Affiliation:
1. Institut de Mathématiques de Toulouse, CNRS, UMR5219 Université de Toulouse Toulouse cedex 09 France
2. Institut Universitaire de France Paris France
3. Department of Mathematical Sciences University of Bath, Claverton Down Bath Somerset UK
Abstract
AbstractWe study the Bolker–Pacala–Dieckmann–Law (BPDL) model of population dynamics in the regime of large population density. The BPDL model is a particle system in which particles reproduce, move randomly in space and compete with each other locally. We rigorously prove global survival as well as a shape theorem describing the asymptotic spread of the population, when the population density is sufficiently large. In contrast to most previous studies, we allow the competition kernel to have an arbitrary, even infinite range, whence the term non‐local competition. This makes the particle system non‐monotone and of infinite‐range dependence, meaning that the usual comparison arguments break down and have to be replaced by a more hands‐on approach. Some ideas in the proof are inspired by works on the non‐local Fisher‐KPP equation, but the stochasticity of the model creates new difficulties.
Funder
Simons Foundation
Agence Nationale de la Recherche
Royal Society
Reference70 articles.
1. Branching Brownian Motion with Decay of Mass and the Nonlocal Fisher‐KPP Equation
2. The front location in branching Brownian motion with decay of mass;Addario‐Berry L.;Ann. Probab.,2017
3. Systems of branching, annihilating, and coalescing particles;Athreya S. R.;Electron. J. Probab.,2012
4. Speed of coming down from infinity for birth-and-death processes
5. C.Barnes L.Mytnik andZ.Sun On the coming down from infinity of local time coalescing Brownian motions arXiv preprint arXiv:2211.15298.