# A Practical Algorithm for Reconstructing Level-1 Phylogenetic Networks

@article{Huber2011APA, title={A Practical Algorithm for Reconstructing Level-1 Phylogenetic Networks}, author={Katharina T. Huber and Leo van Iersel and Steven M. Kelk and Radosław Suchecki}, journal={IEEE/ACM Transactions on Computational Biology and Bioinformatics}, year={2011}, volume={8}, pages={635-649} }

Recently, much attention has been devoted to the construction of phylogenetic networks which generalize phylogenetic trees in order to accommodate complex evolutionary processes. Here, we present an efficient, practical algorithm for reconstructing level-1 phylogenetic networks-a type of network slightly more general than a phylogenetic tree-from triplets. Our algorithm has been made publicly available as the program Lev1athan. It combines ideas from several known theoretical algorithms for…

## Figures from this paper

## 25 Citations

### An algorithm for reconstructing level-2 phylogenetic networks from trinets

- Computer ScienceInf. Process. Lett.
- 2022

### Encoding and Constructing 1-Nested Phylogenetic Networks with Trinets

- Biology, Computer ScienceAlgorithmica
- 2012

This work shows that for a special, well-studied type of phylogenetic network, the trinets displayed by a 1-nested network always encode the network, which uses phylogenetic networks on 3-element subsets of a set, or trinet, rather than triplets.

### Netcombin: An algorithm for constructing optimal phylogenetic network from rooted triplets

- Computer SciencePloS one
- 2020

The experimental results on simulated data obtained from biologically generated sequences data indicate that by considering the trade-off between speed and precision, the Netcombin outperforms the others.

### NetCombin: An algorithm for optimal level-k network construction from triplets

- Computer SciencebioRxiv
- 2020

In this research, a new algorithm called Netcombin is introduced to construct an optimal network which is consistent with input triplets, based on binarization and expanding processes.

### How Much Information is Needed to Infer Reticulate Evolutionary Histories?

- BiologySystematic biology
- 2015

It is shown that even if all of the building blocks for some reticulate evolutionary history were to be taken as the input for any given network building method, the method might still output an incorrect history.

### Phylogenetic Networks - Concepts, Algorithms and Applications

- Biology
- 2010

This book provides the first interdisciplinary overview of phylogenetic networks, beginning with a concise introduction to both phylogenetic trees and phylogenetic Networks, and presenting the fundamental concepts and results for both rooted and unrooted phylogenetics networks.

### Phylogenetic consensus networks: Computing a consensus of 1-nested phylogenetic networks

- Biology
- 2021

The approach builds on a previous result by Roselló et al. that describes an encoding for any 1-nested phylogenetic network in terms of a collection of ordered pairs of subsets of X and uses this characterization to compute a consensus network in O(t|X| + |X|) time.

### Trinets encode tree-child and level-2 phylogenetic networks

- Computer Science, BiologyJournal of mathematical biology
- 2014

It is proved that recoverable binary level-2 networks and binary tree-child networks are also encoded by their trinets, and some additional evidence is provided in support of the conjecture thattrinets encode all recoverable rooted phylogenetic networks.

### Hierarchies from Lowest Stable Ancestors in Nonbinary Phylogenetic Networks

- Computer ScienceJ. Classif.
- 2019

A novel approach to understanding the structure of networks that are not necessarily binary by defining the concept of a closed set and showing that the collection of closed sets of a network forms a hierarchy, and that this hierarchy can be deduced from either the subtrees or subnetworks on all 3-subsets.

### A cubic-time algorithm for computing the trinet distance between level-1 networks

- Computer ScienceInf. Process. Lett.
- 2017

## References

SHOWING 1-10 OF 47 REFERENCES

### Comparison of Tree-Child Phylogenetic Networks

- BiologyIEEE/ACM Transactions on Computational Biology and Bioinformatics
- 2009

An injective representation of these networks as multisets of vectors of natural numbers, their path multiplicity vectors are provided, and this representation is used to define a distance on this class that extends the well-known Robinson-Foulds distance for phylogenetic trees and to give an alignment method for pairs of networks in this class.

### Uniqueness, Intractability and Exact Algorithms: Reflections on Level-k Phylogenetic Networks

- Computer ScienceJ. Bioinform. Comput. Biol.
- 2009

This work gives an exact algorithm for constructing level-1 networks consistent with a maximum number of input triplets, and proves that for all k > or = 1 it is NP-hard to construct a level-k network consistent with allinput triplets.

### Constructing the Simplest Possible Phylogenetic Network from Triplets

- Computer ScienceAlgorithmica
- 2009

It is shown that if T is precisely equal to the set of triplets consistent with some network, then one 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.

### On encodings of phylogenetic networks of bounded level

- BiologyJournal of mathematical biology
- 2012

Phylogenetic networks have now joined phylogenetic trees in the center of phylogenetics research. Like phylogenetic trees, such networks canonically induce collections of phylogenetic trees,…

### A distance metric for a class of tree-sibling phylogenetic networks

- BiologyBioinform.
- 2008

A distance measure on the class of semi-binary tree-sibling time consistent phylogenetic networks, which generalize tree-child time consistent evolutionary networks, and thus also galled-trees, which can be computed in polynomial time by means of simple algorithms.

### Phylogenetic Networks - Concepts, Algorithms and Applications

- Biology
- 2010

This book provides the first interdisciplinary overview of phylogenetic networks, beginning with a concise introduction to both phylogenetic trees and phylogenetic Networks, and presenting the fundamental concepts and results for both rooted and unrooted phylogenetics networks.

### Worst-case optimal approximation algorithms for maximizing triplet consistency within phylogenetic networks

- MathematicsJ. Discrete Algorithms
- 2010

### Metrics for Phylogenetic Networks II: Nodal and Triplets Metrics

- BiologyIEEE/ACM Transactions on Computational Biology and Bioinformatics
- 2009

This paper generalizes to phylogenetic networks two metrics that have already been introduced in the literature for phylogenetic trees: the nodal distance and the triplets distance and proves that they are metrics on any class of tree-child time consistent phylogenetics networks on the same set of taxa, as well as some basic properties for them.

### Extended Newick: it is time for a standard representation of phylogenetic networks

- BiologyBMC Bioinformatics
- 2008

The adoption of the extended Newick format as a standard for the representation of phylogenetic network is an important step towards the publication of explicit phylogenetics networks in peer-reviewed journals and their incorporation in a future database of published phylogenetic networks.