Related papers: Counting Phylogenetic Networks with Few Reticulati…
One strategy for reconstruction of phylogenetic networks is to solve the phylogenetic network problem, which involves inferring phylogenetic trees first and subsequently computing the smallest phylogenetic network that displays all the…
Phylogenetic networks represent evolutionary history of species and can record natural reticulate evolutionary processes such as horizontal gene transfer and gene recombination. This makes phylogenetic networks a more comprehensive…
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…
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…
A compacted binary tree is a graph created from a binary tree such that repeatedly occurring subtrees in the original tree are represented by pointers to existing ones, and hence every subtree is unique. Such representations form a special…
Network Phylogenetic Diversity (Network-PD) is a measure for the diversity of a set of species based on a rooted phylogenetic network (with branch lengths and inheritance probabilities on the reticulation edges) describing the evolution of…
In evolutionary biology, networks are becoming increasingly used to represent evolutionary histories for species that have undergone non-treelike or reticulate evolution. Such networks are essentially directed acyclic graphs with a leaf set…
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…
Rooted phylogenetic networks are rooted acyclic digraphs. They are used to model complex evolution where hybridization, recombination and other reticulation events play important roles. A rigorous definition of network compression is…
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…
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,…
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…
In a recent paper, McDiarmid, Semple, and Welsh (2015) showed that the number of tree-child networks with $n$ leaves has the factor $n^{2n}$ in its main asymptotic growth term. In this paper, we improve this by completely identifying the…
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…
Let $c_n$ denote the number of nodes at a distance $n$ from the root of a rooted tree. A criterion for proving the rationality and computing the rational generating function of the sequence $\{c_n\}$ is described. This criterion is applied…
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.…
The generation of trees with a specified tree edit distance has significant applications across various fields, including computational biology, structured data analysis, and image processing. Recently, generative networks have been…
We use a sign-reversing involution to show that trees on the vertex set [n], considered to be rooted at 1, in which no vertex has exactly one child are counted by 1/n sum_{k=1}^{n} (-1)^(n-k) {n}-choose-{k} (n-1)!/(k-1)! k^(k-1). This…
Phylogenetic networks generalise phylogenetic trees and allow for the accurate representation of the evolutionary history of a set of present-day species whose past includes reticulate events such as hybridisation and lateral gene transfer.…
There has been considerable recent interest in the properties of networks, such as citation networks and the worldwide web, that grow by the addition of vertices, and a number of simple solvable models of network growth have been studied.…