Related papers: A Phylogenetic Trees Analysis of SARS-CoV-2
In evolutionary biology, phylogenetic trees are commonly inferred from a set of characters (partitions) of a collection of biological entities (e.g., species or individuals in a population). Such characters naturally arise from molecular…
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…
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…
A binary phylogenetic network may or may not be obtainable from a tree by the addition of directed edges (arcs) between tree arcs. Here, we establish a precise and easily tested criterion (based on `2-SAT') that efficiently determines…
We prove, that every connected graph with $s$ vertices of degree 3 and $t$ vertices of degree at least~4 has a spanning tree with at least ${2\over 5}t +{1\over 5}s+\alpha$ leaves, where $\alpha \ge {8\over 5}$. Moreover, $\alpha \ge 2$ for…
Phylogenetic trees and networks are leaf-labelled graphs that are used to describe evolutionary histories of species. The Tree Containment problem asks whether a given phylogenetic tree is embedded in a given phylogenetic network. Given a…
In phylogenetics, phylogenetic trees are rooted binary trees, whereas phylogenetic networks are rooted arbitrary acyclic digraphs. Edges are directed away from the root and leaves are uniquely labeled with taxa in phylogenetic networks. For…
Binary trees are fundamental objects in models of evolutionary biology and population genetics. Here, we discuss some of their combinatorial and structural properties as they depend on the tree class considered. Furthermore, the process by…
The relative importance of the intrinsic and extrinsic factors determining the variety of geometric shapes exhibited by dendritic trees remains unclear. This question was addressed by developing a model of the growth of dendritic trees…
In a graph, a spanning tree is said to be a tree t-spanner of the graph if the distance between any two vertices in is at most times their distance in . The tree t-spanner has many applications in networks and distributed environments. In…
Spatial connectivity is an important consideration when modelling infectious disease data across a geographical region. Connectivity can arise for many reasons, including shared characteristics between regions, and human or vector movement.…
A metric phylogenetic tree relating a collection of taxa induces weighted rooted triples and weighted quartets for all subsets of three and four taxa, respectively. New intertaxon distances are defined that can be calculated from these…
We investigate the statistics of trees grown from some initial tree by attaching links to preexisting vertices, with attachment probabilities depending only on the valence of these vertices. We consider the asymptotic mass distribution that…
Recent theory work has found that a special type of spatial partition tree - called a random projection tree - is adaptive to the intrinsic dimension of the data from which it is built. Here we examine this same question, with a combination…
Species tree estimation is a complex problem, due to the fact that different parts of the genome can have different evolutionary histories than the genome itself. One of the causes for this discord is incomplete lineage sorting (also called…
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…
We prove that every connected graph with $s$ vertices of degree not 2 has a spanning tree with at least ${1\over 4}(s-2)+2$ leaves. Let $G$ be a be a connected graph of girth $g$ with $v>1$ vertices. Let maximal chain of successively…
Let G be a finitely generated group. Two simplicial G-trees are said to be in the same deformation space if they have the same elliptic subgroups (if H fixes a point in one tree, it also does in the other). Examples include…
It was recently observed by de Vienne et al. that a simple square root transformation of distances between taxa on a phylogenetic tree allowed for an embedding of the taxa into Euclidean space. While the justification for this was based on…
The COVID-19 pandemic is spreading rapidly around the world, causing countries to impose lockdowns and efforts to develop vaccines on a global scale. However, human-to-animal and animal-to-human transmission cannot be ignored, as severe…