Related papers: Identifying evolutionary trees and substitution pa…
Inference of evolutionary trees and rates from biological sequences is commonly performed using continuous-time Markov models of character change. The Markov process evolves along an unknown tree while observations arise only from the tips…
Diversification models describe the random growth of evolutionary trees, modeling the historical relationships of species through speciation and extinction events. One class of such models allows for independently changing traits, or types,…
Covarion models of character evolution describe inhomogeneities in substitution processes through time. In phylogenetics, such models are used to describe changing functional constraints or selection regimes during the evolution of…
We present a method of dimensional reduction for the general Markov model of sequence evolution on a phylogenetic tree. We show that taking certain linear combinations of the associated random variables (site pattern counts) reduces the…
A major task of evolutionary biology is the reconstruction of phylogenetic trees from molecular data. The evolutionary model is given by a Markov chain on a tree. Given samples from the leaves of the Markov chain, the goal is to reconstruct…
Phylogenetics uses alignments of molecular sequence data to learn about evolutionary trees relating species. Along branches, sequence evolution is modelled using a continuous-time Markov process characterised by an instantaneous rate…
In the last decade, some algebraic tools have been successfully applied to phylogenetic reconstruction. These tools are mainly based on the knowledge of equations describing algebraic varieties associated to phylogenetic trees evolving…
A Profile Mixture Model is a model of protein evolution, describing sequence data in which sites are assumed to follow many related substitution processes on a single evolutionary tree. The processes depend in part on different amino acid…
Phylogenetics uses alignments of molecular sequence data to learn about evolutionary trees. Substitutions in sequences are modelled through a continuous-time Markov process, characterised by an instantaneous rate matrix, which standard…
Mutation rate variation across loci is well known to cause difficulties, notably identifiability issues, in the reconstruction of evolutionary trees from molecular sequences. Here we introduce a new approach for estimating general…
This work considers the problem of learning the structure of multivariate linear tree models, which include a variety of directed tree graphical models with continuous, discrete, and mixed latent variables such as linear-Gaussian models,…
Phylogenetic networks provide a means of describing the evolutionary history of sets of species believed to have undergone hybridization or gene flow during their evolution. The mutation process for a set of such species can be modeled as a…
For a model of molecular evolution to be useful for phylogenetic inference, the topology of evolutionary trees must be identifiable. That is, from a joint distribution the model predicts, it must be possible to recover the tree parameter.…
Understanding the evolution of binary traits, which affects the birth and survival of species and also the rate of molecular evolution, remains challenging. A typical example is the evolution of mating systems in plant species. In this…
We apply the theory of markov random fields on trees to derive a phase transition in the number of samples needed in order to reconstruct phylogenies. We consider the Cavender-Farris-Neyman model of evolution on trees, where all the inner…
The general Markov model of the evolution of biological sequences along a tree leads to a parameterization of an algebraic variety. Understanding this variety and the polynomials, called phylogenetic invariants, which vanish on it, is a…
Markov models of character substitution on phylogenies form the foundation of phylogenetic inference frameworks. Early models made the simplifying assumption that the substitution process is homogeneous over time and across sites in the…
Phylogenetic mixture models are statistical models of character evolution allowing for heterogeneity. Each of the classes in some unknown partition of the characters may evolve by different processes, or even along different trees. The…
Phylogenetic data arising on two possibly different tree topologies might be mixed through several biological mechanisms, including incomplete lineage sorting or horizontal gene transfer in the case of different topologies, or simply…
Coalescent models of evolution account for incomplete lineage sorting by specifying a species tree parameter which determines a distribution on gene trees. It has been shown that the unrooted topology of the species tree parameter of the…