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We discuss the population dynamics with selection and random diffusion, keeping the total population constant, in a fitness landscape associated with Constraint Satisfaction, a paradigm for difficult optimization problems. We obtain a phase…
Atmospheric water vapour is an essential ingredient of weather and climate. Key features of its distribution can be represented by kinematic models which treat it as a passive scalar advected by a prescribed flow and reacting through…
Recent work on stochastic interacting particle systems with two particle species (or single-species systems with kinematic constraints) has demonstrated the existence of spontaneous symmetry breaking, long-range order and phase coexistence…
Consider a species whose population density solves the steady diffusive logistic equation in a heterogeneous environment modeled with the help of a spatially non constant coefficient standing for a resources distribution in a given box. We…
The global dynamics of the two-species Lotka-Volterra competition patch model with asymmetric dispersal is classified under the assumptions of weak competition and the weighted digraph of the connection matrix is strongly connected and…
Clonal interference, competition between multiple co-occurring beneficial mutations, has a major role in adaptation of asexual populations. We provide a simple individual based stochastic model of clonal interference taking into account a…
Formation and competition of associations are studied in a six-species ecological model where each species has two predators and two prey. Each site of a square lattice is occupied by an individual belonging to one of the six species. The…
An ecosystem is a nonlinear dynamical system, its orbits giving rise to the observed complexity in the system. The diverse components of the ecosystem interact in discrete time to give rise to emergent features that determine the trajectory…
In this paper, we study a diffusive Lotka-Volterra competition model under homogeneous Dirichlet boundary conditions. We shall discuss the effects of dispersal rate and spatial heterogeneity on population dynamics. More precisely, we…
Individuals within any species exhibit differences in size, developmental state, or spatial location. These differences coupled with environmental fluctuations in demographic rates can have subtle effects on population persistence and…
Living organisms, ecosystems, and social systems are examples of complex systems in which robustness against inclusion of new elements is an essential feature. A recently proposed simple model has revealed a general mechanism by which such…
We study generalised rock-paper-scissors models with an arbitrary odd number N \geq 5 of species, among which n are weak, with 2 \leq n \leq (N-1)/2. Because of the species' weakness, the probability of individuals conquering territory in…
We demonstrate the presence of chaos in stochastic simulations that are widely used to study biodiversity in nature. The investigation deals with a set of three distinct species that evolve according to the standard rules of mobility,…
The ocean and the atmosphere, and hence the climate, are governed at large scale by interactions between pressure gradient, Coriolis and buoyancy forces. This leads to a quasi-geostrophic balance in which, in a two-dimensional-like fashion,…
We study a competition-diffusion model while performing simultaneous homogenization and strong competition limits. The limit problem is shown to be a Stefan type evolution equation with effective coefficients. We also perform some numerical…
Individual species may experience diverse outcomes, from prosperity to extinction, in an ecological community subject to external and internal variations. Despite the wealth of theoretical results derived from random matrix ensembles, a…
The dynamics of two competing species in a finite size community is one of the most studied problems in population genetics and community ecology. Stochastic fluctuations lead, inevitably, to the extinction of one of the species, but the…
Non-equilibrium thermodynamics has long been an area of substantial interest to ecologists because most fundamental biological processes, such as protein synthesis and respiration, are inherently energy-consuming. Microbial communities are…
If two species exhibit different nonlinear responses to a single shared resource, and if each species modifies the resource dynamics such that this favors its competitor, they may stably coexist. This coexistence mechanism, known as…
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…