Sherratt J A, Lambin X, Sherratt T N
Department of Mathematics, Heriot-Watt University, Edinburgh EH14 4AS, United Kingdom.
Am Nat. 2003 Oct;162(4):503-13. doi: 10.1086/377186. Epub 2003 Oct 16.
Recent field data indicate that in a number of cyclic populations, the cycles are organized spatially with the form of a periodic traveling wave. One way in which this type of wave is generated is when dispersing individuals encounter landscape features that impede movement in certain directions. In this article, we investigate the dependence of such periodic waves on ecological parameters and on the form of the landscape feature. Using a standard predator-prey model as a prototype for a cyclic population, we calculate the speed and amplitude of waves generated by a large landscape feature. This enables us to determine parameters for which the waves are stable; in other cases, they evolve into irregular oscillations. We then undertake for the first time a detailed study of the effects of the size and shape of a landscape feature on the waves that it generates. We show that size rather than shape is the key wave-forming property, with smaller obstacles generating waves with longer wavelength and waves from larger landscape features dominating those from smaller ones. Our results suggest that periodic traveling waves may be much more common than has previously been assumed in real ecological systems, and they enable quantitative predictions on the properties of these waves for particular cases.
近期的实地数据表明，在一些周期性种群中，种群数量变化呈现出周期性行波的空间组织形式。产生这种波的一种方式是，扩散个体遇到阻碍其在某些方向移动的景观特征。在本文中，我们研究了这种周期性波对生态参数以及景观特征形式的依赖性。以一个标准的捕食者 - 猎物模型作为周期性种群的原型，我们计算了由大型景观特征产生的波的速度和振幅。这使我们能够确定波保持稳定的参数；在其他情况下，它们会演变成不规则振荡。然后，我们首次详细研究了景观特征的大小和形状对其所产生的波的影响。我们表明，大小而非形状是形成波的关键属性，较小的障碍物产生波长更长的波，且来自较大景观特征的波主导来自较小景观特征的波。我们的结果表明，周期性行波在实际生态系统中可能比之前所认为的更为常见，并且它们能够针对特定情况对这些波的特性进行定量预测。
