Department of Mathematics and Statistics, University of Ottawa, Ottawa, ON, Canada.
Bull Math Biol. 2012 Dec;74(12):2935-58. doi: 10.1007/s11538-012-9792-3. Epub 2012 Nov 15.
Many species live in advective environments, such as rivers or streams. The community composition in such environments is shaped by the interplay between biotic interactions and hydrologic constraints. Lutscher et al. (Theor. Popul. Biol. 71:267-277, 2007) demonstrated by simulation that advective flow can shift competitive outcome from one species dominating to coexistence or even to the other species dominating. Here, we present a detailed analysis of the Lotka-Volterra advection-diffusion model underlying their simulations. We use variational techniques as well as a spatially implicit approximation to determine all possible advection-induced shifts in competitive outcome. We show that changes in advection follow relatively few and predictable paths. We illustrate our results in various bifurcation diagrams.
许多物种生活在平流环境中，例如河流或溪流。这种环境中的群落组成是由生物相互作用和水力学约束之间的相互作用塑造的。Lutscher 等人（理论种群生物学 71:267-277，2007）通过模拟证明，平流可以改变竞争结果，从一种物种占主导地位到共存，甚至到另一种物种占主导地位。在这里，我们对他们模拟所依据的 Lotka-Volterra 平流扩散模型进行了详细分析。我们使用变分技术以及空间隐式逼近来确定所有可能的平流诱导的竞争结果变化。我们表明，平流的变化遵循相对较少且可预测的路径。我们在各种分岔图中说明了我们的结果。
