# Probabilistic Foundations of Spatial Mean-Field Models in Ecology and Applications

@article{Patterson2020ProbabilisticFO,
title={Probabilistic Foundations of Spatial Mean-Field Models in Ecology and Applications},
author={Denis D. Patterson and Simon A. Levin and Carla Staver and Jonathan Touboul},
journal={SIAM J. Appl. Dyn. Syst.},
year={2020},
volume={19},
pages={2682-2719}
}
• Published 15 November 2019
• Mathematics
• SIAM J. Appl. Dyn. Syst.
Deterministic models of vegetation often summarize, at a macroscopic scale, a multitude of intrinsically random events occurring at a microscopic scale. We bridge the gap between these scales by demonstrating convergence to a mean-field limit for a general class of stochastic models representing each individual ecological event in the limit of large system size. The proof relies on classical stochastic coupling techniques that we generalize to cover spatially extended interactions. The mean…
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