Wu Hong, Wang Yuanshi
School of Mathematics, Sun Yat-sen University, Guangzhou, 510275, People's Republic of China.
Bull Math Biol. 2021 Mar 25;83(5):49. doi: 10.1007/s11538-021-00885-5.
This paper considers two-species competitive systems with one-species' diffusion between patches. Each species can persist alone in the corresponding patch (a source), while the mobile species cannot survive in the other (a sink). Using the method of monotone dynamical systems, we give a rigorous analysis on persistence of the system, prove local/global stability of the equilibria and show new types of bi-stability. These results demonstrate that diffusion could lead to results reversing those without diffusion, which extend the principle of competitive exclusion: Diffusion could lead to persistence of the mobile competitor in the sink, make it reach total abundance larger than if non-diffusing and even exclude the opponent. The total abundance is shown to be a distorted function (surface) of diffusion rates, which extends both previous theory and experimental observations. A novel strategy of diffusion is deduced in which the mobile competitor could drive the opponent into extinction, and then approach the maximal abundance. Initial population density and diffusive asymmetry play a role in the competition. Our work has potential applications in biodiversity conservation and economic competition.
本文考虑了斑块间存在单物种扩散的两物种竞争系统。每个物种都能在相应的斑块（一个源）中独自存续，而可移动物种在另一个斑块（一个汇）中无法存活。利用单调动力系统方法，我们对该系统的持续性进行了严格分析，证明了平衡点的局部/全局稳定性，并展示了新型的双稳性。这些结果表明，扩散可能导致与无扩散情况相反的结果，这扩展了竞争排斥原理：扩散可能导致可移动竞争者在汇中存续，使其总丰度大于不扩散时的情况，甚至排斥对手。总丰度被证明是扩散率的一个扭曲函数（曲面），这扩展了先前的理论和实验观察结果。推导出一种新颖的扩散策略，其中可移动竞争者可以驱使对手灭绝，然后接近最大丰度。初始种群密度和扩散不对称性在竞争中起作用。我们的工作在生物多样性保护和经济竞争方面具有潜在应用。
