Gauthier Delvoye, Olivier Goubet, Frédéric Paccaut
Published 2020-04-03Version 1
A neutral model for the evolution of abundances in a vegetal metacommunity is introduced. Migration between the communities is explicitely modelized in a deterministic way, while the reproduction process is dealt with using Wright-Fisher models, independently within each community. The large population limit of the model is considered. The hydrodynamic limit is proved to be the solution of a partial differential equation with a deterministic part coming from the migration process and a diffusion part due to the Wright-Fisher process. The convergence in law of the piecewise affine extension of the discrete process is also established. Finally, the diversity of the metacommunity is adressed through one of its indicator, the mean extinction time of a species. At the limit, using classical comparison principles, the exchange process between the communities is proved to slow down extinction.
Linear forms of the telegraph random processes driven by partial differential equations
Large population limit of the spectrum of killed birth-and-death processes
Large population limits of Markov processes on random networks
![QR code for arXiv:2004.01417 [math.PR]](http://oss.arxitics.com/images/favicon.svg)