Algorithms for Combining Rooted Triplets into a Galled Phylogenetic Network (original) (raw)
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Constructing level-2 phylogenetic networks from rooted triplets
2008
Jansson and Sung showed in [15] 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. Here we further extend this work by showing that, when the set of input triplets is dense, the problem is even polynomial-time solvable for the construction of level-2 networks. This shows that, assuming density, it is tractable to construct plausible evolutionary histories from input triplets even when such histories are heavily non-tree like. This further strengthens the case for the use of triplet-based methods in the construction of phylogenetic networks. We also show that, in the non-dense case, the level-2 problem remains NP-hard.
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
Solving the tree containment problem in linear time for nearly stable phylogenetic networks
Discrete Applied Mathematics, 2017
A phylogenetic network is a rooted acyclic digraph whose leaves are uniquely labeled with a set of taxa. The tree containment problem asks whether or not a phylogenetic network displays a phylogenetic tree over the same set of labeled leaves. It is a fundamental problem arising from validation of phylogenetic network models. The tree containment problem is NP-complete in general. To identify network classes on which the problem is polynomial time solvable, we introduce two classes of networks by generalizations of tree-child networks through vertex stability, namely nearly stable networks and genetically stable networks. Here, we study the combinatorial properties of these two classes of phylogenetic networks. We also develop a linear-time algorithm for solving the tree containment problem on binary nearly stable networks.
Constructing a smallest refining galled phylogenetic network
2005
Reticulation events occur frequently in many types of species. Therefore, to develop accurate methods for reconstructing phylogenetic networks in order to describe evolutionary history in the presence of reticulation events is important. Previous work has suggested that constructing phylogenetic networks by merging gene trees is a biologically meaningful approach. This paper presents two new efficient algorithms for inferring a phylogenetic network from a set T of gene trees of arbitrary degrees. The first algorithm solves the open problem of constructing a refining galled network for T (if one exists) with no restriction on the number of hybrid nodes; in fact, it outputs the smallest possible solution. In comparison, the previously best method (SpNet) can only construct networks having a single hybrid node. For cases where there exists no refining galled network for T , our second algorithm identifies a minimum subset of the species set to be removed so that the resulting trees can be combined into a galled network. Based on our two algorithms, we propose two general methods named RGNet and RGNet+. Through simulations, we show that our methods outperform the other existing methods neighbor-joining, NeighborNet, and SpNet.
It has remained an open question for some time whether, given a set of not necessarily binary (i.e. "nonbinary") trees T on a set of taxa X , it is possible to determine in time f (r)·poly(m) whether there exists a phylogenetic network that displays all the trees in T , where r refers to the reticulation number of the network and m = |X | + |T |. Here we show that this holds if one or both of the following conditions holds: (1) |T | is bounded by a function of r; (2) the maximum degree of the nodes in T is bounded by a function of r. These sufficient conditions absorb and significantly extend known special cases, namely when all the trees in T are binary or T contains exactly two nonbinary trees . We believe this result is an important step towards settling the issue for an arbitrarily large and complex set of nonbinary trees. For completeness we show that the problem is certainly solveable in time O(m f (r) ).
Computing the maximum agreement of phylogenetic networks
Theoretical Computer Science, 2005
We introduce the maximum agreement phylogenetic subnetwork problem (MASN) of finding a branching structure shared by a set of phylogenetic networks. We prove that the problem is NP-hard even if restricted to three phylogenetic networks and give an O(n 2 )-time algorithm for the special case of two level-1 phylogenetic networks, where n is the number of leaves in the input networks and where N is called a level-f phylogenetic network if every biconnected component in the underlying undirected graph contains at most f nodes having indegree 2 in N . Our algorithm can be extended to yield a polynomial-time algorithm for two level-f phylogenetic networks N1, N2 for any f which is upper-bounded by a constant; more precisely, its running time is O(|V (N1)| · |V (N2)| · 4 f ), where V (Ni) denotes the set of nodes of Ni.
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.
Fast algorithms for computing the tripartition-based distance between phylogenetic networks
2007
Consider two phylogenetic networks N and N ′ of size n. The tripartition-based distance finds the proportion of tripartitions which are not shared by N and N ′ . This distance is proposed by and is a generalization of Robinson-Foulds distance, which is orginally used to compare two phylogenetic trees. This paper gives an O(min{kn log n, n log n + hn})-time algorithm to compute this distance, where h is the number of hybrid nodes in N and N ′ while k is the maximum number of hybrid nodes among all biconnected components in N and N ′ . Note that k << h << n in a phylogenetic network. In addition, we propose algorithms for comparing galled-trees, which are an important, biological meaningful special case of phylogenetic network. We give an O(n)-time algorithm for comparing two galled-trees. We also give an O(n + kh)-time algorithm for comparing a galled-tree with another general network, where h and k are the number of hybrid nodes in the latter network and its biggest biconnected component respectively.