论文标题
关于多物种社区缓慢扩散的演变
On the evolution of slow dispersal in multi-species communities
论文作者
论文摘要
对于任何$ n \ geq 2 $，我们表明有一些扩散速率的选择$ \ {d_i \} _ {i = 1}^n $，因此对于$ n $竞争的物种，它们在生态上相同并且具有独特的扩散率，最慢的分散器能够将其竞争性排除在该物种的其余部分。实际上，这种扩散率的选择在Hausdorff拓扑结构中开放。我们的结果为Dockery等人的猜想提供了一些证据。在1998年。主要工具包括半流的摩尔斯分解，以及用于线性抛物线方程的标准化主浮子束理论。证明的关键步骤是建立Floquet束对扩散率和其他系数的平稳依赖性，这可能具有独立感兴趣。
For any $N \geq 2$, we show that there are choices of diffusion rates $\{d_i\}_{i=1}^N$ such that for $N$ competing species which are ecologically identical and having distinct diffusion rates, the slowest disperser is able to competitive exclude the remainder of the species. In fact, the choices of such diffusion rates is open in the Hausdorff topology. Our result provides some evidence in the affirmative direction regarding the conjecture by Dockery et al. in 1998. The main tools include Morse decomposition of the semiflow, as well as the theory of normalized principal Floquet bundle for linear parabolic equations. A critical step in the proof is to establish the smooth dependence of the Floquet bundle on diffusion rate and other coefficients, which may be of independent interest.
