New common ancestor problems in trees and directed acyclic graphs

Fischer, Johannes; Huson, Daniel H.

doi:10.1016/j.ipl.2010.02.014

Cited by 10 publications

(7 citation statements)

References 14 publications

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“…A lowest common ancestor of X in N is a vertex w such that w ≤ N x for all x ∈ X and no vertex below w has this property. Note that the lowest stable ancestor is unique but that this not necessarily the case for a lowest common ancestor [10]. If a lowest common ancestor of X is unique, then we denote it by LCA(X ).…”

Section: Preliminariesmentioning

confidence: 99%

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: Preliminariesmentioning

confidence: 99%

Trinets encode tree-child and level-2 phylogenetic networks

Iersel

Moulton

2013

J. Math. Biol.

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“…However, it would be interesting to know whether there may be a more efficient algorithm for computing closed sets along the lines of the one presented in for computing SN-sets. This might also use results presented in Fischer and Huson (2010) for computing lowest stable ancestors.…”

Section: Theorem 63 Suppose That N Is a Phylogenetic Network On X Anmentioning

confidence: 99%

“…Following on from that section, we then introduce the key new concept of a closed set. Recall that, given a non-empty subset Y of the leaf-set X, the lowest stable ancestor of Y , LSA(Y ), in a phylogenetic network N is the lowest vertex in N that is a common ancestor of every element in Y and that is contained in every dipath that connects the root of N to some element of Y (Fischer and Huson, 2010). We say that a subset Y ⊆ X is closed (in N ) if |Y | = 1, or if |Y | ≥ 2 and the set of leaves below LSA(Y ) is equal to Y .…”

Section: Introductionmentioning

confidence: 99%

Hierarchies from Lowest Stable Ancestors in Nonbinary Phylogenetic Networks

Huber

Moulton

2018

J Classif

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The reconstruction of the evolutionary history of a set of species is an important problem in classification and phylogenetics. Phylogenetic networks are a generalization of evolutionary trees that are used to represent histories for species that have undergone reticulate evolution, an important evolutionary force for many organisms (e.g. plants or viruses). In this paper, we present a novel approach to understanding the structure of networks that are not necessarily binary. More specifically, we define the concept of a closed set and show that the collection of closed sets of a network forms a hierarchy, and that this hierarchy can be deduced from either the subtrees or subnetworks on all 3-subsets. This allows us to also show that closed sets generalize the concept of the SN-sets of a binary network, sets which have proven very useful in elucidating the structure of binary networks. We also characterize the minimal closed sets (under set inclusion) for a special class of networks (2-terminal networks). Taken together, we anticipate that our results should be useful for the development of new phylogenetic network reconstruction algorithms.

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“…We have proved in Clemente et al (2011) that, when the F-measure is taken as indicator, it suffices to consider candidate nodes that are either candidate sequences themselves, or the LCA of two or more candidate sequences in the reference taxonomy. That is, it suffices to consider as candidate nodes the LCA skeleton tree (Fischer and Huson, 2010) of the set of candidate sequences for a given read.…”

Section: Figmentioning

confidence: 99%

Unbiased Taxonomic Annotation of Metagenomic Samples

Fosso¹,

Pesole²,

Rosselló³

et al. 2017

Bioinformatics Research and Applications

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The classification of reads from a metagenomic sample using a reference taxonomy is usually based on first mapping the reads to the reference sequences and then classifying each read at a node under the lowest common ancestor of the candidate sequences in the reference taxonomy with the least classification error. However, this taxonomic annotation can be biased by an imbalanced taxonomy and also by the presence of multiple nodes in the taxonomy with the least classification error for a given read. In this article, we show that the Rand index is a better indicator of classification error than the often used area under the receiver operating characteristic (ROC) curve and F-measure for both balanced and imbalanced reference taxonomies, and we also address the second source of bias by reducing the taxonomic annotation problem for a whole metagenomic sample to a set cover problem, for which a logarithmic approximation can be obtained in linear time and an exact solution can be obtained by integer linear programming. Experimental results with a proof-of-concept implementation of the set cover approach to taxonomic annotation in a next release of the TANGO software show that the set cover approach further reduces ambiguity in the taxonomic annotation obtained with TANGO without distorting the relative abundance profile of the metagenomic sample.

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New common ancestor problems in trees and directed acyclic graphs

Cited by 10 publications

References 14 publications

Trinets encode tree-child and level-2 phylogenetic networks

Trinets encode tree-child and level-2 phylogenetic networks

Hierarchies from Lowest Stable Ancestors in Nonbinary Phylogenetic Networks

Unbiased Taxonomic Annotation of Metagenomic Samples

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