Related papers: Planar Rooted Phylogenetic Networks

Phylogenetic networks are an extension of phylogenetic trees which are used to represent evolutionary histories in which reticulation events (such as recombination and hybridization) have occurred. A central question for such networks is…

Ranked tree-child networks are a recently introduced class of rooted phylogenetic networks in which the evolutionary events represented by the network are ordered so as to respect the flow of time. This class includes the well-studied…

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…

A graph is a $k$-leaf power of a tree $T$ if its vertices are leaves of $T$ and two vertices are adjacent in $T$ if and only if their distance in $T$ is at most $k$. Then $T$ is a $k$-leaf root of $G$. This notion was introduced by…

Phylogenetic networks can represent evolutionary events that cannot be described by phylogenetic trees. These networks are able to incorporate reticulate evolutionary events such as hybridization, introgression, and lateral gene transfer.…

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…

Many real life networks present an average path length logarithmic with the number of nodes and a degree distribution which follows a power law. Often these networks have also a modular and self-similar structure and, in some cases -…

Phylogenetic networks are a generalization of evolutionary or phylogenetic trees that are commonly used to represent the evolution of species which cross with one another. A special type of phylogenetic network is an {\em $X$-cactus}, which…

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…

Understanding the evolutionary relationship among species is of fundamental importance to the biological sciences. The location of the root in any phylogenetic tree is critical as it gives an order to evolutionary events. None of the…

Phylogenetic networks are a type of leaf-labelled, acyclic, directed graph used by biologists to represent the evolutionary history of species whose past includes reticulation events. A phylogenetic network is tree-child if each non-leaf…

Phylogenetic networks are used to study evolutionary relationships between species in biology. Such networks are often categorized into classes by their topological features, which stem from both biological and computational motivations. We…

An important and well-studied problem in phylogenetics is to compute a \emph{consensus tree} so as to summarize the common features within a collection of rooted phylogenetic trees, all whose leaf-sets are bijectively labeled by the same…

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…

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…

Phylogenetics is a branch of computational biology that studies the evolutionary relationships among biological entities. Its long history and numerous applications notwithstanding, inference of phylogenetic trees from sequence data remains…

Sequence comparison and alignment has had an enormous impact on our understanding of evolution, biology, and disease. Comparison and alignment of biological networks will likely have a similar impact. Existing network alignments use…

Semi-directed networks provide a graphical structure for describing the evolutionary history of organisms in the presence of hybridization. We introduce two algorithms for reconstructing semi-directed level-1 phylogenetic networks from…

The modular decomposition of a symmetric map $\delta\colon X\times X \to \Upsilon$ (or, equivalently, a set of symmetric binary relations, a 2-structure, or an edge-colored undirected graph) is a natural construction to capture key features…

In Francis and Steel (2015), it was shown that there exists non-trivial networks on $4$ leaves upon which the distance metric affords a metric on a tree which is not the base tree of the network. In this paper we extend this result in two…