论文标题
比较原则和应用植物元社区的数学建模
Comparison principles and applications to mathematical modelling of vegetal meta-communities
论文作者
论文摘要
本文介绍了PEGASE项目的目标，其目标是更好地理解解释生活在由生态走廊连接的森林斑块网络中的物种的行为（例如，树篱）。实际上，我们计划研究栖息地分裂对生物多样性的影响。引入了一种简单的中性模型，用于引入植物元社区中丰度的演变。社区之间的迁移以确定性的方式明确建模，而繁殖过程则与在每个社区内独立于使用Wright-Fisher模型进行处理。考虑了该模型的较大人口限制。事实证明，这种分裂方法的流体动力极限是偏微分方程的解决方案，其确定性部分来自迁移过程，并且由于Wright-fisher过程而引起的扩散部分。最后，元社区的多样性通过其指标之一，即物种的平均灭绝时间。在限制下，使用经典比较原则，事实证明，社区之间的交换过程减慢了灭绝。这表明走廊的存在似乎对生物多样性有益。
This article partakes of the PEGASE project the goal of which is a better understanding of the mechanisms explaining the behaviour of species living in a network of forest patches linked by ecological corridors (hedges for instance). Actually we plan to study the effect of the fragmentation of the habitat on biodiversity. A simple 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 of this split-step method 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. 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. This shows that the existence of corridors seems to be good for the biodiversity.
