Constructing level-2 phylogenetic networks from rooted triplets (original) (raw)

Constructing Level-2 Phylogenetic Networks from Triplets

IEEE/ACM Transactions on Computational Biology and Bioinformatics, 2000

Jansson and Sung showed in that, given a dense set of input triplets T (representing hypotheses about the local evolutionary relationships of triplets of species), it is possible to determine in polynomial time whether there exists a level-1 network consistent with T , and if so to construct such a network. They also showed that, unlike in the case of trees (i.e. level-0 networks), the problem becomes NP-hard when the input is non-dense.

Constructing Rooted Phylogenetic Networks from Triplets based on Height Function

2012

The problem of constructing an optimal rooted phylogenetic‎ ‎network from a set of rooted triplets is NP-hard. ‎In this paper‎, ‎we present a novel method called NCH‎, ‎which tries to construct a rooted phylogenetic network with the minimum number‎‎of reticulation nodes from an arbitrary set of rooted triplets based on the concept of the height function of a tree and a network. We report the performance of this method on simulated data. Keywords— Rooted phylogenetic network, Triplet, Density, Consistency, Height function, Reticulation node

Algorithms for Combining Rooted Triplets into a Galled Phylogenetic Network

Siam Journal on Computing, 2006

This paper considers the problem of determining whether a given set T of rooted triplets can be merged without conflicts into a galled phylogenetic network and, if so, constructing such a network. When the input T is dense, we solve the problem in O(|T |) time, which is optimal since the size of the input is Θ(|T |). In comparison, the previously fastest algorithm for this problem runs in O(|T | 2 ) time. We also develop an optimal O(|T |)-time algorithm for enumerating all simple phylogenetic networks leaf-labeled by L that are consistent with T , where L is the set of leaf labels in T , which is used by our main algorithm. Next, we prove that the problem becomes NP-hard if extended to nondense inputs, even for the special case of simple phylogenetic networks. We also show that for every positive integer n, there exists some set T of rooted triplets on n leaves such that any galled network can be consistent with at most 0.4883 · |T | of the rooted triplets in T . On the other hand, we provide a polynomial-time approximation algorithm that always outputs a galled network consistent with at least a factor of 5 12 (> 0.4166) of the rooted triplets in T .

Reconstructing Phylogenetic Level-1 Networks from Nondense Binet and Trinet Sets

Algorithmica, 2015

Binets and trinets are phylogenetic networks with two and three leaves, respectively. Here we consider the problem of deciding if there exists a binary level-1 phylogenetic network displaying a given set T of binary binets or trinets over a taxa set X, and constructing such a network whenever it exists. We show that this is NPhard for trinets but polynomial-time solvable for binets. Moreover, we show that the problem is still polynomial-time solvable for inputs consisting of binets and trinets as long as the cycles in the trinets have size three. Finally, we present an O(3 |X| poly(|X|)) time algorithm for general sets of binets and trinets. The latter two algorithms generalise to instances containing level-1 networks with arbitrarily many leaves, and thus provide some of the first supernetwork algorithms for computing networks from a set of rooted phylogenetic networks.

The Structure of Level-k Phylogenetic Networks

CPM'09, 2009

Evolution is usually described as a phylogenetic tree, but due to some exchange of genetic material, it can be represented as a phylogenetic network which has an underlying tree structure. The notion of level was recently introduced as a parameter on realistic kinds of phylogenetic networks to express their complexity and tree-likeness. We study the structure of level-k networks, and how they can be decomposed into level-k generators. We also provide a polynomial time algorithm which takes as input the set of level-k generators and builds the set of level-(k + 1) generators. Finally, with a simulation study, we evaluate the proportion of level-k phylogenetic networks among networks generated according to the coalescent model with recombination.

Locating a tree in a phylogenetic network

Information Processing Letters, 2010

Phylogenetic trees and networks are leaf-labelled graphs that are used to describe evolutionary histories of species. The Tree Containment problem asks whether a given phylogenetic tree is embedded in a given phylogenetic network. Given a phylogenetic network and a cluster of species, the Cluster Containment problem asks whether the given cluster is a cluster of some phylogenetic tree embedded in the network. Both problems are known to be NP-complete in general. In this article, we consider the restriction of these problems to several well-studied classes of phylogenetic networks. We show that Tree Containment is polynomial-time solvable for normal networks, for binary tree-child networks, and for level-k networks. On the other hand, we show that, even for tree-sibling, time-consistent, regular networks, both Tree Containment and Cluster Containment remain NP-complete.

TripNet: A Method for Constructing Rooted Phylogenetic Networks from Rooted Triplets

PLoS ONE, 2014

We present TripNet, a method for constructing phylogenetic networks from triplets. We will present the motivations behind our approach and its theoretical and empirical justification. To demonstrate the accuracy and efficiency of TripNet, we performed two simulations and also applied the method to five published data sets: Kreitman's data, a set of triplets from real yeast data obtained from the Fungal Biodiversity Center in Utrecht, a collection of 110 highly recombinant Salmonella multi-locus sequence typing sequences, and nrDNA ITS and cpDNA JSA sequence data of New Zealand alpine buttercups of Ranunculus sect. Pseudadonis. Finally, we compare our results with those already obtained by other authors using alternative methods. TripNet, data sets, and supplementary files are freely available for download at (www.bioinf.cs.ipm.ir/softwares/tripnet).

Do Triplets Have Enough Information to Construct the Multi-Labeled Phylogenetic Tree?

PLoS ONE, 2014

The evolutionary history of certain species such as polyploids are modeled by a generalization of phylogenetic trees called multi-labeled phylogenetic trees, or MUL trees for short. One problem that relates to inferring a MUL tree is how to construct the smallest possible MUL tree that is consistent with a given set of rooted triplets, or SMRT problem for short. This problem is NP-hard. There is one algorithm for the SMRT problem which is exact and runs in O(7 n ) time, where n is the number of taxa. In this paper, we show that the SMRT does not seem to be an appropriate solution from the biological point of view. Indeed, we present a heuristic algorithm named MTRT for this problem and execute it on some real and simulated datasets. The results of MTRT show that triplets alone cannot provide enough information to infer the true MUL tree. So, it is inappropriate to infer a MUL tree using triplet information alone and considering the minimum number of duplications. Finally, we introduce some new problems which are more suitable from the biological point of view.

TripNet: A Method for Constructing Phylogenetic Networks from Triplets

Arxiv preprint arXiv: …, 2011

Constructing level-2 phylogenetic networks from rooted triplets (original) (raw)

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