Department of Mathematics, Ohio State University, Columbus, OH, 43210, USA.
Bull Math Biol. 2009 Nov;71(8):1793-817. doi: 10.1007/s11538-009-9425-7. Epub 2009 May 28.
To understand the evolution of dispersal, we study a Lotka-Volterra reaction-diffusion-advection model for two competing species in a heterogeneous environment. The two species are assumed to be identical except for their dispersal strategies: both species disperse by random diffusion and advection along environmental gradients, but with slightly different random dispersal or advection rates. Two new phenomena are found for one-dimensional habitats and monotone intrinsic growth rates: (i) If both species disperse only by random diffusion, i.e., no advection, it was well known that the slower diffuser always wins. We show that if both species have the same advection rate which is suitably large, the faster dispersal will evolve; (ii) If both species have the same random dispersal rate, it was known that the species with a little advection along the resource gradient always wins, provided that the other species is a pure random disperser and the habitat is convex. We show that if both species have the same random dispersal rate and both also have suitably large advection rates, the species with a little smaller advection rate always wins. Implications of these results for the habitat choices of species will be discussed. Some future directions and open problems will be addressed.
为了理解扩散的演化，我们研究了在异质环境中两种竞争物种的Lotka-Volterra 反应-扩散-对流模型。这两种物种除了扩散策略外，其他方面都是相同的：它们都通过随机扩散和环境梯度的平流来扩散，但随机扩散或平流率略有不同。对于一维栖息地和单调内在增长率，我们发现了两个新现象：（i）如果两种物种都只通过随机扩散来扩散，即没有平流，那么较慢的扩散者总是获胜。我们表明，如果两种物种都具有适当大的相同平流率，那么更快的扩散者将进化；（ii）如果两种物种都具有相同的随机扩散率，那么已知在资源梯度上具有少量平流的物种总是获胜，前提是另一个物种是纯随机扩散者，并且栖息地是凸形的。我们表明，如果两种物种都具有相同的随机扩散率，并且都具有适当大的平流率，那么具有稍小平流率的物种总是获胜。我们将讨论这些结果对物种栖息地选择的影响。还将讨论一些未来的方向和开放性问题。
