%0 Journal Article %1 fournier2004microscopic %A Fournier, Nicolas %A Méléard, Sylvie %D 2004 %I Institute of Mathematical Statistics %J The Annals of Applied Probability %K Bolker-Pacala density-dependent_regulation limit_theorems spatial_demography spatial_models %N 4 %P 1880--1919 %R 10.1214/105051604000000882 %T A microscopic probabilistic description of a locally regulated population and macroscopic approximations %U https://doi.org/10.1214%2F105051604000000882 %V 14 %X 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.

@article{fournier2004microscopic, 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.}, added-at = {2019-11-09T06:34:52.000+0100}, author = {Fournier, Nicolas and M\'el\'eard, Sylvie}, biburl = {https://www.bibsonomy.org/bibtex/22f4538f803801e193f4b7596cad4ba30/peter.ralph}, doi = {10.1214/105051604000000882}, interhash = {233ce8c346ca1cd25cb016dbb9842d33}, intrahash = {2f4538f803801e193f4b7596cad4ba30}, journal = {The Annals of Applied Probability}, keywords = {Bolker-Pacala density-dependent_regulation limit_theorems spatial_demography spatial_models}, month = nov, number = 4, pages = {1880--1919}, publisher = {Institute of Mathematical Statistics}, timestamp = {2019-11-09T06:34:52.000+0100}, title = {A microscopic probabilistic description of a locally regulated population and macroscopic approximations}, url = {https://doi.org/10.1214%2F105051604000000882}, volume = 14, year = 2004 }