Related papers: Phylogenomic Models from Tree Symmetries
As researchers collect increasingly large molecular data sets to reconstruct the Tree of Life, the heterogeneity of signals in the genomes of diverse organisms poses challenges for traditional phylogenetic analysis. A class of phylogenetic…
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…
The ongoing explosion of genome sequence data is transforming how we reconstruct and understand the histories of biological systems. Across biological scales, from individual cells to populations and species, trees-based models provide a…
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…
Topological phylogenetic trees can be assigned edge weights in several natural ways, highlighting different aspects of the tree. Here the rooted triple and quartet metrizations are introduced, and applied to formulate novel fast methods of…
We consider species tree estimation under a standard stochastic model of gene tree evolution that incorporates incomplete lineage sorting (as modeled by a coalescent process) and gene duplication and loss (as modeled by a branching…
Ultrametric matrices are a class of covariance matrices that arise in latent tree models. As a parameter space in a statistical model, the set of ultrametric matrices is neither convex nor a smooth manifold. Focus in the literature has…
The inference of the evolutionary history of a collection of organisms is a problem of fundamental importance in evolutionary biology. The abundance of DNA sequence data arising from genome sequencing projects has led to significant…
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…
Molecular phylogeny has focused mainly on improving models for the reconstruction of gene trees based on sequence alignments. Yet, most phylogeneticists seek to reveal the history of species. Although the histories of genes and species are…
The reliability of a phylogenetic inference method from genomic sequence data is ensured by its statistical consistency. Bayesian inference methods produce a sample of phylogenetic trees from the posterior distribution given sequence data.…
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.…
Gene trees are evolutionary trees representing the ancestry of genes sampled from multiple populations. Species trees represent populations of individuals -- each with many genes -- splitting into new populations or species. The coalescent…
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…
Species tree estimation is a complex problem, due to the fact that different parts of the genome can have different evolutionary histories than the genome itself. One of the causes for this discord is incomplete lineage sorting (also called…
Simple stochastic models for phylogenetic trees on species have been well studied. But much paleontology data concerns time series or trees on higher-order taxa, and any broad picture of relationships between extant groups requires use of…
The aim of this review is to present and analyze the probabilistic models of mathematical phylogenetics which have been intensively used in recent years in biology as the cornerstone of attempts to infer and reconstruct the ancestral…
Estimating phylogenetic trees is an important problem in evolutionary biology, environmental policy and medicine. Although trees are estimated, their uncertainties are discarded by mathematicians working in tree space. Here we explicitly…
The goal of these lectures is to review some mathematical aspects of random tree models used in evolutionary biology to model gene trees or species trees. We start with stochastic models of tree shapes (finite trees without edge lengths),…
Motivation: While the majority of gene histories found in a clade of organisms are expected to be generated by a common process (e.g. the coalescent process), it is well-known that numerous other coexisting processes (e.g. horizontal gene…