Related papers: Counting Tree-Child Networks and Their Subclasses

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…

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.…

We propose the class of galled tree-child networks which is obtained as intersection of the classes of galled networks and tree-child networks. For the latter two classes, (asymptotic) counting results and stochastic results have been…

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…

Phylogenetic network is an evolutionary model that uses a rooted directed acyclic graph (instead of a tree) to model an evolutionary history of species in which reticulate events (e.g., hybrid speciation or horizontal gene transfer)…

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…

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}…

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…

Rooted phylogenetic networks are rooted acyclic digraphs. They are used to model complex evolution where hybridization, recombination and other reticulation events play important roles. A rigorous definition of network compression is…

Rooted binary phylogenetic networks are extensions of rooted binary trees, adding reticulation nodes that are designed to represent evolutionary processes that involve hybridization events. Enumerative combinatorics studies have counted…

Inference of phylogenetic networks is of increasing interest in the genomic era. However, the extent to which phylogenetic networks are identifiable from various types of data remains poorly understood, despite its crucial role in…

A large class of phylogenetic networks can be obtained from trees by the addition of horizontal edges between the tree edges. These networks are called tree based networks. Reticulation-visible networks and child-sibling networks are all…

In recent decades, phylogenetic networks have become a standard tool in modeling evolutionary processes. Nevertheless, basic combinatorial questions about them are still largely open. For instance, even the asymptotic counting problem for…

Tree-child networks, one of the prominent network classes in phylogenetics, have been introduced for the purpose of modeling reticulate evolution. Recently, the first author together with Gittenberger and Mansouri (2019) showed that the…

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…

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…

Network reconstruction lies at the heart of phylogenetic research. Two well studied classes of phylogenetic networks include tree-child networks and level-$k$ networks. In a tree-child network, every non-leaf node has a child that is a tree…

Rooted phylogenetic networks are used by biologists to infer and represent complex evolutionary relationships between species that cannot be accurately explained by a phylogenetic tree. Tree-child networks are a particular class of rooted…

Galled trees, evolutionary networks with isolated reticulation cycles, have appeared under several slightly different definitions in the literature. In this paper we establish the actual relationships between the main four such alternative…

Galled trees, directed acyclic graphs that model evolutionary histories with isolated hybridization events, have become very popular due to both their biological significance and the existence of polynomial time algorithms for their…