Cantrell Robert Stephen, Cosner Chris, Lou Yuan
Department of Mathematics, University of Miami, Coral Gables, FL 33124, USA.
Math Biosci. 2006 Dec;204(2):199-214. doi: 10.1016/j.mbs.2006.09.003. Epub 2006 Sep 19.
We study a reaction-diffusion-advection model for two ecologically equivalent competitors with different dispersal strategies inhabiting a spatially heterogeneous environment. The competitors represent different phenotypes of the same species. One is assumed to disperse by simple diffusion, the other by diffusion together with directed movement toward more favorable environments. We show that under suitable conditions on the underlying spatial domain, the competitor that moves toward more favorable environments may have a competitive advantage even if it diffuses more rapidly than the other competitor. This is in contrast with the case in which both competitors disperse by pure diffusion, where the competitor that diffuses more slowly always has the advantage. We determine competitive advantage by examining the invasibility, i.e. stability or instability, of steady states with only one competitor present. The mathematical approach is a perturbation analysis of principal eigenvalues.
我们研究了一个反应扩散对流模型，该模型用于描述两种具有不同扩散策略的生态等效竞争者，它们栖息在一个空间异质的环境中。这些竞争者代表同一物种的不同表型。一种竞争者被假定通过简单扩散进行扩散，另一种则通过扩散以及向更有利环境的定向移动进行扩散。我们表明，在基础空间域的适当条件下，向更有利环境移动的竞争者可能具有竞争优势，即使它比另一个竞争者扩散得更快。这与两种竞争者都通过纯扩散进行扩散的情况形成对比，在纯扩散情况下，扩散较慢的竞争者总是具有优势。我们通过检查仅存在一个竞争者时稳态的入侵性，即稳定性或不稳定性，来确定竞争优势。数学方法是对主特征值进行摄动分析。
