Related papers: Split Network Polytopes and Network Spaces

Driven by the need for better models that allow one to shed light into the question how life's diversity has evolved, phylogenetic networks have now joined phylogenetic trees in the center of phylogenetics research. Like phylogenetic trees,…

As researchers collect increasingly large molecular data sets to reconstruct the Tree of Life, the heterogeneity of signals in the genomes of diverse organisms poses challenges for traditional phylogenetic analysis. A class of phylogenetic…

We associate root polytopes to directed graphs and study them by using ribbon structures. Most attention is paid to what we call the semi-balanced case, i.e., when each cycle has the same number of edges pointing in the two directions.…

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…

Phylogenetic trees and networks are leaf-labelled graphs used to model evolution. Display graphs are created by identifying common leaf labels in two or more phylogenetic trees or networks. The treewidth of such graphs is bounded as a…

Polyploidization is an important evolutionary process which affects organisms ranging from plants to fish and fungi. The signal left behind by it is in the form of a species' ploidy level (number of complete chromosome sets found in a cell)…

A major ambition of systems science is to uncover the building blocks of any biological network to decipher how cellular function emerges from their interactions. Here, we introduce a graph representation of the information flow in these…

Phylogenetic networks are a flexible model of evolution that can represent reticulate evolution and handle complex data. Tree-based networks, which are phylogenetic networks that have a spanning tree with the same root and leaf-set as the…

We introduce a notion of finite sampling consistency for phylogenetic trees and show that the set of finitely sampling consistent and exchangeable distributions on n leaf phylogenetic trees is a polytope. We use this polytope to show that…

One of the defining features of living systems is their adaptability to changing environmental conditions. This requires organisms to extract temporal and spatial features of their environment, and use that information to compute the…

Phylogenetic networks allow modeling reticulate evolution, capturing events such as hybridization and horizontal gene transfer. A fundamental computational problem in this context is the Tree Containment problem, which asks whether a given…

Binets and trinets are phylogenetic networks with two and three leaves, respectively. Here we consider the problem of deciding if there exists a binary level-1 phylogenetic network displaying a given set $\mathcal{T}$ of binary binets or…

Phylogenetic trees describe the evolutionary history of a group of present-day species from a common ancestor. These trees are typically reconstructed from aligned DNA sequence data. In this paper we analytically address the following…

Reconciling gene trees with a species tree is a fundamental problem to understand the evolution of gene families. Many existing approaches reconcile each gene tree independently. However, it is well-known that the evolution of gene families…

The statistical estimation of phylogenies is always associated with uncertainty, and accommodating this uncertainty is an important component of modern phylogenetic comparative analysis. The birth-death polytomy resolver is a method of…

We present an efficient phylogenetic reconstruction algorithm allowing insertions and deletions which provably achieves a sequence-length requirement (or sample complexity) growing polynomially in the number of taxa. Our algorithm is…

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…

Phylogenetic networks are an extension of phylogenetic trees that allow for the representation of reticulate evolution events. One of the classes of networks that has gained the attention of the scientific community over the last years is…

We introduce new methods for phylogenetic tree quartet construction by using machine learning to optimize the power of phylogenetic invariants. Phylogenetic invariants are polynomials in the joint probabilities which vanish under a model of…

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…