Related papers: Graphon-valued stochastic processes from populatio…
Finding the most powerful node in a dynamic random network, the largest set in a partition-valued stochastic process, or the largest family in an evolving population at a given time, can be a very difficult problem. This is particularly the…
We consider two classes of natural stochastic processes on finite unlabeled graphs. These are Euclidean stochastic optimization algorithms on the adjacency matrix of weighted graphs and a modified version of the Metropolis MCMC algorithm on…
The contact process is a simple model for the spread of an infection in a structured population. We investigate the case when the underlying structure evolves dynamically as a degree-dependent dynamical percolation model. Starting with a…
We present an explicit unified stochastic model of fluctuations in population size due to random birth, death, density-dependent competition and environmental fluctuations. Stochastic dynamics provide insight into small populations,…
We study a family of n-dimensional diffusions, taking values in the unit simplex of vectors with nonnegative coordinates that add up to one. These processes satisfy stochastic differential equations which are similar to the ones for the…
We study the evolution of a pathogen with two allelic types infecting a population of hosts, where within-host type frequencies evolve in discrete time. Our framework is built on a two-parameter family of transition kernels on [0,1], which…
The Galton--Watson process is the simplest example of a branching process. The relationship between the offspring distribution, and, when the extinction occurs almost surely, the distribution of the total progeny is well known. In this…
We consider heterogeneously interacting diffusive particle systems and their large population limit. The interaction is of mean field type with weights characterized by an underlying graphon. A law of large numbers result is established as…
We investigate the $\Lambda$-Seed-Bank-Wright-Fisher process, a model describing allele frequency dynamics in populations exhibiting both skewed offspring distributions and dormancy. By performing a change of measure, we condition this…
The measure-valued Fleming-Viot process is a diffusion which models the evolution of allele frequencies in a multi-type population. In the neutral setting the Kingman coalescent is known to generate the genealogies of the "individuals" in…
The drift-barrier hypothesis states that random genetic drift constrains the refinement of a phenotype under natural selection. The influence of effective population size and the genome-wide deleterious mutation rate were studied…
A Galton-Watson branching process with immigration evolving in a random environment is considered. Its associated random walk is assumed to be oscillating. We prove a functional limit theorem in which the process under consideration is…
For a population with any given number of types, we construct a new multivariate Moran process with frequency-dependent selection and establish, analytically, a correspondence to equilibrium Lotka-Volterra phenomenology. This…
In evolutionary dynamics, well-mixed populations are almost always associated with all-to-all interactions; mathematical models are based on complete graphs. In most cases, these models do not predict fixation probabilities in groups of…
This paper deals with the stochastic modeling of a class of heterogeneous population in a random environment, called birth-death-swap. In addition to demographic events, swap events, i.e. moves between subgroups, occur in the population.…
Moran or Wright-Fisher processes are probably the most well known model to study the evolution of a population under various effects. Our object of study will be the Simpson index which measures the level of diversity of the population, one…
This paper generalizes the strong seed-bank model introduced in arXiv:1411.4747 to allow for more general dormancy time distributions, such as a type of Pareto distribution. Inspired by the method of approximation using models with…
Changes in human behavior are increasingly recognized as a major determinant of epidemic dynamics. Although collective activity can be modified through imposed measures to control epidemic progression, spontaneous changes can also arise as…
We consider an approximating sequence of interacting population models with branching, mutation and competition. Each individual is characterized by its trait and the traits of its ancestors. Birth- and death-events happen at exponential…
We are interested in the dynamic of a structured branching population where the trait of each individual moves according to a Markov process. The rate of division of each individual is a function of its trait and when a branching event…