Journal
ANNALS OF APPLIED PROBABILITY
Volume 14, Issue 4, Pages 1880-1919Publisher
INST MATHEMATICAL STATISTICS
DOI: 10.1214/105051604000000882
Keywords
interacting measure-valued processes; regulated population; deterministic macroscopic approximation; nonlinear superprocess; equilibrium
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We consider a discrete model that describes a locally regulated spatial population with mortality selection. This model was studied in parallel by Bolker and Pacala and Dieckmann, Law and Murrell. We first generalize this model by adding spatial dependence. Then we give a pathwise description in terms of Poisson point measures. We show that different normalizations may lead to different macroscopic approximations of this model. The first approximation is deterministic and gives a rigorous sense to the number density. The second approximation is a superprocess previously studied by Etheridge. Finally, we study in specific cases the long time behavior of the system and of its deterministic approximation.
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