Related papers: On average population levels for models with direc…
We study the transport property of diffusion in a finite translationally invariant quantum subsystem described by a tight-binding Hamiltonian with a single energy band and interacting with its environment by a coupling in terms of…
The global-in-time existence of nonnegative bounded weak solutions to a class of cross-diffusion systems for two population species is proved. The diffusivities are assumed to depend linearly on the population densities in such a way that a…
Darwinian evolution can be modeled in general terms as a flow in the space of fitness (i.e. reproductive rate) distributions. In the diffusion approximation, Tsimring et al. have showed that this flow admits "fitness wave" solutions:…
We introduce a modified spatial $\Lambda$-Fleming-Viot process to model the ancestry of individuals in a population occupying a continuous spatial habitat divided into two areas by a sharp discontinuity of the dispersal rate and effective…
We consider a metapopulation made up of $K$ demes, each containing $N$ individuals bearing a heritable quantitative trait. Demes are connected by migration and undergo independent Moran processes with mutation and selection based on trait…
We investigate the long-time dynamics of a SIR epidemic model in the case of a population of pathogens infecting a homogeneous host population. The pathogen population is structured by a genotypic variable. When the initial mass of the…
The existence of global weak solutions to the cross-diffusion model of Shigesada, Kawasaki, and Teramoto for an arbitrary number of species is proved. The model consists of strongly coupled parabolic equations for the population densities…
Populations are often subject to catastrophes that cause mass removal of individuals. Many stochastic growth models have been considered to explain such dynamics. Among the results reported, it has been considered whether dispersion…
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…
A class of parabolic cross-diffusion systems modeling the interaction of an arbitrary number of population species is analyzed in a bounded domain with no-flux boundary conditions. The equations are formally derived from a random-walk…
Density-dependent population growth is a feature of large carnivores like wolves ($\textit{Canis lupus}$), with mechanisms typically attributed to resource (e.g. prey) limitation. Such mechanisms are local phenomena and rely on individuals…
In the present paper, our goal is to establish a framework for the mathematical modelling and the analysis of the spread of an epidemic in a large population commuting regularly, typically along a time-periodic pattern, as is roughly…
Here we study the emergence of spontaneous leadership in large populations. In standard models of opinion dynamics, herding behavior is only obeyed at the local scale due to the interaction of single agents with their neighbors; while at…
The growth of the average kinetic energy of classical particles is studied for potentials that are random both in space and time. Such potentials are relevant for recent experiments in optics and in atom optics. It is found that for small…
We consider stochastic growth models for populations organized in colonies and subject to uniform catastrophes. To assess population viability, we analyze scenarios in which individuals adopt dispersion strategies after catastrophic events.…
Ecological and evolutionary dynamics have been historically regarded as unfolding at broadly separated timescales. However, these two types of processes are nowadays well documented to much more tightly than traditionally assumed,…
In this article, discrete and stochastic changes in (effective) population size are incorporated into the spectral representation of a biallelic diffusion process for drift and small mutation rates. A forward algorithm inspired by…
We consider a stochastic individual-based model for the evolution of a haploid, asexually reproducing population. The space of possible traits is given by the vertices of a (possibly directed) finite graph $G=(V,E)$. The evolution of the…
A discrete-time model of reacting evolving fields, transported by a bidimensional chaotic fluid flow, is studied. Our approach is based on the use of a Lagrangian scheme where {\it fluid particles} are advected by a $2d$ symplectic map…
The theory of life history evolution provides a powerful framework to understand the evolutionary dynamics of pathogens in both epidemic and endemic situations. This framework, however, relies on the assumption that pathogen populations are…