Related papers: Phylogenetic mixtures and linear invariants for eq…
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 invariants are equations that vanish on algebraic varieties associated with Markov processes that model molecular substitutions on phylogenetic trees. For practical applications, it is essential to understand these equations…
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…
This thesis develops and expands upon known techniques of mathematical physics relevant to the analysis of the popular Markov model of phylogenetic trees required in biology to reconstruct the evolutionary relationships of taxonomic units…
Phylogenetic networks are becoming increasingly popular in phylogenetics since they have the ability to describe a wider range of evolutionary events than their tree counterparts. In this paper, we study Markov models on phylogenetic…
The selection of the most suitable evolutionary model to analyze the given molecular data is usually left to biologist's choice. In his famous book, J Felsenstein suggested that certain linear equations satisfied by the expected…
We address phylogenetic reconstruction when the data is generated from a mixture distribution. Such topics have gained considerable attention in the biological community with the clear evidence of heterogeneity of mutation rates. In our…
Phylogenetic networks can represent evolutionary events that cannot be described by phylogenetic trees, such as hybridization, introgression, and lateral gene transfer. Studying phylogenetic networks under a statistical model of DNA…
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…
We explore model based techniques of phylogenetic tree inference exercising Markov invariants. Markov invariants are group invariant polynomials and are distinct from what is known in the literature as phylogenetic invariants, although we…
Phylogenetic invariants are certain polynomials in the joint probability distribution of a Markov model on a phylogenetic tree. Such polynomials are of theoretical interest in the field of algebraic statistics and they are also of practical…
The purpose of this article is to show how the isotropy subgroup of leaf permutations on binary trees can be used to systematically identify tree-informative invariants relevant to models of phylogenetic evolution. In the quartet case, we…
Recently there has been renewed interest in phylogenetic inference methods based on phylogenetic invariants, alongside the related Markov invariants. Broadly speaking, both these approaches give rise to polynomial functions of sequence site…
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…
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…
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 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…
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.…
One reason why classical phylogenetic reconstruction methods fail to correctly infer the underlying topology is because they assume oversimplified models. In this paper we propose a topology reconstruction method consistent with the most…
We prove identifiability of the tree parameters of the 3-class Jukes-Cantor mixture model. The proof uses ideas from algebraic statistics, in particular: finding phylogenetic invariants that separate the varieties associated to different…