Center for Applied Mathematics, Cornell University, Ithaca, NY 14853, USA.
Am Nat. 2010 Nov;176(5):E109-27. doi: 10.1086/656485.
The accumulation of evidence that ecologically important traits often evolve at the same time and rate as ecological dynamics (e.g., changes in species' abundances or spatial distributions) has outpaced theory describing the interplay between ecological and evolutionary processes with comparable timescales. The disparity between experiment and theory is partially due to the high dimensionality of models that include both evolutionary and ecological dynamics. Here we show how the theory of fast-slow dynamical systems can be used to reduce model dimension, and we use that body of theory to study a general predator-prey system exhibiting fast evolution in either the predator or the prey. Our approach yields graphical methods with predictive power about when new and unique dynamics (e.g., completely out-of-phase oscillations and cryptic dynamics) can arise in ecological systems exhibiting fast evolution. In addition, we derive analytical expressions for determining when such behavior arises and how evolution affects qualitative properties of the ecological dynamics. Finally, while the theory requires a separation of timescales between the ecological and evolutionary processes, our approach yields insight into systems where the rates of those processes are comparable and thus is a step toward creating a general ecoevolutionary theory.
越来越多的证据表明，生态重要特征往往与生态动态（例如，物种丰度或空间分布的变化）同时以相同的速度进化，这超出了描述具有可比时间尺度的生态和进化过程相互作用的理论。实验与理论之间的差距部分归因于同时包含进化和生态动态的模型的高维度。在这里，我们展示了快速-缓慢动力系统理论如何用于降低模型维度，并且我们使用该理论研究了在捕食者或猎物中表现出快速进化的一般捕食者-猎物系统。我们的方法产生了具有预测能力的图形方法，可以了解在表现出快速进化的生态系统中何时会出现新的和独特的动态（例如，完全不同步的振荡和隐藏的动态）。此外，我们推导出了确定何时出现这种行为以及进化如何影响生态动态定性特性的解析表达式。最后，虽然该理论要求生态和进化过程之间的时间尺度分离，但我们的方法为那些过程的速率相当的系统提供了深入的了解，因此是朝着创建一般生态进化理论迈出的一步。
