An interacting particle system modelling aggregation behavior: from individuals to populations

In this paper we investigate the stochastic modelling of a spatially structured biological population subject to social interaction. The biological motivation comes from the analysis of field experiments on a species of ants which exhibits a clear tendency to aggregate, still avoiding overcrowding....

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Bibliographic Details
Published inJournal of mathematical biology Vol. 50; no. 1; pp. 49 - 66
Main Authors Morale, Daniela, Capasso, Vincenzo, Oelschl ger, Karl
Format Journal Article
LanguageEnglish
Published Germany Springer Nature B.V 01.01.2005
Subjects
Animals
Ants
Formicidae
Models, Biological
Population Dynamics
Probability
Social Behavior
Stochastic Processes
Studies
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Summary:In this paper we investigate the stochastic modelling of a spatially structured biological population subject to social interaction. The biological motivation comes from the analysis of field experiments on a species of ants which exhibits a clear tendency to aggregate, still avoiding overcrowding. The model we propose here provides an explanation of this experimental behavior in terms of "long-ranged" aggregation and "short-ranged" repulsion mechanisms among individuals, in addition to an individual random dispersal described by a Brownian motion. Further, based on a "law of large numbers", we discuss the convergence, for large N, of a system of stochastic differential equations describing the evolution of N individuals (Lagrangian approach) to a deterministic integro-differential equation describing the evolution of the mean-field spatial density of the population (Eulerian approach).
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ISSN:0303-6812
1432-1416
DOI:10.1007/s00285-004-0279-1