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Galled trees are studied as a recombination model in theoretic population genetics. This class of phylogenetic networks has been generalized to tree-child networks, normal networks and tree-based networks by relaxing a structural condition.…

Populations and Evolution · Quantitative Biology 2019-08-05 Louxin Zhang

A binary phylogenetic network may or may not be obtainable from a tree by the addition of directed edges (arcs) between tree arcs. Here, we establish a precise and easily tested criterion (based on `2-SAT') that efficiently determines…

Populations and Evolution · Quantitative Biology 2015-05-25 Andrew R. Francis , Mike Steel

Invariants for complicated objects such as those arising in phylogenetics, whether they are invariants as matrices, polynomials, or other mathematical structures, are important tools for distinguishing and working with such objects. In this…

Populations and Evolution · Quantitative Biology 2022-04-06 Joan Carles Pons , Tomás M. Coronado , Michael Hendriksen , Andrew Francis

Phylogenetic networks provide a means of describing the evolutionary history of sets of species believed to have undergone hybridization or gene flow during their evolution. The mutation process for a set of such species can be modeled as a…

Populations and Evolution · Quantitative Biology 2022-11-23 Travis Barton , Elizabeth Gross , Colby Long , Joseph Rusinko

In evolutionary studies it is common to use phylogenetic trees to represent the evolutionary history of a set of species. However, in case the transfer of genes or other genetic information between the species or their ancestors has…

Combinatorics · Mathematics 2022-02-15 Katharina T. Huber , Vincent Moulton , Guillaume E. Scholz

Many classes of phylogenetic networks have been proposed in the literature. A feature of several of these classes is that if one restricts a network in the class to a subset of its leaves, then the resulting network may no longer lie within…

Populations and Evolution · Quantitative Biology 2025-09-24 Michael Fuchs , Mike Steel

In phylogenetics, a central problem is to infer the evolutionary relationships between a set of species $X$; these relationships are often depicted via a phylogenetic tree -- a tree having its leaves univocally labeled by elements of $X$…

Data Structures and Algorithms · Computer Science 2016-04-12 Julien Baste , Christophe Paul , Ignasi Sau , Celine Scornavacca

Phylogenetic networks are an extension of phylogenetic trees that allow for the representation of reticulate evolution events. One of the classes of networks that has gained the attention of the scientific community over the last years is…

Populations and Evolution · Quantitative Biology 2023-08-01 Gabriel Cardona , Gerard Ribas , Joan Carles Pons

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

The inference of phylogenetic networks, which model complex evolutionary processes including hybridization and gene flow, remains a central challenge in evolutionary biology. Until now, statistically consistent inference methods have been…

Populations and Evolution · Quantitative Biology 2025-10-14 Niels Holtgrefe , Elizabeth S. Allman , Hector Baños , Leo van Iersel , Vincent Moulton , John A. Rhodes , Kristina Wicke

Recently, so-called treebased phylogenetic networks have gained considerable interest in the literature, where a treebased network is a network that can be constructed from a phylogenetic tree, called the base tree, by adding additional…

Populations and Evolution · Quantitative Biology 2019-11-28 Mareike Fischer , Michelle Galla , Lina Herbst , Yangjing Long , Kristina Wicke

Phylogenetic networks extend phylogenetic trees to model non-vertical inheritance, by which a lineage inherits material from multiple parents. The computational complexity of estimating phylogenetic networks from genome-wide data with…

Populations and Evolution · Quantitative Biology 2022-06-28 Jingcheng Xu , Cécile Ané

Phylogenetic networks are notoriously difficult to reconstruct. Here we suggest that it can be useful to view unknown genetic distance along edges in phylogenetic networks as analogous to unknown resistance in electric circuits. This…

Combinatorics · Mathematics 2020-10-01 Stefan Forcey , Drew Scalzo

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

The need for structures capable of accommodating complex evolutionary signals such as those found in, for example, wheat has fueled research into phylogenetic networks. Such structures generalize the standard phylogenetic tree model by also…

Combinatorics · Mathematics 2015-11-30 Philippe Gambette , Katharina T. Huber , Guillaume E. Scholz

A directed phylogenetic network is tree-child if every non-leaf vertex has a child that is not a reticulation. As a class of directed phylogenetic networks, tree-child networks are very useful from a computational perspective. For example,…

Combinatorics · Mathematics 2026-03-10 Leo van Iersel , Mark Jones , Simone Linz , Norbert Zeh

Phylogenetic networks are generalizations of phylogenetic trees that allow the representation of reticulation events such as horizontal gene transfer or hybridization, and can also represent uncertainty in inference. A subclass of these,…

Populations and Evolution · Quantitative Biology 2019-10-15 Mareike Fischer , Andrew Francis

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 are used to represent reticulate evolution. Unrooted phylogenetic networks form a special class of such networks, which naturally generalize unrooted phylogenetic trees.…

Populations and Evolution · Quantitative Biology 2016-01-11 Katharina T. Huber , Vincent Moulton , Taoyang Wu

Phylogenetic networks are often constructed by merging multiple conflicting phylogenetic signals into a directed acyclic graph. It is interesting to explore whether a network constructed in this way induces biologically-relevant…

Populations and Evolution · Quantitative Biology 2017-07-13 Steven Kelk , Fabio Pardi , Celine Scornavacca , Leo van Iersel