Related papers: Is this network proper forest-based?

We address an open question of Francis and Steel about phylogenetic networks and trees. They give a polynomial time algorithm to decide if a phylogenetic network, N, is tree-based and pose the problem: given a fixed tree T and network N, is…

Phylogenetic networks which are, as opposed to trees, suitable to describe processes like hybridization and horizontal gene transfer, play a substantial role in evolutionary research. However, while non-treelike events need to be taken into…

In phylogenetics, tree-based networks are used to model and visualize the evolutionary history of species where reticulate events such as horizontal gene transfer have occurred. Formally, a tree-based network $N$ consists of a 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…

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…

Phylogenetic networks are used to represent the evolutionary history of species. They are versatile when compared to traditional phylogenetic trees, as they capture more complex evolutionary events such as hybridization and horizontal gene…

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 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…

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…

Phylogenetic networks are used in biology to represent evolutionary histories. The class of orchard phylogenetic networks was recently introduced for their computational benefits, without any biological justification. Here, we show that…

Phylogenetic trees canonically arise as embeddings of phylogenetic networks. We recently showed that the problem of deciding if two phylogenetic networks embed the same sets of phylogenetic trees is computationally hard, \blue{in…

Phylogenetic networks model reticulate evolutionary histories. The last two decades have seen an increased interest in establishing mathematical results and developing computational methods for inferring and analyzing these networks. A…

Phylogenetic networks are increasingly used in evolutionary biology to represent the history of species that have undergone reticulate events such as horizontal gene transfer, hybrid speciation and recombination. One of the most fundamental…

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…

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…

Phylogenetic networks are graphs that are used to represent evolutionary relationships between different taxa. They generalize phylogenetic trees since for example, unlike trees, they permit lineages to combine. Recently, there has been…

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…

Reticulate evolution can be modelled using phylogenetic networks. Tree-based networks, which are one of the more general classes of phylogenetic networks, have recently gained eminence for its ability to represent evolutionary histories…

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…

Attempting to recognize a tree inside a phylogenetic network is a fundamental undertaking in evolutionary analysis. In the last few years, therefore, tree-based phylogenetic networks, which are defined by a spanning tree called a…