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This article partakes of the PEGASE project the goal of which is a betterunderstanding of the mechanisms explaining the behaviour of species living in anetwork of forest patches linked by ecological corridors (hedges for instance).Actually we plan to study the effect of the fragmentation of the habitat onbiodiversity. A simple neutral model for the evolution of abundances in avegetal metacommunity is introduced. Migration between the communities isexplicitely modelized in a deterministic way, while the reproduction process isdealt with using Wright-Fisher models, independently within each community. Thelarge population limit of the model is considered. The hydrodynamic limit ofthis split-step method is proved to be the solution of a partial differentialequation with a deterministic part coming from the migration process and adiffusion part due to the Wright-Fisher process. Finally, the diversity of themetacommunity is adressed through one of its indicator, the mean extinctiontime of a species. At the limit, using classical comparison principles, theexchange process between the communities is proved to slow down extinction.This shows that the existence of corridors seems to be good for thebiodiversity.

Comparison principles and applications to mathematical modelling of vegetal meta-communities