Rate-induced tipping and regime shifts in a spatial ecological system

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.