Abstract
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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