Related papers: Extinction threshold of a population in spatial an…
Understanding the dynamics of metapopulations close to extinction is of vital importance for management. Levins-like models, in which local patches are treated as either occupied or empty, have been used extensively for this purpose, but…
This chapter provides a pedagogical introduction and overview of spatial and temporal correlation and fluctuation effects resulting from the fundamentally stochastic kinetics underlying chemical reactions and the dynamics of populations or…
Having a precise knowledge of the dispersal ability of a population in a heterogeneous environment is of critical importance in agroecology and conservation biology as it can provide management tools to limit the effects of pests or to…
Changing environmental conditions can significantly affect the dynamics of disease spread. These changes may arise naturally or result from human interventions; in the latter case, lockdown measures that lead to abrupt but temporary…
Time evolution of number of species (genera, families, and others), population of them, and size distribution of present ones and life times are studied in terms of a new model, where population of each genetic taxon increases by a (random)…
Approximating the time to extinction of infection is an important problem in infection modelling. A variety of different approaches have been proposed in the literature. We study the performance of a number of such methods, and characterize…
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…
We propose a model to characterize how a diffusing population adapts under a time periodic selection, while its environment undergoes shifts and size changes, leading to significant differences with classical results on fixed domains. After…
We consider spatial population dynamics given by Markov birth-and-death process with constant mortality and birth influenced by establishment or fecundity mechanisms. The independent and density dependent dispersion of spreading are…
We study a class of multi-species birth-and-death processes going almost surely to extinction and admitting a unique quasi-stationary distribution (qsd for short). When rescaled by $K$ and in the limit $K\to+\infty$, the realizations of…
The strong Allee effect plays an important role on the evolution of population in ecological systems. One important concept is the Allee threshold that determines the persistence or extinction of the population in a long time. In general, a…
Consider a supercritical branching random walk in a time-inhomogeneous random environment. We impose a selection (called barrier) on survival in the following way. The position of the barrier may depend on the generation and the…
Cyclic dominance of species has been identified as a potential mechanism to maintain biodiversity, see e.g. B. Kerr, M. A. Riley, M. W. Feldman and B. J. M. Bohannan [Nature {\bf 418}, 171 (2002)] and B. Kirkup and M. A. Riley [Nature {\bf…
I discuss the so-called stochastic individual based model of adaptive dynamics and in particular how different scaling limits can be obtained by taking limits of large populations, small mutation rate, and small effect of single mutations…
We study the behavior of an infinite system of ordinary differential equations modeling the dynamics of a metapopulation, a set of (discrete) populations subject to local catastrophes and connected via migration under a mean field rule; the…
The logistic birth and death process is perhaps the simplest stochastic population model that has both density-dependent reproduction, and a phase transition, and a lot can be learned about the process by studying its extinction time,…
The reproduction speed of a continuous-time branching random walk is proportional to a positive parameter $\lambda$. There is a threshold for $\lambda$, which is called $\lambda_w$, that separates almost sure global extinction from global…
We study an individual based model describing competition in space between two different alleles. Although the model is similar in spirit to classic models of spatial population genetics such as the stepping stone model, here however space…
This article is concerned with a stochastic multi-patch model in which each local population is subject to a strong Allee effect. The model is obtained by using the framework of interacting particle systems to extend a stochastic two-patch…
We consider a simple stochastic model for the spread of a disease caused by two virus strains in a closed homogeneously mixing population of size N. The spread of each strain in the absence of the other one is described by the stochastic…