Related papers: A stochastic model for phylogenetic trees
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.…
We exhibit a stochastic discrete time model that has exactly the Eigen model as its deterministic continuous limit. Such model can be divided into two phases: reproduction followed by neutral selection. This result suggests that Eigen model…
A cell-molecular based evolutionary model of tumor development driven by a stochastic Moran birth-death process is developed, where each cell carries molecular information represented by a four-digit binary string, used to differentiate…
Between pandemics, the influenza virus exhibits periods of incremental evolution via a process known as antigenic drift. This process gives rise to a sequence of strains of the pathogen that are continuously replaced by newer strains,…
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…
A popular line of research in evolutionary biology is the use of time-calibrated phylogenies for the inference of diversification processes. This requires computing the likelihood of a given ultrametric tree as the reconstructed tree…
Habitat loss is one of the biggest threats facing plant species nowadays. We formulate a simple mathematical model of seed dispersal on reduced habitats to discuss survival of the species in relation to the habitat size and seeds production…
This article deals with the emergence of a specific mating preference pattern called homogamy in a population. Individuals are characterized by their genotype at two haploid loci, and the population dynamics is modelled by a non-linear…
We study a discrete-time stochastic process that can also be interpreted as a model for a viral evolution. A distinguishing feature of our process is power-law tails due to dynamics that resembles preferential attachment models. In the…
We introduce a biologically natural, mathematically tractable model of random phylogenetic network to describe evolution in the presence of hybridization. One of the features of this model is that the hybridization rate of the lineages…
In evolutionary biology, phylogenetic trees are commonly inferred from a set of characters (partitions) of a collection of biological entities (e.g., species or individuals in a population). Such characters naturally arise from molecular…
By unifying three foundational principles of modern biology, we develop a mathematical framework to analyze the growing tree of life. Contrary to the static case, where the analogy between phylogenetic trees and the tree that grows in soil…
We consider a random process on recursive trees, with three types of events. Vertices give birth at a constant rate (growth), each edge may be removed independently (fragmentation of the tree) and clusters (or trees) are frozen with a rate…
The properties of randomly evolving special trees having defined and analyzed already in two earlier papers (arXiv:cond-mat/0205650 and arXiv:cond-mat/0211092) have been investigated in the case when the continuous time parameter converges…
Predicting the ancestral sequences of a group of homologous sequences related by a phylogenetic tree has been the subject of many studies, and numerous methods have been proposed to this purpose. Theoretical results are available that show…
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…
Gene gain-loss-duplication models are commonly based on continuous-time birth-death processes. Employed in a phylogenetic context, such models have been increasingly popular in studies of gene content evolution across multiple genomes.…
Phylogenetic networks are a type of leaf-labelled, acyclic, directed graph used by biologists to represent the evolutionary history of species whose past includes reticulation events. A phylogenetic network is tree-child if each non-leaf…
A simplified model for the growth of a population is studied in which random effects arise because reproducing individuals have a certain probability of surviving until the next breeding season and hence contributing to the next generation.…
In evolutionary biology, the speciation history of living organisms is represented graphically by a phylogeny, that is, a rooted tree whose leaves correspond to current species and branchings indicate past speciation events. Phylogenies are…