Related papers: Interpreting how nonlinear diffusion affects the f…
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…
Many species see their range shifted poleward in response to global warming and need to keep pace in order to survive. To understand the effect of climate change on species ranges and its consequences on population dynamics, we consider a…
Understanding how stochastic and non-linear deterministic processes interact is a major challenge in population dynamics theory. After a short review, we introduce a stochastic individual-centered particle model to describe the evolution in…
The dynamics of a reaction-diffusion-advection benthic-drift population model that links changes in the flow regime and habitat availability with population dynamics is studied. In the model, the stream is divided into drift zone and…
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 consider a model for a population in a heterogeneous environment, with logistic type local population dynamics, under the assumption that individuals can switch between two different nonzero rates of diffusion. Such switching behavior…
We consider a nonlocal bistable reaction-diffusion equation, which serves as a model for a population structured by a phenotypic trait, subject to mutation, trait-dependent fitness, and nonlocal competition. Within this replicator-mutator…
We study the large population limit of the Moran process, assuming weak-selection, and for different scalings. Depending on the particular choice of scalings, we obtain a continuous model that may highlight the genetic-drift (neutral…
Stochastic models of diffusion with excluded-volume effects are used to model many biological and physical systems at a discrete level. The average properties of the population may be described by a continuum model based on partial…
In this paper, we study pattern formations in an aggregation and diffusion cell migration model with Dirichlet boundary condition. The formal continuum limit of the model is a nonlinear parabolic equation with a diffusivity which can become…
A cubic discrete coupled logistic equation is proposed to model the predator-prey problem. The coupling depends on the population size of both species and on a positive constant $\lambda$, which could depend on the prey reproduction rate…
This paper is devoted to the study of the persistence versus extinction of species in the reaction-diffusion equation: \begin{equation} u_t-\Delta u=f(t,x_1-ct,y,u) \quad\quad t>0,\ x\in\Omega,\nonumber \end{equation} where $\Omega$ is of…
We analyze the long-term stability of a stochastic model designed to illustrate the adaptation of a population to variation in its environment. A piecewise-deterministic process modeling adaptation is coupled to a Feller logistic diffusion…
This article studies the quasi-stationary behaviour of population processes with unbounded absorption rate, including one-dimensional birth and death processes with catastrophes and multi-dimensional birth and death processes, modeling…
We study the stability of non-conservative deterministic cross diffusion models and prove that they are approximated by stochastic population models when the populations become locally large. In this model, the individuals of two species…
In this paper, we study a finite population undergoing discrete, nonoverlapping generations, that is structured into $D$ demes, each containing $N$ individuals of two possible types, $A$ and $B$, whose viability coefficients, $s_A$ and…
Many species are unsustainable at small population densities (Allee Effect), i.e., below a threshold named Allee threshold, the population decreases instead of growing. In a closed local population, environmental fluctuations always lead to…
The interplay between space and evolution is an important issue in population dynamics, that is in particular crucial in the emergence of polymorphism and spatial patterns. Recently, biological studies suggest that invasion and evolution…
We classify traveling waves and stationary solutions of a reaction-diffusion equation arising in population dynamics with Allee-type effects. The reaction term is given by a quadratic polynomial with a discontinuity at zero, which captures…
The position of propagating population fronts fluctuates because of the discreteness of the individuals and stochastic character of processes of birth, death and migration. Here we consider a Markov model of a population front propagating…