Related papers: A scale-free method for testing the proportionalit…
Phylogenomics, even more so than traditional phylogenetics, needs to represent the uncertainty in evolutionary trees due to systematic error. Here we illustrate the analysis of genome-scale alignments of yeast, using robust measures of the…
In this paper we address the problem of testing whether two observed trees $(t,t')$ are sampled either independently or from a joint distribution under which they are correlated. This problem, which we refer to as correlation detection in…
The Robinson-Foulds (RF) metric is arguably the most widely used measure of phylogenetic tree similarity, despite its well-known shortcomings: For example, moving a single taxon in a tree can result in a tree that has maximum distance to…
The presence of reticulate evolutionary events in phylogenies turn phylogenetic trees into phylogenetic networks. These events imply in particular that there may exist multiple evolutionary paths from a non-extant species to an extant one,…
The algebraic properties of flattenings and subflattenings provide direct methods for identifying edges in the true phylogeny -- and by extension the complete tree -- using pattern counts from a sequence alignment. The relatively small…
The log-det distance between two aligned DNA sequences was introduced as a tool for statistically consistent inference of a gene tree under simple non-mixture models of sequence evolution. Here we prove that the log-det distance, coupled…
Tree-based networks are a class of phylogenetic networks that attempt to formally capture what is meant by "tree-like" evolution. A given non-tree-based phylogenetic network, however, might appear to be very close to being tree-based, or…
The mutational heterogeneity of tumours can be described with a tree representing the evolutionary history of the tumour. With noisy sequencing data there may be uncertainty in the inferred tree structure, while we may also wish to study…
Connected acyclic graphs (trees) are data objects that hierarchically organize categories. Collections of trees arise in a diverse variety of fields, including evolutionary biology, public health, machine learning, social sciences and…
The Sackin and Colless indices are two widely-used metrics for measuring the balance of trees and for testing evolutionary models in phylogenetics. This short paper contributes two results about the Sackin and Colless indices of trees. One…
A rooted tree is balanced if the degree of a vertex depends only on its distance to the root. In this paper we determine the sharp threshold for the appearance of a large family of balanced spanning trees in the random geometric graph…
Tree structures appear in many fields of the life sciences, including phylogenetics, developmental biology and nucleic acid structures. Trees can be used to represent RNA secondary structures, which directly relate to the function of…
Phylogenetic networks generalise phylogenetic trees and allow for the accurate representation of the evolutionary history of a set of present-day species whose past includes reticulate events such as hybridisation and lateral gene transfer.…
The average node-to-node distance of scale-free graphs depends logarithmically on N, the number of nodes, while the probability distribution function (pdf) of the distances may take various forms. Here we analyze these by considering…
Phylogenetic diversity is a popular measure for quantifying the biodiversity of a collection $Y$ of species, while phylogenetic diversity indices provide a way to apportion phylogenetic diversity to individual species. Typically, for some…
Effects like selection in evolution as well as fertility inheritance in the development of populations can lead to a higher degree of asymmetry in evolutionary trees than expected under a null hypothesis. To identify and quantify such…
The evolution of aligned DNA sequence sites is generally modeled by a Markov process operating along the edges of a phylogenetic tree. It is well known that the probability distribution on the site patterns at the tips of the tree…
In this paper we model the tomography of scale free networks by studying the structure of layers around an arbitrary network node. We find, both analytically and empirically, that the distance distribution of all nodes from a specific…
Galled trees, directed acyclic graphs that model evolutionary histories with isolated hybridization events, have become very popular due to both their biological significance and the existence of polynomial time algorithms for their…
We introduce a family of models incorporating random segmental substitutions and point mutations and demonstrate that such models reproduce algebraic length distributions of exact matches with the slope $-4$ observed earlier in pairwise…