Related papers: Large population limit of interacting population d…
Biological invasion, whereby populations of motile and proliferative individuals lead to moving fronts that invade into vacant regions, are routinely studied using partial differential equation (PDE) models based upon the classical…
In this communication we propose a most general equation to study pattern formation for one-species population and their limit domains in systems of length L. To accomplish this we include non-locality in the growth and competition terms…
We consider a two-component reaction-diffusion system that has previously been developed to model invasion of cells into a resident cell population. The system is an idealised version of models of tumour growth in which tumour cells degrade…
We consider a minimal go-or-grow model of cell invasion, whereby cells can either proliferate, following logistic growth, or move, via linear diffusion, and phenotypic switching between these two states is density-dependent. Formal analysis…
We analyse numerically the effects of small population size in the initial transient regime of a simple example population dynamics. These effects play an important role for the numerical determination of large deviation functions 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…
A particle system is said to be non-exchangeable if two particles cannot be exchanged without modifying the overall dynamics. Because of this property, the classical mean-field approach fails to provide a limit equation when the number of…
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…
We are concerned with a nonlinear nonautonomous model represented by an equation describing the dynamics of an age-structured population diffusing in a space habitat $O,$ governed by local Lipschitz vital factors and by a stochastic…
System-environment interactions are intrinsically nonlinear and dependent on the interplay between many degrees of freedom. The complexity may be even more pronounced when one aims to describe biologically motivated systems. In that case,…
Population dynamics provides a numerical tool allowing for the study of rare events by means of simulating a large number of copies of the system, supplemented with a selection rule that favours the rare trajectories of interest. The…
The n-person Prisoner's Dilemma is a widely used model for populations where individuals interact in groups. The evolutionary stability of populations has been analysed in the literature for the case where mutations in the population may be…
While there is a long history of employing moving boundary problems in physics, in particular via Stefan problems for heat conduction accompanied by a change of phase, more recently such approaches have been adapted to study biological…
Diffusion processes have been applied with great success to model the dynamics of large populations throughout science, in particular biology. One advantage is that they bridge two different scales: the microscopic and the macroscopic one.…
We consider a stochastic individual-based model of adaptive dynamics for an asexually reproducing population with mutation, with linear birth and death rates, as well as a density-dependent competition. To depict repeating changes of the…
We study a generalized discrete-time multi-type Wright-Fisher population process. The mean-field dynamics of the stochastic process is induced by a general replicator difference equation. We prove several results regarding the asymptotic…
The growth function of populations is central in biomathematics. The main dogma is the existence of density dependence mechanisms, which can be modelled with distinct functional forms that depend on the size of the population. One important…
We describe a continuous-time modelling framework for biological population dynamics that accounts for demographic noise. In the spirit of the methodology used by statistical physicists, transitions between the states of the system are…
Mathematical models of biological populations commonly use discrete structure classes to capture trait variation among individuals (e.g. age, size, phenotype, intracellular state). Upscaling these discrete models into continuum descriptions…
The propagation of a beneficial mutation in a spatially extended population is usually studied using the phenomenological stochastic Fisher-Kolmogorov (SFKPP) equation. We derive here an individual based, stochastic model founded on the…