arXiv 1908.055072019-08-15q-bio.PE

当非常慢就是太快时--捕食者-食饵系统的崩溃

When very slow is too fast -- collapse of a predator-prey system

Anna Vanselow, Sebastian Wieczorek, Ulrike Feudel

发表信息：: Journal of Theoretical Biology, 479, 64-72 (2019)
DOI：: 10.1016/j.jtbi.2019.07.008

摘要：

关键过渡或制度转变是生态系统状态的突然和意外变化，通常与危险程度的环境变化有关。然而，最近的研究表明，危险的环境变化速度也可能引发关键的转变。与经典的状态转移相反，这种速率引起的临界转变不涉及任何明显的稳定性损失或分叉，因此不能用线性稳定性分析来解释。在这项工作中，我们证明了著名的Rosenzweig-MacArthur捕食者-被捕食者模型可以经历一个率诱导的临界转变，以应对栖息地质量的持续下降，导致捕食者和被捕食者种群的崩溃。令人惊讶的是，即使环境变化比模型中最慢的过程慢，崩溃也会发生。为了解释这种违反直觉的现象，我们结合几何奇异摄动理论的方法与移动平衡的概念，并研究依赖于初始状态和系统参数的环境变化的临界速率。此外，对于一个固定的环境变化率，我们确定了一组初始状态，经历率诱导的人口崩溃。我们的研究结果表明，生态系统对环境条件变化的速度可能比以前假设的更敏感。特别是，环境变化（i）不超过任何危险水平，（ii）慢于生态系统的自然时间尺度，可能引发具有重大生态后果的意外关键转变。这就提出了一个有趣的研究问题，即在自然界中观察到的政权转移主要是由速率引起的还是由分叉引起的。

英文摘要：

Critical transitions or regime shifts are sudden and unexpected changes in the state of an ecosystem, that are usually associated with dangerous levels of environmental change. However, recent studies show that critical transitions can also be triggered by dangerous rates of environmental change. In contrast to classical regime shifts, such rate-induced critical transitions do not involve any obvious loss of stability, or a bifurcation, and thus cannot be explained by the linear stability analysis. In this work, we demonstrate that the well-known Rosenzweig-MacArthur predator-prey model can undergo a rate-induced critical transition in response to a continuous decline in the habitat quality, resulting in a collapse of the predator and prey populations. Rather surprisingly, the collapse occurs even if the environmental change is slower than the slowest process in the model. To explain this counterintuitive phenomenon, we combine methods from geometric singular perturbation theory with the concept of a moving equilibrium, and study critical rates of environmental change with dependence on the initial state and the system parameters. Moreover, for a fixed rate of environmental change, we determine the set of initial states that undergo a rate-induced population collapse. Our results suggest that ecosystems may be more sensitive to how fast environmental conditions change than previously assumed. In particular, unexpected critical transitions with dramatic ecological consequences can be triggered by environmental changes that (i) do not exceed any dangerous levels, and (ii) are slower than the natural timescales of the ecosystem. This poses an interesting research question whether regime shifts observed in the natural world are predominantly rate-induced or bifurcation-induced.

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