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Related papers: Counting Phylogenetic Networks with Few Reticulati…

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Phylogenetic trees and networks are graphs used to model evolutionary relationships, with trees representing strictly branching histories and networks allowing for events in which lineages merge, called reticulation events. While the…

Populations and Evolution · Quantitative Biology 2026-04-17 Martin Frohn , Niels Holtgrefe , Leo van Iersel , Mark Jones , Steven Kelk

Tree-child networks are one of the most prominent network classes for modeling evolutionary processes which contain reticulation events. Several recent studies have addressed counting questions for {\it bicombining tree-child networks}…

Combinatorics · Mathematics 2022-03-16 Yu-Sheng Chang , Michael Fuchs , Hexuan Liu , Michael Wallner , Guan-Ru Yu

We study the enumeration of spinal tree-child phylogenetic networks, a rigid family of tree-child networks in which all internal vertices lie on a single root--to--leaf path. We provide two complementary combinatorial frameworks. First, we…

Combinatorics · Mathematics 2026-05-12 Pau Vives , Anna de Mier , Gabriel Cardona , Joan Carles Pons

Orchard and tree-child networks share an important property with phylogenetic trees: they can be completely reduced to a single node by iteratively deleting cherries and reticulated cherries. As it is the case with phylogenetic trees, the…

Populations and Evolution · Quantitative Biology 2024-03-22 Tomás M. Coronado , Joan Carles Pons , Gabriel Riera

We present the first fixed-parameter algorithm for constructing a tree-child phylogenetic network that displays an arbitrary number of binary input trees and has the minimum number of reticulations among all such networks. The algorithm…

Discrete Mathematics · Computer Science 2019-07-22 Leo van Iersel , Remie Janssen , Mark Jones , Yukihiro Murakami , Norbert Zeh

Galled trees are widely studied as a recombination model in population genetics. This class of phylogenetic networks is generalized into galled networks by relaxing a structural condition. In this work, a linear recurrence formula is given…

Populations and Evolution · Quantitative Biology 2018-12-21 Andreas DM Gunawan , Jeyaram Rathin , Louxin Zhang

Phylogenetic networks are mathematical structures for modeling and visualization of reticulation processes in the study of evolution. Galled networks, reticulation visible networks, nearly-stable networks and stable-child networks are the…

Populations and Evolution · Quantitative Biology 2015-10-02 Andreas D. M. Gunawan , Louxin Zhang

Tree-child networks are an important class of phylogenetic network used to model reticulate evolutionary processes. These networks have attracted increasing attention from researchers with interests in both combinatorics and algorithms. A…

Combinatorics · Mathematics 2026-05-11 Hexuan Liu , Michael Wallner , Guan-Ru Yu

The mathematical analysis of random phylogenetic networks via analytic and algorithmic methods has received increasing attention in the past years. In the present work we introduce branching process methods to their study. This approach…

Probability · Mathematics 2021-02-23 Benedikt Stufler

Phylogenetic networks provide a way to describe and visualize evolutionary histories that have undergone so-called reticulate evolutionary events such as recombination, hybridization or horizontal gene transfer. The level k of a network…

Populations and Evolution · Quantitative Biology 2008-07-21 Leo van Iersel , Steven Kelk , Matthias Mnich

Phylogenetic networks generalize phylogenetic trees by representing reticulate evolution. Tree-based networks and their support trees have been extensively studied, but not all networks are tree-based. To measure how far such networks are…

Populations and Evolution · Quantitative Biology 2026-05-27 Takatora Suzuki

Rooted phylogenetic networks provide an explicit representation of the evolutionary history of a set $X$ of sampled species. In contrast to phylogenetic trees which show only speciation events, networks can also accommodate reticulate…

Combinatorics · Mathematics 2021-01-01 Peter L. Erdos , Charles Semple , Mike Steel

Reticulate evolution gives rise to complex phylogenetic networks, making their interpretation challenging. A typical approach is to extract trees within such networks. Since Francis and Steel's seminal paper, "Which Phylogenetic Networks…

Combinatorics · Mathematics 2025-05-20 Takatora Suzuki , Momoko Hayamizu

Phylogenetic networks are a generalization of phylogenetic trees that allow for the representation of non-treelike evolutionary events, like recombination, hybridization, or lateral gene transfer. In this paper, we present and study a new…

Populations and Evolution · Quantitative Biology 2007-08-28 Gabriel Cardona , Francesc Rossello , Gabriel Valiente

Tree-child networks are an important network class which are used in phylogenetics to model reticulate evolution. In a recent paper, Pons and Batle (2021) conjectured a relation between tree-child networks and certain words. In this short…

Populations and Evolution · Quantitative Biology 2021-10-11 Michael Fuchs , Hexuan Liu , Guan-Ru Yu

Rooted phylogenetic networks allow biologists to represent evolutionary relationships between present-day species by revealing ancestral speciation and hybridization events. A convenient and well-studied class of such networks are…

Populations and Evolution · Quantitative Biology 2026-02-02 Qiang Zhang , Mike Steel

Phylogenetic networks generalize phylogenetic trees in order to model reticulation events. Although the comparison of phylogenetic trees is well studied, and there are multiple ways to do it in an efficient way, the situation is much…

Populations and Evolution · Quantitative Biology 2023-02-21 Gabriel Cardona , Joan Carles Pons , Gerard Ribas , Tomás Martínez Coronado

Phylogenetic networks are a type of leaf-labelled, acyclic, directed graph used by biologists to represent the evolutionary history of species whose past includes reticulation events. A phylogenetic network is tree-child if each non-leaf…

Combinatorics · Mathematics 2017-11-27 Magnus Bordewich , Katharina T Huber , Vincent Moulton , Charles Semple

We find the exponential generating function for permutations with all valleys even and all peaks odd, and use it to determine the asymptotics for its coefficients, answering a question posed by Liviu Nicolaescu. The generating function can…

Combinatorics · Mathematics 2014-08-11 Ira M. Gessel , Yan Zhuang

Phylogenetic networks are an important way to represent evolutionary histories that involve reticulations such as hybridization or horizontal gene transfer, yet fundamental questions such as how many networks there are that satisfy certain…

Populations and Evolution · Quantitative Biology 2025-02-21 Andrew Francis , Michael Hendriksen