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## A practical algorithm for reconstructing level-1 phylogenetic networks

Venue: | IEEE/ACM Transactions on Computational Biology and Bioinformatics |

Citations: | 6 - 2 self |

### Citations

2519 |
A simple method for estimating evolutionary rate of base substitutions through comparative studies of nucleotide sequences
- Kimura
- 1980
(Show Context)
Citation Context ... 2700 and 8926) in [21, Chapter 14]. Furthermore, for the three induced sub-alignments 1-2699, 2700- 8925, and 8926-9953 the Neighbor Joining method [20] (with subtype C as outgroup and the K2P model =-=[18]-=-) was used to represent the data in terms of arc-weighted phylogenetic trees (see [21, page 159] for a depiction of those trees). Since the resolution patterns for J and G in the first tree, H and C i... |

748 |
Molecular Evolution and Phylogenetics.
- Nei, Kumar
- 2000
(Show Context)
Citation Context ...data set two breakpoints were identified (positions 2700 and 8926) in [21, Chapter 14]. Furthermore, for the three induced sub-alignments 1-2699, 2700- 8925, and 8926-9953 the Neighbor Joining method =-=[20]-=- (with subtype C as outgroup and the K2P model [18]) was used to represent the data in terms of arc-weighted phylogenetic trees (see [21, page 159] for a depiction of those trees). Since the resolutio... |

269 |
TREEPUZZLE: maximum likelihood phylogenetic analysis using quartets and parallel computing.
- Schmidt, Strimmer, et al.
- 2002
(Show Context)
Citation Context ...a phylogenetic tree, two main triplet-based approaches for phylogenetic network reconstruction immediately suggest themselves. One is to essentially first employ a method such as TreePuzzle (see e.g. =-=[22]-=-) to generate a set of quartets1 from a sequence alignment, to then derive a set T of triplets from that set and then to use the set T to reconstruct a phylogenetic network. The other is to essentiall... |

157 |
Inferring a tree from lowest common ancestors with an application to the optimization of relational expressions.
- Aho, Sagiv, et al.
- 1981
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Citation Context ... put L := L(T ). The first step of Lev1athan’s partitioning strategy is to determine whether an Aho move is possible for T . This move is based on an algorithm originally introduced by Aho et. al. in =-=[1]-=-. Following [24] where this algorithm is referred to as Build algorithm, this algorithm relies on the clustering graph G[L′,T ] induced by T on any subset L ′ ⊆ L. For the convenience of the reader, w... |

84 |
Dendroscope: an interactive viewer for large phylogenetic trees.
- Huson, Richter, et al.
- 2007
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Citation Context ...conclude this section with remarking that although using different philosophies, the other two known approaches i.e. Cluster networks and Galled networks (both of which are implemented in Dendroscope =-=[14]-=-) also had problems with this data set, postulating between 2 and 4 recombination events (data not shown). 7. Conclusions In this paper, we have presented a heuristic for constructing level-1 networks... |

63 |
Phylogenetic Supertrees: Combining Information to Reveal the Tree of Life (Kluwer Academic, the Netherlands,
- Bininda-Emonds
- 2004
(Show Context)
Citation Context ...elk@cwi.nl. 1 2 KATHARINA T. HUBER, LEO VAN IERSEL, STEVEN KELK AND RADOS LAW SUCHECKI b c d e f g h ia Figure 1. A phylogenetic network with leaf set {a, . . . , i} in the form of a level-1 network. =-=[2]-=- which aims to reconstruct a phylogenetic tree by puzzling it together from smaller trees. Inspired by this - and guided by the fundamental observations that (i) a phylogenetic tree is uniquely descri... |

39 | Comparison of tree-child phylogenetic networks,
- Cardona, Rossello, et al.
- 2009
(Show Context)
Citation Context ...sely that proper subset relationship. 18 KATHARINA T. HUBER, LEO VAN IERSEL, STEVEN KELK AND RADOS LAW SUCHECKI The final measure we considered is the µ-distance dµ which was originally introduced in =-=[7]-=-. To define this measure which was shown in [5, 7] to be a metric for a certain class of networks (i.e. tree-child networks), which includes the class of level-1 networks as a subclass, we require som... |

37 |
The phylogenetics handbook: a practical approach to DNA and protein phylogeny. Cambridge (UK):
- Salemi, AM, et al.
- 2003
(Show Context)
Citation Context ...1 Phylogenetic Networks 25 some of them helped to identify cases where a network generated by Lev1athan from Tǫ(M) coincided with the original network M. Our re-analysis of a biological data set from =-=[21]-=- using Lev1athan indicated that this data set is more complex than it appears at first sight. The resulting conflicting triplet infomation misled Lev1athan (and also the other two network construction... |

35 | Drawing graphs with dot".(
- Gansner, EleftheriosKoutsofios, et al.
- 2010
(Show Context)
Citation Context ...8]. In the latter case the (weighted) union of the triplet sets induced by the trees in T is taken by Lev1athan as triplet set T . It outputs a (possibly post-processed) level-1 network in DOT format =-=[11]-=- and/or eNewick format [27]. The goal of Lev1athan is to construct a level-1 network N that maximizes the number of triplets in T that are consistent with it. In an optional post-processing phase the ... |

33 | Constructing level-2 phylogenetic networks from triplets. In:
- Iersel, Keijsper, et al.
- 2008
(Show Context)
Citation Context ...ed. For example, it has been shown that, for each fixed non-negative integer k, the problem of constructing a level-k network consistent with a dense set of input triplets is polynomial-time solvable =-=[26, 28]-=-. The higher the level, the higher the complexity of evolutionary scenarios that can be represented. However, the running time grows exponentially with k and initial experiments with the related heuri... |

30 | Computing the quartet distance between evolutionary trees
- Bryant, Tsang, et al.
- 2000
(Show Context)
Citation Context ...etwork P. Note that this measure is different from the triplets distance introduced in [6]. The third of our triplet based measures is inspired by the quartet distance for unrooted phylogenetic trees =-=[3]-=- and is called the network-network symmetric difference. For M and NM the network- network symmetric difference S(M,NM) betweenM and NM is defined as the quantity S(M,NM) = |T (M)∆T (NM)|. S(M,NM) is ... |

28 | Inferring a Level-1 Phylogenetic Network from a Dense Set of Rooted Triplets - Jansson, Sung - 2006 |

26 | W.-K.: Algorithms for combining rooted triplets into a galled phylogenetic network.
- Jansson, Nguyen, et al.
- 2006
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Citation Context ...gorithms to construct them. Indeed, Jansson, Sung and Nguyen showed that it can be decided in polynomial time whether there exists a level-1 network with leaf set X consistent with all input triplets =-=[16, 17]-=-, if the input triplet set is dense, i.e. if a triplet is given for each combination of three taxa in X. Their algorithm will also construct such a network, if it exists. However, a level-1 network co... |

21 | S: Using Max Cut to Enhance Rooted Trees Consistency
- Snir, Rao
(Show Context)
Citation Context ...l observation that, when attempting to construct a level-1 network consistent with the maximum number of triplets in a given set, it can never be suboptimal to make an Aho move, when this is possible =-=[25]-=-. r f g z x y (a) (b) N N ′r f g z x y Figure 3. The triplets in T (N ) are also consistent with N ′ and N ′ is minimal with this property. If the Aho move is not successful, the next step is to try a... |

20 | Constructing the simplest possible phylogenetic network from triplets,”
- Iersel, Kelk
- 2011
(Show Context)
Citation Context ... level, the higher the complexity of evolutionary scenarios that can be represented. However, the running time grows exponentially with k and initial experiments with the related heuristic Simplistic =-=[30, 29]-=- show that, since these algorithms insist on full consistency with the input triplets, only a small amount of noise is required in the input data to artificially inflate the level of the produced netw... |

19 | Phylogenetic Networks
- Huson, Rupp, et al.
- 2010
(Show Context)
Citation Context ...on might have been driven by such processes has grown over the years. This in turn has generated much interest in these structures from mathematicians and computer scientists working in phylogenetics =-=[9, 13, 15, 23]-=-. The desire of biologists to use ever-longer sequences, combined with the computational complexities involved in dealing with such sequences, has meant that much research in mathematical methodology ... |

16 | Uniqueness, intractability and exact algorithms: reflections on level-k phylogenetic networks. arXiv:0712.2932v3 [q-bio.PE]
- Iersel, Kelk, et al.
- 2008
(Show Context)
Citation Context ...r any set T of triplets, a phylogenetic network that, in a well-defined sense, is consistent with all triplets in T can easily be constructed if the complexity of the network is essentially unbounded =-=[17, 31]-=-. Such networks are however only of marginal biological relevance. Researchers have therefore turned their attention to studying restricted classes of phylogenetic networks. One such class is that of ... |

15 | K.T.: Worst-case optimal approximation algorithms for maximizing triplet consistency within phylogenetic networks. arXiv:0710.3258v3 [q-bio.PE]
- Byrka, Gawrychowski, et al.
- 2008
(Show Context)
Citation Context ...truction. For example it was first shown in [16] how to construct in polynomial time such a network consistent with 5/12 ≈ 0.42 of the input triplets. This was subsequently improved to 0.488 . . . in =-=[4]-=-, which is worst-case optimal. Both algorithms are mathematically interesting, but have the drawback that they produce networks with a highly rigid topology which are biologically unrealistic. Lev1ath... |

15 |
Constructing the maximum consensus tree from rooted triples
- Wu
- 2004
(Show Context)
Citation Context ...ample some kind of confidence level one might have in that triplet, then our heuristic aims to maximize the total weight of the input triplets consistent with N . Optimizing such functions is NP-hard =-=[31, 32]-=-, even for the case of determining a tree consistent with the maximum number of triplets from an unweighted, dense triplet set. Having said that, an exponential-time exact algorithm was proposed in [3... |

12 |
Metrics for phylogenetic networks II: Nodal and triplets On a matching distance between rooted phylogenetic trees 681 metrics,
- Cardona, Llabrés, et al.
- 2009
(Show Context)
Citation Context ...C(T,P) = |T ∩ T (P)| |T | . In other words, C(T,P) is the fraction of triplets in T that is consistent with the network P. Note that this measure is different from the triplets distance introduced in =-=[6]-=-. The third of our triplet based measures is inspired by the quartet distance for unrooted phylogenetic trees [3] and is called the network-network symmetric difference. For M and NM the network- netw... |

11 |
Metrics for phylogenetic networks i: generalizations of the robinsonfoulds metric,”
- Cardona, Llabres, et al.
- 2009
(Show Context)
Citation Context ...INA T. HUBER, LEO VAN IERSEL, STEVEN KELK AND RADOS LAW SUCHECKI The final measure we considered is the µ-distance dµ which was originally introduced in [7]. To define this measure which was shown in =-=[5, 7]-=- to be a metric for a certain class of networks (i.e. tree-child networks), which includes the class of level-1 networks as a subclass, we require some more notation. Suppose N is a phylogenetic netwo... |

10 | Level-k phylogenetic network can be constructed from a dense triplet set in polynomial time
- To, Habib
(Show Context)
Citation Context ...ed. For example, it has been shown that, for each fixed non-negative integer k, the problem of constructing a level-k network consistent with a dense set of input triplets is polynomial-time solvable =-=[26, 28]-=-. The higher the level, the higher the complexity of evolutionary scenarios that can be represented. However, the running time grows exponentially with k and initial experiments with the related heuri... |

9 |
Reconstructing Evolution - New Mathematical and Computational Advances, chapter Hybridization Networks
- Semple
- 2007
(Show Context)
Citation Context ...on might have been driven by such processes has grown over the years. This in turn has generated much interest in these structures from mathematicians and computer scientists working in phylogenetics =-=[9, 13, 15, 23]-=-. The desire of biologists to use ever-longer sequences, combined with the computational complexities involved in dealing with such sequences, has meant that much research in mathematical methodology ... |

8 | On encodings of phylogenetic networks of bounded level
- Gambette, Huber
- 2012
(Show Context)
Citation Context ...by Lev1athan when ǫ = 1.0. This is a consequence of the fact that Lev1athan prioritises JNS moves and that a level-1 network M is completely defined by T (M) up to, but not including, galls of size 4 =-=[10]-=-. This is a drawback of any triplet based phylogenetic network approach since such approaches have to make a choice between the three galls on a set X ={a, b, c} that are all consistent with T = {ab|c... |

7 |
The newick tree format
- Felsenstein, Archie, et al.
- 1986
(Show Context)
Citation Context ...n which is implemented in Java and freely available for download [12]. It takes as input a set T of triplets or, more generally, a set T of phylogenetic trees (e.g. gene trees) given in Newick format =-=[8]-=-. In the latter case the (weighted) union of the triplet sets induced by the trees in T is taken by Lev1athan as triplet set T . It outputs a (possibly post-processed) level-1 network in DOT format [1... |

7 | Netgen: generating phylogenetic networks with diploid hybrids
- Morin, Moret
- 2006
(Show Context)
Citation Context ...rd desktop computer ranged from 2-3 seconds for the simplest networks to 30 seconds for the most complex ones. 6.2. Generating random level-1 networks. A survey of the literature suggested the NetGen =-=[19]-=- program to be the only available approach for systematically generating networks. Whilst NetGen addresses the issues of size (i.e. number of vertices) and network complexity one would encounter when ... |

2 |
Who’s who in phylogenetic networks
- Gambette
- 2009
(Show Context)
Citation Context ...on might have been driven by such processes has grown over the years. This in turn has generated much interest in these structures from mathematicians and computer scientists working in phylogenetics =-=[9, 13, 15, 23]-=-. The desire of biologists to use ever-longer sequences, combined with the computational complexities involved in dealing with such sequences, has meant that much research in mathematical methodology ... |

2 | Reconstructing Evolution - New Mathematical and Computational Advances, chapter Split Networks and reticulate networks - Huson - 2007 |

1 |
LEV1ATHAN: A level-1 heuristic
- Huber, Iersel, et al.
- 2009
(Show Context)
Citation Context ...rk complexity. A second strategy is to place a ceiling on the complexity of the networks that can be constructed and to no longer demand full triplet consistency. Implemented in the program Lev1athan =-=[12]-=-, this paper adopts this second strategy and presents the first heuristic algorithm for constructing level-1 networks from triplets. Given any set of triplets, our heuristic always constructs a level-... |

1 |
Extended newick: it is time for a standard representation of phylogenetic networks
- Valiente
- 2008
(Show Context)
Citation Context ...(weighted) union of the triplet sets induced by the trees in T is taken by Lev1athan as triplet set T . It outputs a (possibly post-processed) level-1 network in DOT format [11] and/or eNewick format =-=[27]-=-. The goal of Lev1athan is to construct a level-1 network N that maximizes the number of triplets in T that are consistent with it. In an optional post-processing phase the generated network can then ... |

1 |
SIMPLISTIC: Simple network heuristic
- Iersel, Kelk
- 2008
(Show Context)
Citation Context ... level, the higher the complexity of evolutionary scenarios that can be represented. However, the running time grows exponentially with k and initial experiments with the related heuristic Simplistic =-=[30, 29]-=- show that, since these algorithms insist on full consistency with the input triplets, only a small amount of noise is required in the input data to artificially inflate the level of the produced netw... |