Persistence of ecological systems under climate change depends on how fast the environment is changing and on how species respond to that change. The rate of environmental change is a key factor affecting the responses. Adaptation, migration to more favorable habitats, and extinction are fundamental responses that species exhibit to climate change, but extinction is the most extreme one when species are unable to keep pace with climate change. The dynamics of extinction has long been addressed by theories of stochasticity, alternate states, and tipping points. But we are still lacking a non-equilibrium theory that explains how the rate of environmental change affects species responses, especially persistence. Here, we present spatial and non-spatial models of prey–predator interactions with Allee effect and show diverse responses characterized by different rates of environmental change. We show a community collapse to increasing rates of environmental change and also a stabilizing mechanism through unstable states of the non-spatial model. On the other hand, the spatially distributed community through dispersal exhibits multiple responses that include rescue effect, rate-driven extinction, and unexpected critical transitions and regime shifts. Furthermore, our results show a tracking of unstable states describing the role of unstable states in extinction debt and in maintaining spatial heterogeneity. Thus, this study reveals how the rate of environmental change reshapes community responses and predicts community persistence away from equilibrium states and also away from critical points.

气候变化下生态系统的持久性取决于环境变化的速度以及物种对这种变化的反应方式。环境变化的速度是影响应对措施的关键因素。适应，迁移到更有利的栖息地以及物种灭绝是物种对气候变化的基本反应，但是当物种无法跟上气候变化的速度时，物种灭绝是最极端的反应。长期以来，灭绝的动态一直是由随机性，交替状态和临界点理论解决的。但是我们仍然缺乏非平衡理论，该理论无法解释环境变化的速度如何影响物种的反应，尤其是持久性。这里，我们介绍了具有Allee效应的食饵-捕食者相互作用的空间模型和非空间模型，并显示了以不同环境变化速率为特征的多种响应。我们显示了社区崩溃以增加环境变化的速度，以及通过非空间模型的不稳定状态建立的稳定机制。另一方面，通过散布在空间上分布的群落表现出多种响应，包括救援效果，速率驱动的灭绝以及意外的关键转变和政权转移。此外，我们的结果显示出对不稳定状态的跟踪，描述了不稳定状态在灭绝债务和维持空间异质性中的作用。从而，