Abstract:A phylogenetic network is a generalization of a phylogenetic tree, allowing structural properties that are not tree-like. In a seminal paper, Wang et al.(1) studied the problem of constructing a phylogenetic network, allowing recombination between sequences, with the constraint that the resulting cycles must be disjoint. We call such a phylogenetic network a "galled-tree". They gave a polynomial-time algorithm that was intended to determine whether or not a set of sequences could be generated on galled-tree. U… Show more
“…Wang et al then considered a restricted problem in which all recombination events are associated with nodedisjoint recombination cycles. Gusfield et al (2004a) gave necessary and sufficient conditions to identify these networks, which they called ''galled-trees,'' and they added a much more specific and realistic model of recombination events. Gusfield et al (2004b) gave a more detailed study of these node-disjoint cycles.…”
“…Wang et al then considered a restricted problem in which all recombination events are associated with nodedisjoint recombination cycles. Gusfield et al (2004a) gave necessary and sufficient conditions to identify these networks, which they called ''galled-trees,'' and they added a much more specific and realistic model of recombination events. Gusfield et al (2004b) gave a more detailed study of these node-disjoint cycles.…”
“…2 below). This type of network was first considered in [20] and is closely related to so-called galled-trees [3,7]. Level-1 networks have been used to, for example, analyse virus evolution [10], and are of practical importance since their simple structure allows for efficient construction [7,10,15] and comparison [17].…”
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 taxon set X , and constructing such a network whenever it exists. We show that this is NP-hard 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.
B Leo van Iersel
“…They then consider a restricted problem in which all recombination events are associated with node-disjoint recombination cycles, and they present a sufficient condition to identify such networks. Gusfield et al [2] give necessary and sufficient conditions to identify these networks, which they call "galled-trees," and they add a much more specific and realistic model of recombination events. In [3] they give a more detailed study of these node-disjoint cycles.…”
Section: Introductionmentioning
confidence: 99%
“…Thus, for extant taxa u and v we typically assume a distance d(u, v) that measures the evolutionary change between u and v. Like Wang et al [15] and Gusfield et al [2] this paper models only the case of binary characters in rooted acyclic directed graphs. Unlike [15] and [2] we shall assume that the network itself is given. We then study the problem of inferring complete distance information (such as all the branch lengths) within the network.…”
Phylogenetic relationships among taxa have usually been represented by rooted trees in which the leaves correspond to extant taxa and interior vertices correspond to extinct ancestral taxa. Recently, more general graphs than trees have been investigated in order to be able to represent hybridization, lateral gene transfer, and recombination events. A model is presented in which the genome at a vertex is represented by a binary string. In the presence of hybridization and the absence of convergent evolution and homoplasies, the evolution is modeled by an acyclic digraph. In general, it is shown how distances are computed in terms of the "originating weights" at vertices. An example shows that the distance between two vertices may not correspond to the sum of branch lengths on any path in the graph. If two vertices always have a most recent common ancestor, however, then distances can be measured along certain paths. Sufficient conditions are presented so that all the distances in a network are determined by the distances between leaves, including the root. In particular it is shown how to infer the originating weights at interior vertices from such information.
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