The Fleming-Viot limit of an interacting spatial population with fast density regulation (Q392695)

From the author's abstract: The author deals with population models in which the individuals reproduce, die and also migrate in space. The population size scales according to some parameter \(N\), which can have different interpretations depending on the context. Each individual is assigned a mass of \(1/N\) and the total mass in the system is called population density. The dynamics has an intrinsic density regulation mechanism that drives the population density towards an equilibrium. It is shown that under a timescale separation between the slow migration mechanism and the fast density regulation mechanism, the population dynamics converges to a Fleming-Viot process as the scaling parameter \(N\to\infty\). All the results are proved in a multi-type setting, where there are \(q\) types of individuals reproducing each other. Certain applications in ecology and cell biology are considered.