论Allee效应和大规模迁移在物种生存和灭绝中的作用
On the role of Allee effect and mass migration in survival and extinction of a species
摘要：
我们使用相互作用的粒子系统，以探讨生存和灭绝的一个物种的殖民地位于每个网站的$\mathbb {Z}^d$。在所研究的四种模型中，当地种群中的个体可以繁殖、死亡或迁移到邻近的地点。我们证明，当当地人口密度小（Allee效应）时，死亡率的增加可能对生存至关重要，并且当Allee效应很强时，大群个体的迁移是避免灭绝的一种可能的解决方案。我们使用的吸引力和比较定向渗透，无论是证明灭绝的物种，或构造非平凡的不变测度为每个模型。
英文摘要：
We use interacting particle systems to investigate survival and extinction of a species with colonies located on each site of $\mathbb {Z}^d$. In each of the four models studied, an individual in a local population can reproduce, die or migrate to neighboring sites. We prove that an increase of the death rate when the local population density is small (the Allee effect) may be critical for survival, and that the migration of large flocks of individuals is a possible solution to avoid extinction when the Allee effect is strong. We use attractiveness and comparison with oriented percolation, either to prove the extinction of the species, or to construct nontrivial invariant measures for each model.
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