Related papers: Enumeration of $d$-combining Tree-Child Networks
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…
It was recently shown that a large class of phylogenetic networks, the `labellable' networks, is in bijection with the set of `expanding' covers of finite sets. In this paper, we show how several prominent classes of phylogenetic networks…
Phylogenetic networks are used to represent evolutionary scenarios in biology and linguistics. To find the most probable scenario, it may be necessary to compare candidate networks, to distinguish different networks, and to see when one…
We consider models for growing networks incorporating two effects not previously considered: (i) different species of nodes, with each species having different properties (such as different attachment probabilities to other node species);…
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…
A phylogenetic network is a directed acyclic graph that visualises an evolutionary history containing so-called reticulations such as recombinations, hybridisations or lateral gene transfers. Here we consider the construction of a simplest…
Trees have long been used as a graphical representation of species relationships. However complex evolutionary events, such as genetic reassortments or hybrid speciations which occur commonly in viruses, bacteria and plants, do not fit into…
Hybridization networks are representations of evolutionary histories that allow for the inclusion of reticulate events like recombinations, hybridizations, or lateral gene transfers. The recent growth in the number of hybridization network…
In evolutionary studies it is common to use phylogenetic trees to represent the evolutionary history of a set of species. However, in case the transfer of genes or other genetic information between the species or their ancestors has…
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…
A normal (phylogenetic) network with $k$ reticulations displays $2^k$ phylogenetic trees. In this paper, we establish an analogous result for tree-child (phylogenetic) networks with no underlying $3$-cycles. In particular, we show that a…
A directed phylogenetic network is tree-child if every non-leaf vertex has a child that is not a reticulation. As a class of directed phylogenetic networks, tree-child networks are very useful from a computational perspective. For example,…
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…
Networks are ubiquitous in biology and computational approaches have been largely investigated for their inference. In particular, supervised machine learning methods can be used to complete a partially known network by integrating various…
Normal networks are an important class of phylogenetic networks that have compelling mathematical properties which align with intuition about inference from genetic data. While tools enabling widespread use of phylogenetic networks in the…
Recently proposed budding tree is a decision tree algorithm in which every node is part internal node and part leaf. This allows representing every decision tree in a continuous parameter space, and therefore a budding tree can be jointly…
It is known that any two trees on the same $n$ leaves can be displayed by a network with $n-2$ reticulations, and there are two trees that cannot be displayed by a network with fewer reticulations. But how many reticulations are needed to…
Phylogenetic networks are an important way to represent evolutionary histories that involve reticulations such as hybridization or horizontal gene transfer, yet fundamental questions such as how many networks there are that satisfy certain…
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 generalize phylogenetic trees, and have been introduced in order to describe evolution in the case of transfer of genetic material between coexisting species. There are many classes of phylogenetic networks, which can…