Related papers: On an aggregation in birth-and-death stochastic dy…
A new class of particle systems with sequential interaction is proposed to approximate the McKean-Vlasov process that originally arises as the limit of the mean-field interacting particle system. The weighted empirical measure of this…
Stochastic models that incorporate birth, death and immigration (also called birth-death and innovation models) are ubiquitous and applicable to many research topics such as quantifying species sizes in ecological populations, describing…
How are granular details of stochastic growth and division of individual cells reflected in smooth deterministic growth of population numbers? We provide an integrated, multiscale perspective of microbial growth dynamics by formulating a…
This article studies the quasi-stationary behaviour of multidimensional birth and death processes, modeling the interaction between several species, absorbed when one of the coordinates hits 0. We study models where the absorption rate is…
This paper is focused on a class of spatial birth and death process of the Euclidean space where the birth rate is constant and the death rate of a given point is the shot noise created at its location by the other points of the current…
We study the stochastic evolution of four species in cyclic competition in a well mixed environment. In systems composed of a finite number $N$ of particles these simple interaction rules result in a rich variety of extinction scenarios,…
A central problem in population ecology is understanding the consequences of stochastic fluctuations. Analytically tractable models with Gaussian driving noise have led to important, general insights, but they fail to capture rare,…
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 introduce a broad class of spatial models to describe how spatially heterogeneous populations live, die, and reproduce. Individuals are represented by points of a point measure, whose birth and death rates can depend both on spatial…
We deal with two following classes of equilibrium stochastic dynamics of infinite particle systems in continuum: hopping particles (also called Kawasaki dynamics), i.e., a dynamics where each particle randomly hops over the space, and…
This contribution is concerned with mathematical models for the dynamics of the genetic composition of populations evolving under recombination. Recombination is the genetic mechanism by which two parent individuals create the mixed type of…
Condensation phenomena arise through a collective behaviour of particles. They are observed in both classical and quantum systems, ranging from the formation of traffic jams in mass transport models to the macroscopic occupation of the…
We investigate extinction of a long-lived self-regulating stochastic population, caused by intrinsic (demographic) noise. Extinction typically occurs via one of two scenarios depending on whether the absorbing state n=0 is a repelling…
Classical age-structured mass-action models such as the McKendrick-von Foerster equation have been extensively studied but they are structurally unable to describe stochastic fluctuations or population-size-dependent birth and death rates.…
We investigate the thermodynamics as well as the population dynamics of ecosystems based on a stochastic approach in which the number of individuals of the several species of the ecosystem are treated as stochastic variables. The several…
In this paper we study a class of stochastic individual-based models that describe the evolution of haploid populations where each individual is characterised by a phenotype and a genotype. The phenotype of an individual determines its…
We consider an infinite locally finite system (configuration) $\gamma$ of particles distributed over a Euclidean space $X$. Each particle located at $x\in X$ carries an internal parameter (mark, or ``spin'') $\sigma_{x}\in S=\mathbb{R}.$…
We are interested in the long-time behavior of a diploid population with sexual reproduction, characterized by its genotype composition at one bi-allelic locus. The population is modeled by a 3-dimensional birth-and-death process with…
We study the probabilistic evolution of a birth and death continuous time measure-valued process with mutations and ecological interactions. The individuals are characterized by (phenotypic) traits that take values in a compact metric…
Recently, a first step was made by the authors towards a systematic investigation of the effect of reaction-step-size noise - uncertainty in the step size of the reaction - on the dynamics of stochastic populations. This was done by…