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

Huber, Katharina T.; Iersel, Leo van; Moulton, Vincent; Scornavacca, Céline; Wu, Taoyang

doi:10.1007/s00453-015-0069-8

Cited by 32 publications

(25 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The closest works to our proposed method here are those of Huber et al (2017); Hejase et al (2018). In (Huber et al, 2017), the authors devised an algorithm that is restricted to combining binet and trinet topologies (no divergence times) into level-1 networks (A phylogenetic network is level-1 if no two cycles in its underlying undirected graphs share a node). The work of Hejase et al (2018) proposed another divide-and-conquer method to infer subnetworks and combine them.…”

Section: Introductionmentioning

confidence: 99%

A Divide-and-Conquer Method for Scalable Phylogenetic Network Inference from Multi-locus Data

Zhu¹,

Liu²,

Ogilvie³

et al. 2019

Preprint

View full text Add to dashboard Cite

Reticulate evolutionary histories, such as those arising in the presence of hybridization, are best modeled as phylogenetic networks. Recently developed methods allow for statistical inference of phylogenetic networks while also accounting for other processes, such as incomplete lineage sorting (ILS). However, these methods can only handle a small number of loci from a handful of genomes. In this paper, we introduce a novel two-step method for scalable inference of phylogenetic networks from the sequence alignments of multiple, unlinked loci. The method infers networks on subproblems and then merges them into a network on the full set of taxa. To reduce the number of trinets to infer, we formulate a Hitting Set version of the problem of finding a small number of subsets, and implement a simple heuristic to solve it. We studied their performance, in terms of both running time and accuracy, on simulated as well as on biological data sets. The two-step method accurately infers phylogenetic networks at a scale that is infeasible with existing methods. The results are a significant and promising step towards accurate, large-scale phylogenetic network inference.

show abstract

Section: Introductionmentioning

confidence: 99%

A Divide-and-Conquer Method for Scalable Phylogenetic Network Inference from Multi-locus Data

Zhu¹,

Liu²,

Ogilvie³

et al. 2019

Preprint

View full text Add to dashboard Cite

show abstract

“…, τ 12 on X = {x, y, z} from [7] that are also level-1 networks in our sense. In the same paper it was observed that even the slightly more general 1-nested networks are uniquely determined by their induced trinet sets (see also [8] for more on constructing level-1 networks from trinets, and [14] for an extension of this result to other classes of phylogenetic networks).…”

Section: δ-Triplets δ-Tricycles and δ-Forksmentioning

confidence: 93%

Beyond Representing Orthology Relations by Trees

Huber

2016

Algorithmica

View full text Add to dashboard Cite

Reconstructing the evolutionary past of a family of genes is an important aspect of many genomic studies. To help with this, simple operations on a set of sequences called orthology relations may be employed. In addition to being interesting from a practical point of view they are also attractive from a theoretical perspective in that e. g. a characterization is known for when such a relation is representable by a certain type of phylogenetic tree. For an orthology relation inferred from real biological data it is however generally too much to hope for that it satisfies that characterization. Rather than trying to correct the data in some way or another which has its own drawbacks, as an alternative, we propose to represent an orthology relation δ in terms of a structure more general than a phylogenetic tree called a phylogenetic network. To compute such a network in the form of a level-1 representation for δ, we introduce the novel Network-Popping algorithm which has several attractive properties. In addition, we characterize orthology relations δ on some set X that have a level-1 representation in terms of eight natural properties for δ as well as in terms for level-1 representations of orthology relations on certain subsets of X. Date

show abstract

“…2015 for a related algorithm). In particular, a sink set of can be found in polynomial time by computing the strongly connected components of (Tarjan 1972) and checking for each of them whether it is a sink set.…”

Section: Complexity Of Binet Compatibilitymentioning

confidence: 99%

Binets: Fundamental Building Blocks for Phylogenetic Networks

et al. 2017

Self Cite

View full text Add to dashboard Cite

Phylogenetic networks are a generalization of evolutionary trees that are used by biologists to represent the evolution of organisms which have undergone reticulate evolution. Essentially, a phylogenetic network is a directed acyclic graph having a unique root in which the leaves are labelled by a given set of species. Recently, some approaches have been developed to construct phylogenetic networks from collections of networks on 2- and 3-leaved networks, which are known as binets and trinets, respectively. Here we study in more depth properties of collections of binets, one of the simplest possible types of networks into which a phylogenetic network can be decomposed. More specifically, we show that if a collection of level-1 binets is compatible with some binary network, then it is also compatible with a binary level-1 network. Our proofs are based on useful structural results concerning lowest stable ancestors in networks. In addition, we show that, although the binets do not determine the topology of the network, they do determine the number of reticulations in the network, which is one of its most important parameters. We also consider algorithmic questions concerning binets. We show that deciding whether an arbitrary set of binets is compatible with some network is at least as hard as the well-known graph isomorphism problem. However, if we restrict to level-1 binets, it is possible to decide in polynomial time whether there exists a binary network that displays all the binets. We also show that to find a network that displays a maximum number of the binets is NP-hard, but that there exists a simple polynomial-time 1/3-approximation algorithm for this problem. It is hoped that these results will eventually assist in the development of new methods for constructing phylogenetic networks from collections of smaller networks.

show abstract

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

Cited by 32 publications

References 28 publications

A Divide-and-Conquer Method for Scalable Phylogenetic Network Inference from Multi-locus Data

A Divide-and-Conquer Method for Scalable Phylogenetic Network Inference from Multi-locus Data

Beyond Representing Orthology Relations by Trees

Binets: Fundamental Building Blocks for Phylogenetic Networks

Contact Info

Product

Resources

About