• Corpus ID: 54981120

Counting phylogenetic networks with few reticulation vertices: tree-child and normal networks

@article{Fuchs2018CountingPN,
  title={Counting phylogenetic networks with few reticulation vertices: tree-child and normal networks},
  author={Michael Fuchs and Bernhard Gittenberger and Marefatollah Mansouri},
  journal={Australas. J Comb.},
  year={2018},
  volume={73},
  pages={385-423}
}
In recent decades, phylogenetic networks have become a standard tool in modeling evolutionary processes. Nevertheless, basic combinatorial questions about them are still largely open. For instance, even the asymptotic counting problem for the class of phylogenetic networks and subclasses is unsolved. In this paper, we propose a method based on generating functions to count networks with few reticulation vertices for two subclasses which are important in applications: tree-child networks and… 
View PDF on arXiv
19 Citations
Highly Influential Citations
1
Background Citations
5
Methods Citations
1

Figures from this paper

19 Citations

Generation of Tree-Child phylogenetic networks

This paper addresses the problem of generating all possible binary tree-child networks with a given number of leaves in an efficient way via reduction/augmentation operations that extend and generalize analogous operations for phylogenetic trees and are biologically relevant.

Counting Phylogenetic Networks with Few Reticulation Vertices: Exact Enumeration and Corrections

In previous work, we gave asymptotic counting results for the number of tree-child and normal networks with $k$ reticulation vertices and explicit exponential generating functions of the counting…

Counting phylogenetic networks with few reticulation vertices: A second approach

Counting phylogenetic networks of level 1 and 2

This paper provides enumeration formulas (exact and asymptotic) for rooted and unrooted level-1 and level-2 phylogenetic networks with a given number of leaves and proves that the distribution of some parameters of these networks are asymPTotically normally distributed.

Counting general phylogenetic networks

We provide precise asymptotic estimates for the number of general phylogenetic networks by using analytic combinatorial methods. Recently, this approach is studied by Fuchs, Gittenberger, and the…

A branching process approach to level‐k phylogenetic networks

It is shown that the depth process of vertices in a large network converges towards a Brownian excursion after rescaling by n−1/2 and Benjamini–Schramm convergence of large random level‐k networks towards a novel random infinite network.

Counting and enumerating tree-child networks and their subclasses

Generation of Binary Tree-Child phylogenetic networks

This paper addresses the problem of generating all possible binary tree-child networks with a given number of leaves in an efficient way via reduction/augmentation operations that extend and generalize analogous operations for phylogenetic trees, and are biologically relevant.

Enumeration of d-Combining Tree-Child Networks

Results and conjectures on the distributional behavior of the number of reticulation nodes of a network which is drawn uniformly at random from the set of all tree-child networks with the same number of leaves are given.

Generating normal networks via leaf insertion and nearest neighbor interchange

It is proved that all tree-child (resp. normal) networks with k reticulate nodes on n taxa can be uniquely generated via three operations from all the tree- Child networks, which is a generalization of an enumeration procedure for phylogenetic trees into one for normal networks.

References

SHOWING 1-10 OF 35 REFERENCES

Phylogenetic Networks that Display a Tree Twice

This work investigates the question of whether or not a phylogenetic network embeds a tree twice and gives a quadratic-time algorithm to solve this problem for a class of networks that is more general than tree-child networks.

Combinatorial Scoring of Phylogenetic Networks

A novel method for measuring the specificity of a given phylogenetic network in terms of the total number of distributions of character states at the leaves that the network may impose, applicable for arbitrary trees and networks under some reasonable assumptions.

Comparison of Tree-Child Phylogenetic Networks

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.

Algorithms for Reticulate Networks of Multiple Phylogenetic Trees

This paper presents a fast fixed-parameter algorithm for constructing one or all optimal type-I reticulate networks of multiple phylogenetic trees, and uses the algorithm together with other ideas to obtain an algorithm for estimating a lower bound on the reticulation number of an optimaltype-II reticulated network of the input trees.

Unicyclic networks: compatibility and enumeration

  • C. SempleM. Steel
  • Biology
    IEEE/ACM Transactions on Computational Biology and Bioinformatics
  • 2006
This work characterize when a set of binary phylogenetic trees is displayed by a unicyclic network in terms of tree rearrangement operations, which leads to a triple-wise compatibility theorem and a simple, fast algorithm to determine 1-cycle compatibility.

Lost in space? Generalising subtree prune and regraft to spaces of phylogenetic networks.

Counting Trees in a Phylogenetic Network Is \#P-Complete

It is proved that counting the number of phylogenetic trees inferred by a (binary) phylogenetic network is \#P-complete.

Tree-like reticulation networks--when do tree-like distances also support reticulate evolution?

Determining the asymptotic number of phylogenetic trees

Formulas are found for the exact numbers of phylogenetic trees with n labels, and numerical results are presented for selected n⩽40, and the asymptotic behaviour of these numbers as n → ∞ is determined.

Size of a phylogenetic network