Reconstruction of certain phylogenetic networks from the genomes at their leaves

Willson, Stephen J.

doi:10.1016/j.jtbi.2008.02.015

Cited by 16 publications

(18 citation statements)

References 16 publications

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“…Others include restrictions on the children of vertices, for example tree-child networks [6] or tree-sibling networks [7]. Certain unique reconstructions for normal networks are given in [25].…”

Section: Introductionmentioning

confidence: 99%

“…The paper [15] shows that the problem, given a network N and a cluster U , of deciding whether U ∈ T rCl(N ) is NPcomplete. The paper [25] presents examples of distinct regular networks (indeed normal networks) M and N which have the same leaf sets and which have precisely the same tree clusters; thus T rCl(M ) = T rCl(N ) but M and N are not isomorphic. The author therefore finds it somewhat surprising that, as shown in the current paper, the trees themselves do determine the network uniquely for a broad class of networks.…”

Section: Introductionmentioning

confidence: 99%

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Regular Networks Can be Uniquely Constructed from Their Trees

Willson

2011

IEEE/ACM Trans. Comput. Biol. and Bioinf.

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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 T r(N ) denote the set of all trees displayed by the network N . In general, there may be many other networks M such that T r(M ) = T r(N ). A network is regular if it is isomorphic with its cover digraph. If N is regular and D is a collection of trees displayed by N , this paper studies some procedures to try to reconstruct N given D. If the input is D = T r(N ), one procedure is described which will reconstruct N . Hence if N and M are regular networks and T r(N ) = T r(M ), it follows that N = M , proving that a regular network is uniquely determined by its displayed trees. If D is a (usually very much smaller) collection of displayed trees that satisfies certain hypotheses, modifications of the procedure will still reconstruct N given D.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Regular Networks Can be Uniquely Constructed from Their Trees

Willson

2011

IEEE/ACM Trans. Comput. Biol. and Bioinf.

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“…Previous results by the author [24] indicate one such method with some strong assumptions in addition to normality. This current paper suggests that the assumption of normality cannot be eliminated.…”

Section: Discussionmentioning

confidence: 93%

“…Previous work by the author [22], [23], [24] includes theorems about polynomialtime methods for reconstructing normal networks from information on their leaves (with additional assumptions as well). These papers show that some basic network-reconstruction problems are tractable on certain families of normal networks.…”

Section: Introductionmentioning

confidence: 99%

Properties of Normal Phylogenetic Networks

Willson

2009

Bull. Math. Biol.

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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.

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“…Much work has been done on reconstructing minimal ARGs, i.e., ARGs with the minimum number of nodes of indegree 2 to model the evolution of a set of binary sequences under the infinite-site model; e.g., see [36,37,91,92,93,94]. Recently, Willson provided a new method for reconstructing certain phylogenetic networks from binary sequences when backmutations are allowed to occur at network-nodes [104]. While we focused on binary characters in the preceding discussion, perfect phylogenetic networks can be defined on multi-state characters as well.…”

Section: Character Compatibility Of Phylogenetic Networkmentioning

confidence: 99%

Evolutionary Phylogenetic Networks: Models and Issues

Nakhleh

2010

Problem Solving Handbook in Computational Biology and Bioinformatics

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Phylogenetic networks are special graphs that generalize phylogenetic trees to allow for modeling of non-treelike 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.

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Reconstruction of certain phylogenetic networks from the genomes at their leaves

Cited by 16 publications

References 16 publications

Regular Networks Can be Uniquely Constructed from Their Trees

Regular Networks Can be Uniquely Constructed from Their Trees

Properties of Normal Phylogenetic Networks

Evolutionary Phylogenetic Networks: Models and Issues

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