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Analyzing changes in network evolution is central to statistical network inference, as underscored by recent challenges of predicting and distinguishing pandemic-induced transformations in organizational and communication networks. We…
We observe $n$ sequences at each of $m$ sites, and assume that they have evolved from an ancestral sequence that forms the root of a binary tree of known topology and branch lengths, but the sequence states at internal nodes are unknown.…
Phylogenetic networks are becoming increasingly popular in phylogenetics since they have the ability to describe a wider range of evolutionary events than their tree counterparts. In this paper, we study Markov models on phylogenetic…
The evolutionary relationships between species are typically represented in the biological literature by rooted phylogenetic trees. However, a tree fails to capture ancestral reticulate processes, such as the formation of hybrid species or…
A consensus tree is a phylogenetic tree that synthesizes a given collection of phylogenetic trees, all of which share the same leaf labels but may have different topologies, typically obtained through bootstrapping. Our research focuses on…
We consider the problem of inferring the topology of a network using the measurements available at the end nodes, without cooperation from the internal nodes. To this end, we provide a simple method to obtain path interference which…
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…
Evolutionary scenarios displaying reticulation events are often represented by rooted phylogenetic networks. Due to biological reasons, those events occur very rarely, and, thus, networks containing a minimum number of such events,…
When estimating a phylogeny from a multiple sequence alignment, researchers often assume the absence of recombination. However, if recombination is present, then tree estimation and all downstream analyses will be impacted, because…
Phylogenetic mixture models, in which the sites in sequences undergo different substitution processes along the same or different trees, allow the description of heterogeneous evolutionary processes. As data sets consisting of longer…
Construction of phylogenetic trees and networks for extant species from their characters represents one of the key problems in phylogenomics. While solution to this problem is not always uniquely defined and there exist multiple methods for…
A fundamental problem in the study of phylogenetic networks is to determine whether or not a given phylogenetic network contains a given phylogenetic tree. We develop a quadratic-time algorithm for this problem for binary nearly-stable…
We study the behavior of phylogenetic tree shapes in the tropical geometric interpretation of tree space. Tree shapes are formally referred to as tree topologies; a tree topology can also be thought of as a tree combinatorial type, which is…
Phylogenetic networks generalize phylogenetic trees, and have been introduced in order to describe evolution in the case of transfer of genetic material between coexisting species. There are many classes of phylogenetic networks, which can…
We prove that Nakhleh's latest dissimilarity measure for phylogenetic networks is a metric on the classes of tree-child phylogenetic networks, of semi-binary time consistent tree-sibling phylogenetic networks, and of multi-labeled…
Phylogenetic trees are leaf-labelled trees used to model the evolution of species. In practice it is not uncommon to obtain two topologically distinct trees for the same set of species, and this motivates the use of distance measures to…
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…
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…
Ultametrics are an important class of distances used in applications such as phylogenetics, clustering and classification theory. Ultrametrics are essentially distances that can be represented by an edge-weighted rooted tree so that all 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…