Related papers: When Do Phylogenetic Mixture Models Mimic Other Ph…
Identifiability of phylogenetic models is a necessary condition to ensure that the model parameters can be uniquely determined from data. Mixture models are phylogenetic models where the probability distributions in the model are convex…
Mixture models provide a flexible representation of heterogeneity in a finite number of latent classes. From the Bayesian point of view, Markov Chain Monte Carlo methods provide a way to draw inferences from these models. In particular,…
Phylogenetic trees (i.e. evolutionary trees, additive trees or X-trees) play a key role in the processes of modeling and representing species evolution. Genome evolution of a given group of species is usually modeled by a species…
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…
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…
Mixtures of product distributions are a powerful device for learning about heterogeneity within data populations. In this class of latent structure models, de Finetti's mixing measure plays the central role for describing the uncertainty…
In mathematical phylogenetics, evolutionary relationships are often represented by trees and networks. The latter are typically used whenever the relationships cannot be adequately described by a tree, which happens when so-called…
Phylogenetic networks describe the evolution of a set of taxa for which reticulate events have occurred at some point in their evolutionary history. Of particular interest is when the evolutionary history between a set of just three taxa…
The parameters of many classes of birth-death processes cannot be inferred uniquely from phylogenetic trees: infinitely many parameter combinations yield the same distribution of phylogenetic trees. Here, we show that parameter…
Continuous mixtures of distributions are widely employed in the statistical literature as models for phenomena with highly divergent outcomes; in particular, many familiar heavy-tailed distributions arise naturally as mixtures of…
The perfect phylogeny mixture (PPM) model is useful due to its simplicity and applicability in scenarios where mutations can be assumed to accumulate monotonically over time. It is the underlying model in many tools that have been used, for…
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.…
Phylogenetic trees are widely used to understand the evolutionary history of organisms. Tree shapes provide information about macroevolutionary processes. However, macroevolutionary models are unreliable for inferring the true processes…
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 forest of mutations associated to a multitype branching forest is obtained by merging together all vertices of its clusters and by preserving connections between them. We first show that the forest of mutations of any mulitype branching…
Networks are widely used in the biological, physical, and social sciences as a concise mathematical representation of the topology of systems of interacting components. Understanding the structure of these networks is one of the outstanding…
We analyse a maximum-likelihood approach for combining phylogenetic trees into a larger `supertree'. This is based on a simple exponential model of phylogenetic error, which ensures that ML supertrees have a simple combinatorial description…
In evolutionary studies it is common to use phylogenetic trees to represent the evolutionary history of a set of species. However, in case the transfer of genes or other genetic information between the species or their ancestors has…
Mixture models are probabilistic models aimed at uncovering and representing latent subgroups within a population. In the realm of network data analysis, the latent subgroups of nodes are typically identified by their connectivity…
Fixed effects models are very flexible because they do not make assumptions on the distribution of effects and can also be used if the heterogeneity component is correlated with explanatory variables. A disadvantage is the large number of…