# 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…

## 19 Citations

### Generation of Tree-Child phylogenetic networks

- Computer ScienceArXiv
- 2019

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

- Mathematics
- 2020

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

- Computer ScienceDiscret. Appl. Math.
- 2022

### Counting phylogenetic networks of level 1 and 2

- MathematicsJournal of Mathematical Biology
- 2020

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

- MathematicsAustralas. J Comb.
- 2022

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

- Computer Science, MathematicsRandom Struct. Algorithms
- 2022

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

- Computer ScienceJ. Comput. Syst. Sci.
- 2020

### Generation of Binary Tree-Child phylogenetic networks

- Computer SciencePLoS Comput. Biol.
- 2019

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

- Computer ScienceAofA
- 2022

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

- BiologyBMC Bioinformatics
- 2019

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.

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