Trinets encode tree-child and level-2 phylogenetic networks

@article{Iersel2014TrinetsET,
  title={Trinets encode tree-child and level-2 phylogenetic networks},
  author={Leo van Iersel and Vincent Moulton},
  journal={Journal of Mathematical Biology},
  year={2014},
  volume={68},
  pages={1707-1729}
}
  • L. Iersel, V. Moulton
  • Published 1 October 2012
  • Computer Science, Biology
  • Journal of Mathematical Biology
Phylogenetic networks generalize evolutionary trees, and are commonly used to represent evolutionary histories of species that undergo reticulate evolutionary processes such as hybridization, recombination and lateral gene transfer. Recently, there has been great interest in trying to develop methods to construct rooted phylogenetic networks from triplets, that is rooted trees on three species. However, although triplets determine or encode rooted phylogenetic trees, they do not in general… 
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References

SHOWING 1-10 OF 43 REFERENCES
Encoding and Constructing 1-Nested Phylogenetic Networks with Trinets
TLDR
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.
Comparison of Tree-Child Phylogenetic Networks
TLDR
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.
On encodings of phylogenetic networks of bounded level
Phylogenetic networks have now joined phylogenetic trees in the center of phylogenetics research. Like phylogenetic trees, such networks canonically induce collections of phylogenetic trees,
Phylogenetic Networks: Introduction to phylogenetic networks
TLDR
This chapter gives an introduction to the topic of phylogenetics networks, very briefly describing the fundamental concepts and summarizing some of the most important methods that are available for the computation of phylogenetic networks.
When two trees go to war.
Evolutionary Phylogenetic Networks: Models and Issues
TLDR
This chapter focuses less on surveying existing tools, and addresses in more detail issues that are central to the accurate reconstruction of phylogenetic networks, which explicitly model reticulate evolutionary events.
Uniqueness, Intractability and Exact Algorithms: Reflections on Level-k Phylogenetic Networks
TLDR
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.
A Practical Algorithm for Reconstructing Level-1 Phylogenetic Networks
TLDR
An efficient, practical algorithm for reconstructing level-1 phylogenetic networks-a type of network slightly more general than a phylogenetic tree-from triplets that is able to construct networks consistent with a high percentage of input triplets, even when theseinput triplets are affected by a low to moderate level of noise.
Phylogenetic Networks - Concepts, Algorithms and Applications
TLDR
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.
A distance metric for a class of tree-sibling phylogenetic networks
TLDR
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.
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