多物种群落中慢扩散演化的研究
On the evolution of slow dispersal in multi-species communities
AI总结：
本研究证明在多物种竞争群落中，存在扩散速率选择使得最慢扩散者能竞争排除其他物种，为1998年Dockery猜想提供肯定证据，主要工具包括Morse分解和Floquet丛理论。
摘要：
对于任意 $N \geq 2$，我们证明存在扩散速率 $\{d_i\}_{i=1}^N$ 的选择，使得对于 $N$ 个生态学上相同且具有不同扩散速率的竞争物种，最慢的扩散者能够竞争性排除其余物种。事实上，此类扩散速率的选择在 Hausdorff 拓扑下是开放的。我们的结果为 Dockery 等人 1998 年的猜想提供了肯定方向的某些证据。主要工具包括半流的 Morse 分解，以及线性抛物方程的归一化主 Floquet 丛理论。证明中的一个关键步骤是建立 Floquet 丛对扩散速率及其他系数的光滑依赖性，这可能具有独立的研究兴趣。
英文摘要：
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.
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