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The aim of this paper is to tackle part of the program set by Diekmann et al. in their seminal paper Diekmann et al. (2001). We quote It remains to investigate whether, and in what sense, the nonlinear determin-istic model formulation is the limit of a stochastic model for initial population size tending to infinity We set a precise and general framework for a stochastic individual based model : it is a piecewise deterministic Markov process defined on the set of finite measures. We then establish a law of large numbers under conditions easy to verify. Finally we show how this applies to old and new examples.
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 forces in g
In this paper I will review twenty years of work on the question: When is there coexistence in stochastic spatial models? The answer, announced in Durrett and Levin [Theor. Pop. Biol. 46 (1994) 363--394], and that we explain in this paper is that thi
Here, we consider an SIS epidemic model where the individuals are distributed on several distinct patches. We construct a stochastic model and then prove that it converges to a deterministic model as the total population size tends to infinity. Furth
In this article, we consider time-changed models of population evolution $mathcal{X}^f(t)=mathcal{X}(H^f(t))$, where $mathcal{X}$ is a counting process and $H^f$ is a subordinator with Laplace exponent $f$. In the case $mathcal{X}$ is a pure birth pr
Classical ecological theory predicts that environmental stochasticity increases extinction risk by reducing the average per-capita growth rate of populations. To understand the interactive effects of environmental stochasticity, spatial heterogeneity