Department of Mathematics, Ohio State University, Columbus, OH, USA.
J Biol Dyn. 2009 Jul;3(4):410-29. doi: 10.1080/17513750802491849.
This article is concerned with the evolution of certain types of density-dependent dispersal strategy in the context of two competing species with identical population dynamics and same random dispersal rates. Such density-dependent movement, often referred to as cross-diffusion and self-diffusion, assumes that the movement rate of each species depends on the density of both species and that the transition probability from one place to its neighbourhood depends solely on the arrival spot (independent of the departure spot). Our results suggest that for a one-dimensional homogeneous habitat, if the gradients of two cross- and self-diffusion coefficients have the same direction, the species with the smaller gradient will win, i.e. the dispersal strategy with the smaller gradient of cross- and self-diffusion coefficient will evolve. In particular, it suggests that the species with constant cross- and self-diffusion coefficients may have competitive advantage over species with non-constant cross- and self-diffusion coefficients. However, if the two gradients have opposite directions, neither of the two dispersal strategies wins as these two species can coexist.
本文关注的是在两种具有相同种群动态和相同随机扩散率的竞争物种的背景下，某些类型的密度依赖扩散策略的进化。这种密度依赖的运动通常被称为交叉扩散和自扩散，它假设每个物种的运动率取决于两种物种的密度，并且从一个地方到其邻域的转移概率仅取决于到达点（与离开点无关）。我们的研究结果表明，对于一维均匀栖息地，如果两个交叉扩散系数和自扩散系数的梯度具有相同的方向，那么梯度较小的物种将获胜，即具有较小的交叉扩散系数和自扩散系数梯度的扩散策略将进化。特别地，这表明具有恒定交叉扩散系数和自扩散系数的物种可能比具有非恒定交叉扩散系数和自扩散系数的物种具有竞争优势。然而，如果两个梯度具有相反的方向，那么这两种扩散策略都不会获胜，因为这两种物种可以共存。
