We study how a rate of environmental change affects stability and persistence of an ecological community. Using an explicit rate of change in the environmental parameters of a spatially coupled ecological system, we study the rate-dependent responses associated with extinction of a metacommunity. Our results elucidate various scenarios of rate-induced extinction (R-tipping) such as tipping through increasing amplitude of oscillations, tipping through synchronized dynamics, and tipping through tracking unstable states. Further, we show rate-dependent delayed responses away from bifurcation points, but with tracking unstable states. Our results emphasize that the rate of environmental change can reveal the unexpected extinction dynamics which may not be predicted from stable equilibrium states and bifurcation points of the system. Thus, our results illustrate the importance of rate-dependent responses to understand stability and persistence of an ecological system.

我们研究环境变化的速度如何影响生态群落的稳定性和持久性。使用空间耦合生态系统的环境参数的显式变化率，我们研究了与元群落灭绝相关的速率依赖反应。我们的结果阐明了速率引起的消光 (R-tipping) 的各种情况，例如通过增加振荡幅度进行倾斜、通过同步动力学进行倾斜以及通过跟踪不稳定状态进行倾斜。此外，我们展示了远离分叉点的速率相关延迟响应，但跟踪不稳定状态。我们的结果强调，环境变化的速度可以揭示意外的灭绝动态，而这可能无法从系统的稳定平衡状态和分叉点预测。因此，