Related papers: The expected value under the Yule model of the squ…
A multilabeled tree (or MUL-tree) is a rooted tree in which every leaf is labelled by an element from some set, but in which more than one leaf may be labelled by the same element of that set. In phylogenetics, such trees are used in…
The Robinson-Foulds (RF) distance is by far the most widely used measure of dissimilarity between trees. Although the distribution of these distances has been investigated for twenty years, an algorithm that is explicitly polynomial time…
One of the main applications of balance indices is in tests of null models of evolutionary processes. The knowledge of an exact formula for a statistic of a balance index, holding for any number n of leaves, is necessary in order to use…
In this work we study the limit distribution of an appropriately normalized cophenetic index of the pure-birth tree conditioned on $n$ contemporary tips. We show that this normalized phylogenetic balance index is a submartingale that…
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,…
An evolutionary tree is a cascade of bifurcations starting from a single common root, generating a growing set of daughter species as time goes by. Species here is a general denomination for biological species, spoken languages or any other…
The quartet distance is a measure of similarity used to compare two unrooted phylogenetic trees on the same set of $n$ leaves, defined as the number of subsets of four leaves related by a different topology in both trees. After a series of…
The method of flexi-Weighted Least Squares on evolutionary trees uses simple polynomial or exponential functions of the evolutionary distance in place of model-based variances. This has the advantage that unexpected deviations from…
We consider the model of random trees introduced by Devroye [SIAM J. Comput. 28 (1999) 409-432]. The model encompasses many important randomized algorithms and data structures. The pieces of data (items) are stored in a randomized fashion…
We consider a class of spatio-temporal models which extend popular econometric spatial autoregressive panel data models by allowing the scalar coefficients for each location (or panel) different from each other. To overcome the innate…
The subtree prune-and-regraft (SPR) distance metric is a fundamental way of comparing evolutionary trees. It has wide-ranging applications, such as to study lateral genetic transfer, viral recombination, and Markov chain Monte Carlo…
Although the analysis of rooted tree shape has wide-ranging applications, notions of tree balance have developed independently in different domains. In computer science, a balanced tree is one that enables efficient updating and retrieval…
The early development of a zygote can be mathematically described by a developmental tree. To compare developmental trees of different species, we need to define distances on trees. If children cells after a division are not…
A phylogenetic tree shows the evolutionary relationships among species. Internal nodes of the tree represent speciation events and leaf nodes correspond to species. A goal of phylogenetics is to combine such trees into larger trees, called…
Phylogenetic networks are generalizations of trees that allow for the modeling of non-tree like evolutionary processes. Split networks give a useful way to construct networks with intuitive distance structures induced from the associated…
Phylogenetic Diversity (PD) is a prominent quantitative measure of the biodiversity of a collection of present-day species (taxa). This measure is based on the evolutionary distance among the species in the collection. Loosely speaking, if…
The paper written in 1925 by G. Udny Yule that we celebrate in this special issue introduces several novelties and results that we recall in detail. First, we discuss Yule (1925)'s main legacies over the past century, focusing on empirical…
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 present two algorithms for computing the geodesic distance between phylogenetic trees in tree space, as introduced by Billera, Holmes, and Vogtmann (2001). We show that the possible combinatorial types of shortest paths between two trees…
The rooted subtree prune and regraft (rSPR) distance between two rooted binary phylogenetic trees is a well-studied measure of topological dissimilarity that is NP-hard to compute. Here we describe an improved linear kernel for the problem.…