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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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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
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"... Restrictions on meaningful phylogenetic networks Abstract: It is common to assume that a phylogenetic network is a rooted acyclic digraph. Let X denote the set of leaves. The author argues that, if the network is to be uniquely determined by data on X, then additional assumptions about the network a ..."
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Restrictions on meaningful phylogenetic networks Abstract: It is common to assume that a phylogenetic network is a rooted acyclic digraph. Let X denote the set of leaves. The author argues that, if the network is to be uniquely determined by data on X, then additional assumptions about the network are needed. Under a simple model of genetic inheritance with no homoplasies, the network should be assumed regular (in the sense of Baroni et al 2004; see Baroni and Steel 2006). A vertex is called "hybrid " if it has at least two parents and "normal " if it has exactly one parent. If v is a vertex, a "normal path from v to X " is a directed path starting at v and ending at some member of X, such that each vertex on the path (other than possibly v itself) is normal. Under a simple model of inheritance that allows homoplasies only at hybrid vertices, there is unique determination of the genomes at vertices provided that from each vertex v there is a normal path to X. If from every vertex there exists a normal path to X, then in fact the graph is regular. Hence the author argues that the search for meaningful phylogenetic networks should be restricted to networks such that from each vertex there is a normal path to X.Restrictions on meaningful phylogenetic networks