Results 1  10
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16
Constructing level2 phylogenetic networks from triplets
, 2009
"... Jansson and Sung showed that, given a dense set of input triplets T (representing hypotheses about the local evolutionary relationships of triplets of taxa), it is possible to determine in polynomial time whether there exists a level1 network consistent with T, and if so, to construct such a netwo ..."
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Cited by 33 (9 self)
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Jansson and Sung showed that, given a dense set of input triplets T (representing hypotheses about the local evolutionary relationships of triplets of taxa), it is possible to determine in polynomial time whether there exists a level1 network consistent with T, and if so, to construct such a network [24]. Here, we extend this work by showing that this problem is even polynomial time solvable for the construction of level2 networks. This shows that, assuming density, it is tractable to construct plausible evolutionary histories from input triplets even when such histories are heavily nontreelike. This further strengthens the case for the use of tripletbased methods in the construction of phylogenetic networks. We also implemented the algorithm and applied it to yeast data.
Constructing the simplest possible phylogenetic network from triplets,”
 Algorithmica,
, 2011
"... Abstract A phylogenetic network is a directed acyclic graph that visualizes an evolutionary history containing socalled reticulations such as recombinations, hybridizations or lateral gene transfers. Here we consider the construction of a simplest possible phylogenetic network consistent with an i ..."
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Cited by 20 (5 self)
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Abstract A phylogenetic network is a directed acyclic graph that visualizes an evolutionary history containing socalled reticulations such as recombinations, hybridizations or lateral gene transfers. Here we consider the construction of a simplest possible phylogenetic network consistent with an input set T , where T contains at least one phylogenetic tree on three leaves (a triplet) for each combination of three taxa. To quantify the complexity of a network we consider both the total number of reticulations and the number of reticulations per biconnected component, called the level of the network. We give polynomialtime algorithms for constructing a level1 respectively a level2 network that contains a minimum number of reticulations and is consistent with T (if such a network exists). In addition, we show that if T is precisely equal to the set of triplets consistent with some network, then we can construct such a network with smallest possible level in time O(T  k+1 ), if k is a fixed upper bound on the level of the network.
New Results on Optimizing Rooted Triplets Consistency
"... Abstract. A set of phylogenetic trees with overlapping leaf sets is consistent if it can be merged without conflicts into a supertree. In this paper, we study the polynomialtime approximability of two related optimization problems called the maximum rooted triplets consistency problem (MaxRTC) and ..."
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Cited by 13 (2 self)
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Abstract. A set of phylogenetic trees with overlapping leaf sets is consistent if it can be merged without conflicts into a supertree. In this paper, we study the polynomialtime approximability of two related optimization problems called the maximum rooted triplets consistency problem (MaxRTC) and the minimum rooted triplets inconsistency problem (MinRTI) in which the input is a set R of rooted triplets, and where the objectives are to find a largest cardinality subset of R which is consistent and a smallest cardinality subset of R whose removal from R results in a consistent set, respectively. We first show that a simple modification to Wu’s BestPairMergeFirst heuristic [25] results in a bottomupbased 3approximation for MaxRTC. We then demonstrate how any approximation algorithm for MinRTI could be used to approximate MaxRTC, and thus obtain the first polynomialtime approximation algorithm for MaxRTC with approximation ratio smaller than 3. Next, we prove that for a set of rooted triplets generated under a uniform random model, the maximum fraction of triplets which can be consistent with any tree is approximately one third, and then provide a deterministic construction of a triplet set having a similar property which is subsequently used to prove that both MaxRTC and MinRTI are NPhard even if restricted to minimally dense instances. Finally, we prove that MinRTI cannot be approximated within a ratio of Ω(log n) in polynomial time, unless P = NP. 1
On the elusiveness of clusters
"... Abstract—Rooted phylogenetic networks are often used to represent conflicting phylogenetic signals. Given a set of clusters, a network is said to represent these clusters in the softwired sense if, for each cluster in the input set, at least one tree embedded in the network contains that cluster. Mo ..."
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Cited by 10 (9 self)
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Abstract—Rooted phylogenetic networks are often used to represent conflicting phylogenetic signals. Given a set of clusters, a network is said to represent these clusters in the softwired sense if, for each cluster in the input set, at least one tree embedded in the network contains that cluster. Motivated by parsimony we might wish to construct such a network using as few reticulations as possible, or minimizing the level of the network, i.e. the maximum number of reticulations used in any “tangled ” region of the network. Although these are NPhard problems, here we prove that, for every fixedk ≥ 0, it is polynomialtime solvable to construct a phylogenetic network with level equal to k representing a cluster set, or to determine that no such network exists. However, this algorithm does not lend itself to a practical implementation. We also prove that the comparatively efficient CASS algorithm correctly solves this problem (and also minimizes the reticulation number) when input clusters are obtained from two not necessarily binary gene trees on the same set of taxa but does not always minimize level for general cluster sets. Finally, we describe a new algorithm which generates in polynomialtime all binary phylogenetic networks with exactly r reticulations representing a set of input clusters (for every fixed r ≥ 0).
LEVELK PHYLOGENETIC NETWORK CAN BE CONSTRUCTED FROM A DENSE TRIPLET SET IN POLYNOMIAL TIME
, 2009
"... Given a dense triplet set T, there arise two interesting questions [7]: Does there exists any phylogenetic network consistent with T? And if so, can we find an effective algorithm to construct one? For cases of networks of levels k = 0 or 1 or 2, these questions were answered in [1, 6, 7, 8, 10] wit ..."
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Cited by 10 (1 self)
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Given a dense triplet set T, there arise two interesting questions [7]: Does there exists any phylogenetic network consistent with T? And if so, can we find an effective algorithm to construct one? For cases of networks of levels k = 0 or 1 or 2, these questions were answered in [1, 6, 7, 8, 10] with effective polynomial algorithms. For higher levels k, partial answers were recently obtained in [11] with an O(T  k+1) time algorithm for simple networks. In this paper we give a complete answer to the general case, solving a problem of [7]. The main idea is to use a special property of SNsets in a levelk network. As a consequence, we can also find the levelk network with the minimum number of reticulations in polynomial time.
Constructing minimal phylogenetic networks from softwired clusters is fixed parameter tractable
, 2011
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A practical algorithm for reconstructing level1 phylogenetic networks
 IEEE/ACM Transactions on Computational Biology and Bioinformatics
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QUARTETS AND UNROOTED PHYLOGENETIC NETWORKS
, 2012
"... Accepted (Day Month Year) Phylogenetic networks were introduced to describe evolution in the presence of exchanges of genetic material between coexisting species or individuals. Split networks in particular were introduced as a special kind of abstract network to visualize conflicts between phylogen ..."
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Cited by 1 (0 self)
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Accepted (Day Month Year) Phylogenetic networks were introduced to describe evolution in the presence of exchanges of genetic material between coexisting species or individuals. Split networks in particular were introduced as a special kind of abstract network to visualize conflicts between phylogenetic trees which may correspond to such exchanges. More recently, methods were designed to reconstruct explicit phylogenetic networks (whose vertices can be interpreted as biological events) from triplet data. In this article, we link abstract and explicit networks through their combinatorial properties, by introducing the unrooted analogue of levelk networks. In particular, we give an equivalence theorem between circular split systems and unrooted level1 networks. We also show how to adapt to quartets some existing results on triplets, in order to reconstruct unrooted levelk phylogenetic networks. These results give an interesting perspective on the combinatorics of phylogenetic networks and also raise algorithmic and combinatorial questions.
All that glisters is not galled
 Math Biosci
"... Abstract. Galled trees, evolutionary networks with isolated reticulation cycles, have appeared under several slightly different definitions in the literature. In this paper we establish the actual relationships between the main four such alternative definitions: namely, the original galled trees, le ..."
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Abstract. Galled trees, evolutionary networks with isolated reticulation cycles, have appeared under several slightly different definitions in the literature. In this paper we establish the actual relationships between the main four such alternative definitions: namely, the original galled trees, level1 networks, nested networks with nesting depth 1, and evolutionary networks with arcdisjoint reticulation cycles. 1