Phylogenetic Networks that Display a Tree Twice

Cordue, Paul; Linz, Simone; Semple, Charles

doi:10.1007/s11538-014-0032-x

Cited by 21 publications

(23 citation statements)

References 19 publications

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“…This contradicts our assumption that ℓ ′ and ℓ ′′ belong to a cherry in T . (3) The proof is similar to that of case (2).…”

Section: Appendix: Omitted Proofsmentioning

confidence: 66%

“…If a tree node is stable on a leaf ℓ, then its unique parent is also stable on ℓ, but the stability of a reticulation does not imply that of its parents. Cordue, Linz and Semple [2] recently introduced a class of stable networks that we call nearly tree-child networks and which satisfy the property that every reticulation has a parent connected to some leaf by a tree path (see Figure 1.A for an example).…”

Section: Propositionmentioning

confidence: 99%

“…Motivated by the study in [2], we make progress in this work towards determining the complexity of the TC problem on stable networks by presenting a quadratic-time algorithm for a new class that we call genetically stable networks. As we shall show, these networks comprise a subclass of stable, tree-sibling networks, including tree-child networks.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Solving the Tree Containment Problem for Genetically Stable Networks in Quadratic Time

Gambette¹,

Gunawan

Labarre³

et al. 2016

Lecture Notes in Computer Science

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Abstract.A phylogenetic network is a rooted acyclic digraph whose leaves are labeled with a set of taxa. The tree containment problem is a fundamental problem arising from model validation in the study of phylogenetic networks. It asks to determine whether or not a given network displays a given phylogenetic tree over the same leaf set. It is known to be NP-complete in general. Whether or not it remains NP-complete for stable networks is an open problem. We make progress towards answering that question by presenting a quadratic time algorithm to solve the tree containment problem for a new class of networks that we call genetically stable networks, which include tree-child networks and comprise a subclass of stable networks.

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“…This contradicts our assumption that ℓ ′ and ℓ ′′ belong to a cherry in T . (3) The proof is similar to that of case (2).…”

Section: Appendix: Omitted Proofsmentioning

confidence: 66%

Section: Propositionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Solving the Tree Containment Problem for Genetically Stable Networks in Quadratic Time

Gambette¹,

Gunawan

Labarre³

et al. 2016

Lecture Notes in Computer Science

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“…Gambette et al also proved that the TCP is polynomial time solvable for binary nearly stable networks and that each reticulation-visible network contains at most 4(n − 1) reticulations [11]. Other studies related to the TCP include [5], [21] and [28].…”

Section: Introductionmentioning

confidence: 99%

A decomposition theorem and two algorithms for reticulation-visible networks

Gunawan

DasGupta

Zhang

2017

Information and Computation

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In studies of molecular evolution, phylogenetic trees are rooted binary trees, whereas phylogenetic networks are rooted acyclic digraphs. Edges are directed away from the root and leaves are uniquely labeled with taxa in phylogenetic networks. For the purpose of validating evolutionary models, biologists check whether or not a phylogenetic tree (resp. cluster) is contained in a phylogenetic network on the same taxa. These tree and cluster containment problems are known to be NP-complete. A phylogenetic network is reticulation-visible if every reticulation node separates the root of the network from at least a leaf. We answer an open problem by proving that the problem is solvable in quadratic time for reticulationvisible networks. The key tool used in our answer is a powerful decomposition theorem. It also allows us to design a linear-time algorithm for the cluster containment problem for networks of this type and to prove that every galled network with n leaves has 2(n − 1) reticulation nodes at most.

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“…Intuitively, an advantage of considering branch lengths is that it should allow one to locate more precisely a gene history within a network, and, more generally, it should give more specific answers to the tree containment problem. For example, whereas a tree topology may be contained in multiple different locations inside a network [9], this will happen much more rarely when branch lengths are taken into account (see, e.g., T 1 in Fig. 1).…”

Section: Introductionmentioning

confidence: 99%

Do Branch Lengths Help to Locate a Tree in a Phylogenetic Network?

et al. 2016

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Phylogenetic networks are increasingly used in evolutionary biology to represent the history of species that have undergone reticulate events such as horizontal gene transfer, hybrid speciation and recombination. One of the most fundamental questions that arise in this context is whether the evolution of a gene with one copy in all species can be explained by a given network. In mathematical terms, this is often translated in the following way: is a given phylogenetic tree contained in a given phylogenetic network? Recently this tree containment problem has been widely investigated from a computational perspective, but most studies have only focused on the topology of the phylogenies, ignoring a piece of information that, in the case of phylogenetic trees, is routinely inferred by evolutionary analyses: branch lengths. These measure the amount of change (e.g., nucleotide substitutions) that has occurred along each branch of the phylogeny. Here, we study a number of versions of the tree containment problem that explicitly account for branch lengths. We show that, although length information has the potential to locate more precisely a tree within a network, the problem is computationally hard in its most general form. On a positive note, for a number of special cases of biological relevance, we provide algorithms that solve this problem efficiently. This includes the case of networks of limited complexity, for which it is possible to recover, among the trees contained by the network with the same topology as the input tree, the closest one in terms of branch lengths.

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Phylogenetic Networks that Display a Tree Twice

Cited by 21 publications

References 19 publications

Solving the Tree Containment Problem for Genetically Stable Networks in Quadratic Time

Solving the Tree Containment Problem for Genetically Stable Networks in Quadratic Time

A decomposition theorem and two algorithms for reticulation-visible networks

Do Branch Lengths Help to Locate a Tree in a Phylogenetic Network?

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