binary nearlystable phylogenetic networks. We also show that the number of reticulations in a reticulation visible or nearly stable phylogenetic network is bounded from above by a function linear in the number of taxa. 1