Related papers: Two-type branching processes with immigration, and…
We study the dynamics of a two-site model in which the tunneling amplitude between the sites is not constant but rather a high-frequency noise. Obviously, the population imbalance in this model decays exponentially with time. Remarkably,…
We consider an asexually reproducing population on a finite type space whose evolution is driven by exponential birth, death and competition rates, as well as the possibility of mutation at a birth event. On the individual-based level this…
We consider the behaviour of branching-selection particle systems in the large population limit. The dynamics of these systems is the combination of the following three components: (a) Motion: particles move on the real line according to a…
Populations exhibiting partial migration consist of two groups of individuals: Those that mi- grate between habitats, and those that remain fixed in a single habitat. We propose several discrete-time population models to investigate the…
We consider population models in which the individuals reproduce, die and also migrate in space. The population size scales according to some parameter $N$, which can have different interpretations depending on the context. Each individual…
The approximation of the Feynman-Kac semigroups by systems of interacting particles is a very active research field, with applications in many different areas. In this paper, we study the parallelization of such approximations. The total…
Highly-diverse ecosystems exhibit a broad distribution of population sizes and species turnover, where species at high and low abundances are exchanged over time. We show that these two features generically emerge in the fluctuating phase…
We analyse a family of two-types Wright-Fisher models with selection in a random environment and skewed offspring distribution. We provide a calculable criterion to quantify the impact of different shapes of selection on the fate of the…
Models of population growth and extinction are an increasingly popular subject of study. However, consequences of stochasticity and noise in shaping distributions and outcomes are not sufficiently explored. Here we consider a distributed…
We derive the asymptotic behavior of the total, active and inactive branch lengths of the seed bank coalescent, when the size of the initial sample grows to infinity. Those random variables have important applications for populations…
Dispersal of species to find a more favorable habitat is important in population dynamics. Dispersal rates evolve in response to the relative success of different dispersal strategies. In a simplified deterministic treatment (J. Dockery, V.…
In this paper, we introduce a two-sex controlled branching model to describe the interaction between predator and prey populations with sexual reproduction. This process is a two-type branching process, where the first type corresponds to…
In the present article, we investigate the effects of dormancy on an abstract population genetic level. We first provide a short review of seed bank models in population genetics, and the role of dormancy for the interplay of evolutionary…
Extinction of a long-lived isolated stochastic population can be described as an exponentially slow decay of quasi-stationary probability distribution of the population size. We address extinction of a population in a two-population system…
We consider two sequential models of deposition and aggregation for particles. The first model (No Diffusion) simulates surface diffusion through a deterministic capture area, while the second (Sequential Diffusion) allows the atoms to…
We propose and analyze a new class of controlled multi-type branching processes with a per-step linear resource constraint, motivated by potential applications in viral marketing and cancer treatment. We show that the optimal exponential…
We propose a modelling framework to analyse the stochastic behaviour of heterogeneous, multi-scale cellular populations. We illustrate our methodology with a particular example in which we study a population with an oxygen-regulated…
We consider a population of agents that are heterogeneous with respect to (i) their strategy when interacting $n_{g}$ times with other agents in an iterated prisoners dilemma game, (ii) their spatial location on $K$ different islands. After…
In this work we describe a new model for the evolution of a diploid structured population backwards in time that allows for large migrations and uneven offspring distributions. The model generalizes both the mean-field model of Birkner et…
We study a stochastic model proposed recently in the genetic literature to explain the heterogeneity of cell populations or of gene products. Cells are located in two colonies, whose sizes fluctuate as birth and migration processes in…