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Rooted acyclic graphs appear naturally when the phylogenetic relationship of a set $X$ of taxa involves not only speciations but also recombination, horizontal transfer, or hybridization, that cannot be captured by trees. A variety of…

Populations and Evolution · Quantitative Biology 2022-04-29 Marc Hellmuth , David Schaller , Peter F. Stadler

An important problem in evolutionary biology is to reconstruct the evolutionary history of a set $X$ of species. This history is often represented as a phylogenetic network, that is, a connected graph with leaves labelled by elements in $X$…

Combinatorics · Mathematics 2017-02-01 Leo van Iersel , Vincent Moulton

Phylogenetic networks provide a more general description of evolutionary relationships than rooted phylogenetic trees. One way to produce a phylogenetic network is to randomly place $k$ arcs between the edges of a rooted binary phylogenetic…

Populations and Evolution · Quantitative Biology 2025-03-19 Michael Fuchs , Mike Steel , Qiang Zhang

Distance-based phylogenetic algorithms attempt to solve the NP-hard least squares phylogeny problem by mapping an arbitrary dissimilarity map representing biological data to a tree metric. The set of all dissimilarity maps is a Euclidean…

Populations and Evolution · Quantitative Biology 2013-07-24 Ruth Davidson , Seth Sullivant

Phylogenetic networks generalize phylogenetic trees by allowing reticulate evolutionary events such as horizontal gene transfer and hybridization. Among the many subclasses of phylogenetic networks, orchard networks have attracted…

Populations and Evolution · Quantitative Biology 2026-05-20 Peng Li , Zhiwei Liu , Yangjing Long

Phylogenetic networks are rooted, labelled directed acyclic graphs which are commonly used to represent reticulate evolution. There is a close relationship between phylogenetic networks and multi-labelled trees (MUL-trees). Indeed, any…

Populations and Evolution · Quantitative Biology 2015-06-16 Katharina T. Huber , Vincent Moulton , Mike Steel , Taoyang Wu

We introduce a new phylogenetic reconstruction algorithm which, unlike most previous rigorous inference techniques, does not rely on assumptions regarding the branch lengths or the depth of the tree. The algorithm returns a forest which is…

Populations and Evolution · Quantitative Biology 2011-09-30 Constantinos Daskalakis , Elchanan Mossel , Sebastien Roch

The number of the non-shared edges of two phylogenies is a basic measure of the dissimilarity between the phylogenies. The non-shared edges are also the building block for approximating a more sophisticated metric called the nearest…

Data Structures and Algorithms · Computer Science 2007-05-23 Wing-Kai Hon , Ming-Yang Kao , Tak-Wah Lam , Wing-Kin Sung , Siu-Ming Yiu

Phylogenetic networks provide a framework for representing evolutionary histories involving reticulate events such as hybridization or horizontal gene transfer. A central problem is to infer such networks from local structural information.…

Discrete Mathematics · Computer Science 2026-05-12 Patricia A. Ebert , Marc Hellmuth

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.…

Populations and Evolution · Quantitative Biology 2012-10-02 Leo van Iersel , Vincent Moulton

Phylogenetic networks are a generalization of phylogenetic trees that allow for the representation of evolutionary events acting at the population level, like recombination between genes, hybridization between lineages, and lateral gene…

Populations and Evolution · Quantitative Biology 2007-11-26 Gabriel Cardona , Francesc Rossello , Gabriel Valiente

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

Background: Convolutional Neural Networks can be effectively used only when data are endowed with an intrinsic concept of neighbourhood in the input space, as is the case of pixels in images. We introduce here Ph-CNN, a novel deep learning…

Quantitative Methods · Quantitative Biology 2017-09-08 Diego Fioravanti , Ylenia Giarratano , Valerio Maggio , Claudio Agostinelli , Marco Chierici , Giuseppe Jurman , Cesare Furlanello

We consider the problem of estimating the evolutionary history of a set of species (phylogeny or species tree) from several genes. It is known that the evolutionary history of individual genes (gene trees) might be topologically distinct…

Populations and Evolution · Quantitative Biology 2016-11-18 Gautam Dasarathy , Robert Nowak , Sebastien Roch

Reconciling a gene tree with a species tree is an important task that reveals much about the evolution of genes, genomes, and species, as well as about the molecular function of genes. A wide array of computational tools have been devised…

Populations and Evolution · Quantitative Biology 2012-12-11 Yun Yu , Luay Nakhleh

In mathematical phylogenetics, evolutionary relationships are often represented by trees and networks. The latter are typically used whenever the relationships cannot be adequately described by a tree, which happens when so-called…

Populations and Evolution · Quantitative Biology 2025-12-05 Mirko Wilde , Mareike Fischer

In biodiversity conservation it is often necessary to prioritize the species to conserve. Existing approaches to prioritization, e.g. the Fair Proportion Index and the Shapley Value, are based on phylogenetic trees and rank species…

Populations and Evolution · Quantitative Biology 2018-02-07 Kristina Wicke , Mareike Fischer

An important problem in phylogenetics is the construction of phylogenetic trees. One way to approach this problem, known as the supertree method, involves inferring a phylogenetic tree with leaves consisting of a set $X$ of species from a…

Populations and Evolution · Quantitative Biology 2017-11-21 Katharine T. Huber , Vincent Moulton , Charles Semple , Taoyang Wu

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

Phylogenetic trees represent certain species and their likely ancestors. In such a tree, present-day species are leaves and an edge from u to v indicates that u is an ancestor of v. Weights on these edges indicate the phylogenetic distance.…

Populations and Evolution · Quantitative Biology 2025-10-08 Jannik Schestag