Related papers: Comparison of Galled Trees
Frequencies of $k$-mers in sequences are sometimes used as a basis for inferring phylogenetic trees without first obtaining a multiple sequence alignment. We show that a standard approach of using the squared-Euclidean distance between…
In this paper, we consider the problem of reconstructing trees from traces in the tree edit distance model. Previous work by Davies et al. (2019) analyzed special cases of reconstructing labeled trees. In this work, we significantly expand…
Ancestral mixture model, proposed by Chen and Lindsay (2006), is an important model to build a hierarchical tree from high dimensional binary sequences. Mixture trees created from ancestral mixture models involve in the inferred…
Phylogenetic networks are increasingly used in evolutionary biology to represent the history of species that have undergone reticulate events such as horizontal gene transfer, hybrid speciation and recombination. One of the most fundamental…
In recent years, there has been an effort to extend the classical notion of phylogenetic balance, originally defined in the context of trees, to networks. One of the most natural ways to do this is with the so-called $B_2$ index. In this…
In this article, we propose tree edit distance with variables, which is an extension of the tree edit distance to handle trees with variables and has a potential application to measuring the similarity between mathematical formulas,…
Several real-world and abstract structures and systems are characterized by marked hierarchy to the point of being expressed as trees. Because the study of these entities often involves sampling (or discovering) the tree nodes in a specific…
Inferences about the evolution of continuous traits based on reconstruction of ancestral states has often been considered more error-prone than analysis of independent contrasts. Here we show that both methods in fact yield identical…
We consider the problem of uniformly generating a spanning tree, of a connected undirected graph. This process is useful to compute statistics, namely for phylogenetic trees. We describe a Markov chain for producing these trees. For cycle…
Rotation distance between trees measures the number of simple operations it takes to transform one tree into another. There are no known polynomial-time algorithms for computing rotation distance. In the case of ordered rooted trees, we…
We introduce a scale-free method for testing the proportionality of branch lengths between two phylogenetic trees that have the same topology and contain the same set of taxa. This method scales both trees to a total length of 1 and sums up…
In this paper we give a complete characterization of the statistical equivalence classes of CEGs and of staged trees. We are able to show that all graphical representations of the same model share a common polynomial description. Then,…
Rooted phylogenetic networks provide a more complete representation of the ancestral relationship between species than phylogenetic trees when reticulate evolutionary processes are at play. One way to reconstruct a phylogenetic network is…
Rotation distances measure the differences in structure between rooted ordered binary trees. The one-dimensional skeleta of associahedra are rotation graphs, where two vertices representing trees are connected by an edge if they differ by a…
Trees corresponding to $\Lambda$- and $\Xi$-$n$-coalescents can be both quite similar and fundamentally different compared to bifurcating tree models based on Kingman's $n$-coalescent. This has consequences for inference of a well-fitting…
Phylogenetic trees are the fundamental mathematical representation of evolutionary processes in biology. They are also objects of interest in pure mathematics, such as algebraic geometry and combinatorics, due to their discrete geometry.…
The last decade brought a significant increase in the amount of data and a variety of new inference methods for reconstructing the detailed evolutionary history of various cancers. This brings the need of designing efficient procedures for…
The evolution of molecular and phenotypic traits is commonly modelled using Markov processes along a phylogeny. This phylogeny can be a tree, or a network if it includes reticulations, representing events such as hybridization or admixture.…
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…
Rooted phylogenetic networks are used to describe evolutionary histories that contain non-treelike evolutionary events such as hybridization and horizontal gene transfer. In some cases, such histories can be described by a phylogenetic…