Implications of spatial heterogeneity for regime shifts in ecosystems

Although alternative stable states are commonly found in simple models, it seems reasonable to assume that the response of real ecosystems to environmental change should often be smoothed by spatial heterogeneity and other stabilizing mechanisms. Here, we systematically explore the effect of spatial heterogeneity on regime shifts for three different models, which we run on a one-dimensional lattice with different spatial distributions of an environmental factor (e.g., soil fertility, water level). If dispersion between patches is negligible, the response to gradual change in some overall stressor (e.g., precipitation, nutrient load) is straightforward. Because of the environmental heterogeneity, each patch shifts to the other stable state at different values of the overall control variable. Therefore, the response of the ecosystem as a whole is gradual (i.e., the average of many asynchronous small shifts) instead of catastrophic. However, in response to a reverse change in the global stressor, the system always shows hysteresis, as each individual patch shifts back to the original state at a different value of the control parameter than the critical threshold for the forward shift. If dispersion between patches occurs, the response to change in the overall control parameter becomes dependent on the spatial pattern of environmental heterogeneity. If the environmental parameter is randomly distributed in space, the overall response tends to remain surprisingly catastrophic, and hysteresis is hardly reduced as compared to the homogeneous case. By contrast, in a smooth environmental gradient, the response of the overall system is gradual, and hysteresis is much smaller. In fact, hysteresis is largely reduced to the initial phases, in which none of the patches have shifted to the alternative state yet. As soon as the first patch shifts, a domino effect occurs, pushing over the neighboring patches. In conclusion, our results suggest that spatial heterogeneity may weaken the tendency for large-scale catastrophic regime shifts if dispersion is unimportant or if local environmental characteristics vary along a smooth gradient