Related papers: Defining phylogenetic networks using ancestral pro…

A graph is a $k$-leaf power of a tree $T$ if its vertices are leaves of $T$ and two vertices are adjacent in $T$ if and only if their distance in $T$ is at most $k$. Then $T$ is a $k$-leaf root of $G$. This notion was introduced by…

Sequence comparison and alignment has had an enormous impact on our understanding of evolution, biology, and disease. Comparison and alignment of biological networks will likely have a similar impact. Existing network alignments use…

Network representations of systems from various scientific and societal domains are neither completely random nor fully regular, but instead appear to contain recurring structural building blocks. These features tend to be shared by…

A contemporary and fundamental problem faced by many evolutionary biologists is how to puzzle together a collection $\mathcal P$ of partial trees (leaf-labelled trees whose leaves are bijectively labelled by species or, more generally,…

A binary phylogenetic network on a taxon set $X$ is a rooted acyclic digraph in which the degree of each nonleaf node is three and its leaves (i.e.degree-one nodes) are uniquely labeled with the taxa of $X$. It is tree-child if each nonleaf…

Tree-child networks are an important network class which are used in phylogenetics to model reticulate evolution. In a recent paper, Pons and Batle (2021) conjectured a relation between tree-child networks and certain words. In this short…

Phylogenetics is a branch of computational biology that studies the evolutionary relationships among biological entities. Its long history and numerous applications notwithstanding, inference of phylogenetic trees from sequence data remains…

'Tree-based' phylogenetic networks proposed by Francis and Steel have attracted much attention of theoretical biologists in the last few years. At the heart of the definitions of tree-based phylogenetic networks is the notion of 'support…

Combining a set of phylogenetic trees into a single phylogenetic network that explains all of them is a fundamental challenge in evolutionary studies. Existing methods are computationally expensive and can either handle only small numbers…

A hierarchical structure describing the inter-relationships of species has long been a fundamental concept in systematic biology, from Linnean classification through to the more recent quest for a 'Tree of Life.' In this paper we use an…

Many methods have been developed for finding the commonalities between different organisms to study their phylogeny. The structure of metabolic networks also reveal valuable insights into metabolic capacity of species as well as into the…

Balanced minimum evolution is a distance-based criterion for the reconstruction of phylogenetic trees. Several algorithms exist to find the optimal tree with respect to this criterion. One approach is to minimize a certain linear functional…

In recent decades, phylogenetic networks have become a standard tool in modeling evolutionary processes. Nevertheless, basic combinatorial questions about them are still largely open. For instance, even the asymptotic counting problem for…

Phylogenetic (i.e. leaf-labeled) trees play a fundamental role in evolutionary research. A typical problem is to reconstruct such trees from data like DNA alignments (whose columns are often referred to as characters), and a simple…

Tree alignment graphs (TAGs) provide an intuitive data structure for storing phylogenetic trees that exhibits the relationships of the individual input trees and can potentially account for nested taxonomic relationships. This paper…

This work addresses the intrinsic relationship between trees and networks (i.e. graphs). A complete (invertible) mapping is presented which allows trees to be mapped into weighted graphs and then backmapped into the original tree without…

Often questions arise about old or extinct networks. What proteins interacted in a long-extinct ancestor species of yeast? Who were the central players in the Last.fm social network 3 years ago? Our ability to answer such questions has been…

The Tree of Life is the graphical structure that represents the evolutionary process from single-cell organisms at the origin of life to the vast biodiversity we see today. Reconstructing this tree from genomic sequences is challenging due…

We compare the phylogenetic tensors for various trees and networks for two, three and four taxa. If the probability spaces between one tree or network and another are not identical then there will be phylogenetic tensors that could have…

Popular methods for exploring the space of rooted phylogenetic trees use rearrangement moves such as rNNI (rooted Nearest Neighbour Interchange) and rSPR (rooted Subtree Prune and Regraft). Recently, these moves were generalized to rooted…