Related papers: Persistence and extinction for stochastic ecologic…

This paper investigates the dynamics of vegetation patterns in water-limited ecosystems using a generalized Klausmeier model that incorporates non-local plant dispersal within a finite habitat. We establish the well-posedness of the system…

Populations of replicating entities frequently experience sudden or cyclical changes in environment. We explore the implications of this phenomenon via a environmental switching parameter in several common evolutionary dynamics models…

We investigate coupled stochastic differential equations governing N non-negative continuous random variables that satisfy a conservation principle. In various fields a conservation law requires that a set of fluctuating variables be…

We consider a broad class of stochastic lattice predator-prey models, whose main features are overviewed. In particular, this article aims at drawing a picture of the influence of spatial fluctuations, which are not accounted for by the…

The extinction of species is a major problem of concern with a large literature. Our investigation gives insight into when species extinctions must occur, with an emphasis on determining which species might possibly die out and on how fast…

We analyse the asymptotic behaviour of integro-differential equations modelling $N$ populations in interaction, all structured by different traits. Interactions are modelled by non-local terms involving linear combinations of the total…

Many physical and natural systems, including the population of species, evolve in habitats with spatial stochastic variations of the individuals' motility. We study here the effect of those fluctuations on invasion and genetic loss. A…

Spatial metapopulation models are fundamental to theoretical ecology, enabling to study how landscape structure influences global species dynamics. Traditional models, including recent generalizations, often rely on the deterministic limit…

The introduction of stochasticity into continuous ecological models frequently relies on phenomenological, diagonal diffusion terms that lack a rigorous microscopic basis. We demonstrate that this standard practice fundamentally…

Many mathematical frameworks of evolutionary game dynamics assume that the total population size is constant and that selection affects only the relative frequency of strategies. Here, we consider evolutionary game dynamics in an extended…

We are interested in modeling the Darwinian evolution resulting from the interplay of phenotypic variation and natural selection through ecological interactions, in the specific scales of the biological framework of adaptive dynamics.…

Many socio-economic and biological processes can be modeled as systems of interacting individuals. The behaviour of such systems can be often described within game-theoretic models. In these lecture notes, we introduce fundamental concepts…

We consider the classical two-dimensional Rosenzweig-MacArthur prey-predator model with a degenerate noise, whereby only the prey variable is subject to small environmental fluctuations. This model has already been introduced in…

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 develop a stochastic two-patch epidemic model with nonlinear recidivism to investigate infectious disease dynamics in heterogeneous populations. Extending a deterministic framework, we introduce stochasticity to account for random…

Explaining biodiversity is a fundamental issue in ecology. A long-standing puzzle lies in the paradox of the plankton: many species of plankton feeding on a limited variety of resources coexist, apparently flouting the competitive exclusion…

This paper presents a study of the two-predators-two-preys discrete-time Lotka-Volterra model with self- inhibition terms for preys with direct applications to ecological problems. Parameters in the model are modified so that each of them…

The effect of stochasticity, in the form of Gaussian white noise, in a predator-prey model with two distinct time-scales is presented. A supercritical singular Hopf bifurcation yields a Type II excitability in the deterministic model. We…

This paper deals with coexistence and extinction of time periodic Volterra-Lotka type competing systems with nonlocal dispersal. Such issues have already been studied for time independent systems with nonlocal dispersal and time periodic…

Including spatial structure and stochastic noise invalidates the classical Lotka-Volterra picture of stable regular population cycles emerging in models for predator-prey interactions. Growth-limiting terms for the prey induce a continuous…