Related papers: Rank conditions on phylogenetic networks
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…
Rooted phylogenetic networks allow biologists to represent evolutionary relationships between present-day species by revealing ancestral speciation and hybridization events. A convenient and well-studied class of such networks are…
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,…
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…
This thesis develops and expands upon known techniques of mathematical physics relevant to the analysis of the popular Markov model of phylogenetic trees required in biology to reconstruct the evolutionary relationships of taxonomic units…
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…
The reconstruction of phylogenetic trees from molecular sequence data relies on modelling site substitutions by a Markov process, or a mixture of such processes. In general, allowing mixed processes can result in different tree topologies…
Recently, so-called treebased phylogenetic networks have gained considerable interest in the literature, where a treebased network is a network that can be constructed from a phylogenetic tree, called the base tree, by adding additional…
Phylogenetic networks can model more complicated evolutionary phenomena that trees fail to capture such as horizontal gene transfer and hybridization. The same Markov models that are used to model evolution on trees can also be extended to…
Rooted phylogenetic networks provide a way to describe species' relationships when evolution departs from the simple model of a tree. However, networks inferred from genomic data can be highly tangled, making it difficult to discern the…
We present a method of dimensional reduction for the general Markov model of sequence evolution on a phylogenetic tree. We show that taking certain linear combinations of the associated random variables (site pattern counts) reduces the…
We find surprisingly simple formulas for the limiting probability that the rank of a randomly selected vertex in a randomly selected phylogenetic tree or generalized phylogenetic tree is a given integer.
The evolution of molecular and phenotypic traits is commonly modelled using Markov processes along a phylogeny. This phylogeny can be a tree, or a network if it includes reticulations, representing events such as hybridization or admixture.…
Phylogenetic networks are a generalization of phylogenetic trees that are used to represent non-tree-like evolutionary histories that arise in organisms such as plants and bacteria, or uncertainty in evolutionary histories. An…
Phylogenetic networks are a generalization of phylogenetic trees that are used to represent reticulate evolution. Unrooted phylogenetic networks form a special class of such networks, which naturally generalize unrooted phylogenetic trees.…
The purpose of this article is to show how the isotropy subgroup of leaf permutations on binary trees can be used to systematically identify tree-informative invariants relevant to models of phylogenetic evolution. In the quartet case, we…
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 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…
Tree-based networks are a class of phylogenetic networks that attempt to formally capture what is meant by "tree-like" evolution. A given non-tree-based phylogenetic network, however, might appear to be very close to being tree-based, or…
Phylogenetic networks are a generalization of phylogenetic trees allowing for the representation of non-treelike evolutionary events such as hybridization. Typically, such networks have been analyzed based on their `level', i.e. based on…