Related papers: Which Phylogenetic Networks are Level-k Networks w…

An evolutionary tree (phylogenetic tree) is a binary, rooted, unordered tree that models the evolutionary history of currently living species in which leaves are labeled by species. In this paper, we investigate the problem of finding the…

Many complex systems can be described in terms of networks of interacting units. Recent studies have shown that a wide class of both natural and artificial nets display a surprisingly widespread feature: the presence of highly heterogeneous…

A phylogenetic tree is an important way in Bioinformatics to find the evolutionary relationship among biological species. In this research, a proposed model is described for the estimation of a phylogenetic tree for a given set of data. To…

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 a generalization of phylogenetic trees that allow for the representation of evolutionary events acting at the population level, like recombination between genes, hybridization between lineages, and lateral gene…

It has remained an open question for some time whether, given a set of not necessarily binary (i.e. "nonbinary") trees T on a set of taxa X, it is possible to determine in time f(r).poly(m) whether there exists a phylogenetic network that…

Transport networks are crucial to the functioning of natural systems and technological infrastructures. For flow networks in many scenarios, such as rivers or blood vessels, acyclic networks (i.e., trees) are optimal structures when…

Phylogenetics begins with reconstructing biological family trees from genetic data. Since Nature is not limited to tree-like histories, we use networks to organize our data, and have discovered new polytopes, metric spaces, and simplicial…

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…

We introduce a new phylogenetic reconstruction algorithm which, unlike most previous rigorous inference techniques, does not rely on assumptions regarding the branch lengths or the depth of the tree. The algorithm returns a forest which is…

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…

Semidirected networks have received interest in evolutionary biology as the appropriate generalization of unrooted trees to networks, in which some but not all edges are directed. Yet these networks lack proper theoretical study. We define…

Phylogenetic (i.e. leaf-labeled) trees play a fundamental role in evolutionary research. A typical problem is to reconstruct such trees from data like DNA alignments (whose columns are often referred to as characters), and a simple…

Given a rooted, binary phylogenetic network and a rooted, binary phylogenetic tree, can the tree be embedded into the network? This problem, called \textsc{Tree Containment}, arises when validating networks constructed by phylogenetic…

Tree Containment is a fundamental problem in phylogenetics useful for verifying a proposed phylogenetic network, representing the evolutionary history of certain species. Tree Containment asks whether the given phylogenetic tree (for…

In this paper we investigate networks whose evolution is governed by the interaction of a random assembly process and an optimization process. In the first process, new nodes are added one at a time and form connections to randomly selected…

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…

Phylogenetic trees are leaf-labelled trees used to model the evolution of species. In practice it is not uncommon to obtain two topologically distinct trees for the same set of species, and this motivates the use of distance measures to…

When hybridization or other forms of lateral gene transfer have occurred, evolutionary relationships of species are better represented by phylogenetic networks than by trees. While inference of such networks remains challenging, several…

Network representations of systems from various scientific and societal domains are neither completely random nor fully regular, but instead appear to contain recurring structural building blocks. These features tend to be shared by…