Related papers: Persistence analysis of the age-structured populat…
Ecological resilience refers to the ability of a system to retain its state when subject to state variables perturbations or parameter changes. While understanding and quantifying resilience is crucial to anticipate the possible regime…
We consider a system of independent branching random walks on $\R$ which start off a Poisson point process with intensity of the form $e_{\lambda}(du)=e^{-\lambda u}du$, where $\lambda\in\R$ is chosen in such a way that the overall…
The Markov evolution is studied of an infinite age-structured population of migrants arriving in and departing from a continuous habitat $X \subseteq\mathds{R}^d$ -- at random and independently of each other. Each population member is…
We consider population dynamics on a network of patches, each of which has a the same local dynamics, with different population scales (carrying capacities). It is reasonable to assume that if the patches are coupled by very fast migration…
This paper is a follow-up to a previous work where we considered populations with time-varying growth rates living in patches and irreducible migration matrix between the patches. Each population, when isolated, would become extinct.…
We study a population of $N$ particles, which evolve according to a diffusion process and interact through a dynamical network. In turn, the evolution of the network is coupled to the particles' positions. In contrast with the mean-field…
This review paper presents the known results on the asymptotics of the survival probability and limit theorems conditioned on survival of critical and subcritical branching processes in IID random environments. The key assumptions of the…
We consider a biological population whose environment varies periodically in time, exhibiting two very different "seasons" : one is favorable and the other one is unfavorable. For monotone differential models with concave nonlinearities, we…
A stochastic forest model of young and old age class trees is studied. First, we prove existence, uniqueness and boundedness of global nonnegative solutions. Second, we investigate asymptotic behavior of solutions by giving a sufficient…
This work proposes and analyzes a family of spatially inhomogeneous epidemic models. This is our first effort to use stochastic partial differential equations (SPDEs) to model epidemic dynamics with spatial variations and environmental…
The paper is devoted to the study of the asymptotic behaviour of Moran process in random environment, say random selection. In finite population, the Moran process may be degenerate in finite time, thus we will study its limiting process in…
Understanding how a diversity of plants in agroecosystems affects the adaptation of pathogens in a key issue in agroecology. We analyze PDE systems describing the dynamics of adaptation of two phenotypically structured populations, under…
The simplest model of a smart spatial redistribution of individuals is proposed. A single-species population is considered, to be composed of two discrete subpopulations inhabiting two stations; migration is a transfer between them. The…
We give necessary and sufficient conditions for a sequence to be exactly realizable as the sequence of numbers of periodic points in a dynamical system. Using these conditions, we show that no non-constant polynomial is realizable, and give…
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…
Environmental changes greatly influence the evolution of populations. Here, we study the dynamics of a population of two strains, one growing slightly faster than the other, competing for resources in a time-varying binary environment…
Age-structured models with nonlocal diffusion arise naturally in describing the population dynamics of biological species and the transmission dynamics of infectious diseases in which individuals disperse nonlocally and interact each other…
We consider a linear size-structured population model with diffusion in the size-space. Individuals are recruited into the population at arbitrary sizes. The model is equipped with generalized Wentzell-Robin (or dynamic) boundary…
In this work we introduce and analyze a linear size-structured population model with infinite states-at-birth. We model the dynamics of a population in which individuals have two distinct life-stages: an "active" phase when individuals…
This paper is concerned with spatial spreading dynamics of a nonlocal dispersal population model in a shifting environment where the favorable region is shrinking. It is shown that the species will become extinct in the habitat once the…