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


 
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1. Title Title of document The Fleming-Viot limit of an interacting spatial population with fast density regulation
 
2. Creator Author's name, affiliation, country Ankit Gupta; ETH Zurich; Switzerland
 
3. Subject Discipline(s)
 
3. Subject Keyword(s) spatial population; density dependence; Fleming-Viot process; cell polarity; site fidelity; carcinogenesis
 
3. Subject Subject classification 60J68; 60J85 ; 60G57; 60F99
 
4. Description Abstract

We consider 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. We show 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 $N \to \infty$. We first prove this result for a basic model in which the birth and death rates can only depend on the population density. In this case we obtain a neutral Fleming-Viot process. We then extend this model by including position-dependence in the birth and death rates, as well as, offspring dispersal and immigration mechanisms. We show how these extensions add mutation and selection to the limiting Fleming-Viot process. All the results are proved in a multi-type setting, where there are $q$ types of individuals reproducing each other. To illustrate the usefulness of our convergence result, we discuss certain applications in ecology and cell biology.
 
5. Publisher Organizing agency, location
 
6. Contributor Sponsor(s) ANR (French national research agency)
 
7. Date (YYYY-MM-DD) 2012-12-18
 
8. Type Status & genre Peer-reviewed Article
 
8. Type Type
 
9. Format File format PDF
 
10. Identifier Uniform Resource Identifier http://ejp.ejpecp.org/article/view/1964
 
10. Identifier Digital Object Identifier 10.1214/EJP.v17-1964
 
11. Source Journal/conference title; vol., no. (year) Electronic Journal of Probability; Vol 17
 
12. Language English=en en
 
14. Coverage Geo-spatial location, chronological period, research sample (gender, age, etc.)
 
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