Department of Mathematics, Ohio State University, Columbus, OH 43210, USA.
J Biol Dyn. 2012;6:117-30. doi: 10.1080/17513758.2010.529169. Epub 2011 Jun 24.
We address several conjectures raised in Cantrell et al. [Evolution of dispersal and ideal free distribution, Math. Biosci. Eng. 7 (2010), pp. 17-36 [ 9 ]] concerning the dynamics of a diffusion-advection-competition model for two competing species. A conditional dispersal strategy, which results in the ideal free distribution of a single population at equilibrium, was found in Cantrell et al. [ 9 ]. It was shown in [ 9 ] that this special dispersal strategy is a local evolutionarily stable strategy (ESS) when the random diffusion rates of the two species are equal, and here we show that it is a global ESS for arbitrary random diffusion rates. The conditions in [ 9 ] for the coexistence of two species are substantially improved. Finally, we show that this special dispersal strategy is not globally convergent stable for certain resource functions, in contrast with the result from [ 9 ], which roughly says that this dispersal strategy is globally convergent stable for any monotone resource function.
我们解决了 Cantrell 等人在 [Evolution of dispersal and ideal free distribution, Math. Biosci. Eng. 7 (2010), pp. 17-36 [9]] 中提出的几个猜想，这些猜想涉及到一个用于两种竞争物种的扩散-对流-竞争模型的动力学。在 Cantrell 等人的研究中发现了一种条件扩散策略，这种策略导致了单一种群在平衡时的理想自由分布。[9] 表明，当两种物种的随机扩散率相等时，这种特殊的扩散策略是局部进化稳定策略（ESS），而在这里我们证明，对于任意随机扩散率，它都是全局 ESS。[9] 中关于两种物种共存的条件得到了实质性的改进。最后，我们表明，对于某些资源函数，这种特殊的扩散策略不是全局收敛稳定的，这与[9]中的结果相反，[9]中的结果大致表明，对于任何单调资源函数，这种扩散策略都是全局收敛稳定的。
