A microscopic probabilistic description of a locally regulated population and macroscopic approximations

Details A microscopic probabilistic description of a locally regulated population and macroscopic approximations A microscopic probabilistic description of a locally regulated population and macroscopic approximations

2005-03-24

arxiv.org/abs/math/0503546v1

Annals of Applied Probability 2004, Vol. 14, No. 4, 1880-1919

Mathematics

Probability

Published at http://dx.doi.org/10.1214/105051604000000882 in the Annals of Applied Probability (http://www.imstat.org/aap/) by

Scientific paper

10.1214/105051604000000882

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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