Related papers: Generalising rate heterogeneity across sites in st…
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…
Phylogenetic trees are simple models of evolutionary processes. They describe conditionally independent divergent evolution of taxa from common ancestors. Phylogenetic trees commonly do not have enough flexibility to adequately model all…
Rate variation among the sites of a molecular sequence is commonly found in applications of phylogenetic inference. Several approaches exist to account for this feature but they do not usually enable the investigator to pinpoint the sites…
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…
More than ever, today we are left with the abundance of molecular data outpaced by the advancements of the phylogenomic methods. Especially in the case of presence of many genes over a set of species under the phylogeny question, more…
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…
The rates-across-sites assumption in phylogenetic inference posits that the rate matrix governing the Markovian evolution of a character on an edge of the putative phylogenetic tree is the product of a character-specific scale factor and a…
A number of methods have been developed to infer differential rates of species diversification through time and among clades using time-calibrated phylogenetic trees. However, we lack a general framework that can delineate and quantify…
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…
Phylogenetic stochastic mapping is a method for reconstructing the history of trait changes on a phylogenetic tree relating species/organisms carrying the trait. State-of-the-art methods assume that the trait evolves according to 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…
Scientific studies in many areas of biology routinely employ evolutionary analyses based on the probabilistic inference of phylogenetic trees from molecular sequence data. Evolutionary processes that act at the molecular level are highly…
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…
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.…
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…
A phylogenetic tree is an important way in Bioinformatics to find the evolutionary relationship among biological species. In this research, a proposed model is described for the estimation of a phylogenetic tree for a given set of data. To…
Phylogenetic trees describe the relationships between species in the evolutionary process, and provide information about the rates of diversification. To understand the mechanisms behind macroevolution, we consider a class of multitype…
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…
We consider the evolution of populations under the joint action of mutation and differential reproduction, or selection. The population is modelled as a finite-type Markov branching process in continuous time, and the associated…
Rapid developments in genetics and biology have led to phylogenetic methods becoming an important direction in the study of cancer and viral evolution. Although our understanding of gene biology and biochemistry has increased and is…