Related papers: Combinatorial comparison of general galled trees, …

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…

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…

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…

Phylogenetic networks provide a general framework for modeling reticulate evolutionary processes such as hybridization, recombination, and horizontal gene transfer. In this paper, we study the asymptotic counting of binary phylogenetic…

The evolutionary relationships among organisms have traditionally been represented using rooted phylogenetic trees. However, due to reticulate processes such as hybridization or lateral gene transfer, evolution cannot always be adequately…

Phylogenetic networks are becoming of increasing interest to evolutionary biologists due to their ability to capture complex non-treelike evolutionary processes. From a combinatorial point of view, such networks are certain types of rooted…

Construction of phylogenetic trees and networks for extant species from their characters represents one of the key problems in phylogenomics. While solution to this problem is not always uniquely defined and there exist multiple methods for…

Phylogenetic networks generalize phylogenetic trees in order to model reticulation events. Although the comparison of phylogenetic trees is well studied, and there are multiple ways to do it in an efficient way, the situation is much…

Tree-child networks are a recently-described class of directed acyclic graphs that have risen to prominence in phylogenetics (the study of evolutionary trees and networks). Although these networks have a number of attractive mathematical…

Phylogenetic networks are a type of directed acyclic graph that represent how a set $X$ of present-day species are descended from a common ancestor by processes of speciation and reticulate evolution. In the absence of reticulate evolution,…

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…

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…

A rooted phylogenetic network is a directed acyclic graph with a single root, whose sinks correspond to a set of species. As such networks are useful for representing the evolution of species that have undergone reticulate evolution, there…

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…

We give exact and asymptotic counting results for the number of galled networks and reticulation-visible networks with few reticulation vertices. Our results are obtained with the component graph method, which was introduced by L. Zhang and…

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…

Phylogenetic trees are widely used to display estimates of how groups of species evolved. Each phylogenetic tree can be seen as a collection of clusters, subgroups of the species that evolved from a common ancestor. When phylogenetic trees…

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…

Rooted phylogenetic networks are used to describe evolutionary histories that contain non-treelike evolutionary events such as hybridization and horizontal gene transfer. In some cases, such histories can be described by a phylogenetic…