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Phylogenetic networks are used to represent the evolutionary history of species. Recently, the new class of orchard networks was introduced, which were later shown to be interpretable as trees with additional horizontal arcs. This makes the…

Combinatorics · Mathematics 2023-05-09 Leo van Iersel , Mark Jones , Esther Julien , Yukihiro Murakami

Jansson and Sung showed that, given a dense set of input triplets T (representing hypotheses about the local evolutionary relationships of triplets of species), it is possible to determine in polynomial time whether there exists a level-1…

Populations and Evolution · Quantitative Biology 2007-07-20 Leo van Iersel , Judith Keijsper , Steven Kelk , Leen Stougie

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

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

In the Maximize Phylogenetic Diversity problem, we are given a phylogenetic tree that represents the genetic proximity of species, and we are asked to select a subset of species of maximum phylogenetic diversity to be preserved through…

Computational Complexity · Computer Science 2026-02-16 Niels Holtgrefe , Jannik Schestag , Norbert Zeh

Genetic and comparative genomic studies indicate that extant genomes are more properly considered to be a fusion product of random mutations over generations and genomic material transfers between individuals of different lineages. This has…

Quantitative Methods · Quantitative Biology 2018-01-16 Andreas D. M. Gunawan , Bingxin Lu , Louxin Zhang

Phylogenetic networks play an important role in evolutionary biology as, other than phylogenetic trees, they can be used to accommodate reticulate evolutionary events such as horizontal gene transfer and hybridization. Recent research has…

Populations and Evolution · Quantitative Biology 2024-03-19 Linda Knüver , Mareike Fischer , Marc Hellmuth , Kristina Wicke

Phylogenomics heavily relies on well-curated sequence data sets that consist, for each gene, exclusively of 1:1-orthologous. Paralogs are treated as a dangerous nuisance that has to be detected and removed. We show here that this severe…

Discrete Mathematics · Computer Science 2017-12-19 Marc Hellmuth , Nicolas Wieseke , Marcus Lechner , Hans-Peter Lenhof , Martin Middendorf , Peter F. Stadler

In the study of rooted phylogenetic networks, analyzing the set of rooted phylogenetic trees that are embedded in such a network is a recurring task. From an algorithmic viewpoint, this analysis almost always requires an exhaustive search…

Combinatorics · Mathematics 2023-08-21 Simone Linz , Charles Semple

The evolutionary relationships between species are typically represented in the biological literature by rooted phylogenetic trees. However, a tree fails to capture ancestral reticulate processes, such as the formation of hybrid species or…

Populations and Evolution · Quantitative Biology 2024-12-09 Johanna Heiss , Daniel H. Huson , Mike Steel

In this paper we identify several serious problems that arise in the use of syntactic data from the SSWL database for the purpose of computational phylogenetic reconstruction. We show that the most naive approach fails to produce reliable…

Computation and Language · Computer Science 2016-07-12 Kevin Shu , Sharjeel Aziz , Vy-Luan Huynh , David Warrick , Matilde Marcolli

Detecting variation in the evolutionary process along chromosomes is increasingly important as whole-genome data becomes more widely available. For example, factors such as incomplete lineage sorting, horizontal gene transfer, and…

Populations and Evolution · Quantitative Biology 2017-01-03 Elizabeth S. Allman , Laura S. Kubatko , John A. Rhodes

Phylogenetic networks represent evolutionary history of species and can record natural reticulate evolutionary processes such as horizontal gene transfer and gene recombination. This makes phylogenetic networks a more comprehensive…

Populations and Evolution · Quantitative Biology 2021-06-15 Remie Janssen , Pengyu Liu

We investigate parameterized algorithms for computing the average-tree phylogenetic diversity (APD) in rooted phylogenetic networks, studying the problem under different structural parameters that capture the deviation of a network from a…

Data Structures and Algorithms · Computer Science 2026-05-01 Leo van Iersel , Mark Jones , Jannik Schestag , Celine Scornavacca , Mathias Weller

Recent work has proven the existence of extreme inbreeding in a European ancestry sample taken from the contemporary UK population \cite{nature_01}. This result brings our attention again to a math problem related to inbreeding family trees…

Populations and Evolution · Quantitative Biology 2021-09-08 C. Jarne , F A. Gómez Albarracín , M. Caruso

Phylogenetic networks generalize phylogenetic trees by allowing the modelization of events of reticulate evolution. Among the different kinds of phylogenetic networks that have been proposed in the literature, the subclass of binary…

Data Structures and Algorithms · Computer Science 2020-07-01 Gabriel Cardona , Joan Carles Pons , Celine Scornavacca

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

Here we show that, given a set of clusters C on a set of taxa X, where |X|=n, it is possible to determine in time f(k).poly(n) whether there exists a level-<= k network (i.e. a network where each biconnected component has reticulation…

Computational Complexity · Computer Science 2011-08-19 Steven Kelk , Celine Scornavacca

Binets and trinets are phylogenetic networks with two and three leaves, respectively. Here we consider the problem of deciding if there exists a binary level-1 phylogenetic network displaying a given set $\mathcal{T}$ of binary binets or…

Data Structures and Algorithms · Computer Science 2014-11-26 Katharina Huber , Leo van Iersel , Vincent Moulton , Celine Scornavacca , Taoyang Wu