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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 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 trees are simple models of evolutionary processes. They describe conditionally independent divergent evolution of taxa from common ancestors. Phylogenetic trees commonly do not have enough flexibility to adequately model all…

Populations and Evolution · Quantitative Biology 2025-11-11 Jonathan D. Mitchell , Barbara R. Holland

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

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

Reconstructing the evolutionary past of a family of genes is an important aspect of many genomic studies. To help with this, simple operations on a set of sequences called orthology relations may be employed. In addition to being…

Discrete Mathematics · Computer Science 2016-03-16 K. T. Huber , G. E. Scholz

Phylogenetic networks have gained prominence over the years due to their ability to represent complex non-treelike evolutionary events such as recombination or hybridization. Popular combinatorial objects used to construct them are triplet…

Combinatorics · Mathematics 2016-10-19 P. Gambette , K. T. Huber , S. Kelk

A fundamental problem in the study of phylogenetic networks is to determine whether or not a given phylogenetic network contains a given phylogenetic tree. We develop a quadratic-time algorithm for this problem for binary nearly-stable…

Data Structures and Algorithms · Computer Science 2022-08-29 Philippe Gambette , Andreas D. M. Gunawan , Anthony Labarre , Stéphane Vialette , Louxin Zhang

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

In evolutionary biology, networks are becoming increasingly used to represent evolutionary histories for species that have undergone non-treelike or reticulate evolution. Such networks are essentially directed acyclic graphs with a leaf set…

Populations and Evolution · Quantitative Biology 2023-08-23 Katharina T. Huber , Leo van Iersel , Vincent Moulton , Guillaume Scholz

The rich and varied ways that genetic material can be passed between species has motivated extensive research into the theory of phylogenetic networks. Features that align with biological processes, or with desirable mathematical…

Populations and Evolution · Quantitative Biology 2025-08-12 Andrew Francis

The evolution processes of complex systems carry key information in the systems' functional properties. Applying machine learning algorithms, we demonstrate that the historical formation process of various networked complex systems can be…

Physics and Society · Physics 2024-03-25 Junya Wang , Yi-Jiao Zhang , Cong Xu , Jiaze Li , Jiachen Sun , Jiarong Xie , Ling Feng , Tianshou Zhou , Yanqing Hu

Phylogenetic networks are a generalization of phylogenetic trees that are used in biology to represent reticulate or non-treelike evolution. Recently, several algorithms have been developed which aim to construct phylogenetic networks from…

Populations and Evolution · Quantitative Biology 2011-10-05 K. T. Huber , V. Moulton

Phylogenetic networks are a generalization of phylogenetic trees that are used to represent non-tree-like evolutionary histories that arise in organisms such as plants and bacteria, or uncertainty in evolutionary histories. An…

Populations and Evolution · Quantitative Biology 2017-12-08 Andrew Francis , Katharina Huber , Vincent Moulton

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 to leaf-labeled directed acyclic graphs that represent ancestral relationships between species whose past includes non-tree-like events such as hybridization and horizontal…

Combinatorics · Mathematics 2021-04-13 Janosch Döcker , Simone Linz , Charles Semple

Phylogenetic networks extend phylogenetic trees to allow for modeling reticulate evolutionary processes such as hybridization. They take the shape of a rooted, directed, acyclic graph, and when parameterized with evolutionary parameters,…

Populations and Evolution · Quantitative Biology 2018-08-28 R. A. L. Elworth , H. A. Ogilvie , J. Zhu , L. Nakhleh

Phylogenetic networks are a generalisation of phylogenetic trees that allow for more complex evolutionary histories that include hybridisation-like processes. It is of considerable interest whether a network can be considered `tree-like' or…

Populations and Evolution · Quantitative Biology 2017-11-21 Michael Hendriksen

One strategy for reconstruction of phylogenetic networks is to solve the phylogenetic network problem, which involves inferring phylogenetic trees first and subsequently computing the smallest phylogenetic network that displays all the…

Combinatorics · Mathematics 2023-09-26 Laurent Bulteau , Louxin Zhang

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