Resilience of alternative states in spatially extended ecosystems.

Alternative stable states in ecology have been well studied in isolated, well-mixed systems. However, in reality, most ecosystems exist on spatially extended landscapes. Applying existing theory from dynamic systems, we explore how such a spatial setting should be expected to affect ecological resilience. We focus on the effect of local disturbances, defining resilience as the size of the area of a strong local disturbance needed to trigger a shift. We show that in contrast to well-mixed systems, resilience in a homogeneous spatial setting does not decrease gradually as a bifurcation point is approached. Instead, as an environmental driver changes, the present dominant state remains virtually 'indestructible', until at a critical point (the Maxwell point) its resilience drops sharply in the sense that even a very local disturbance can cause a domino effect leading eventually to a landscape-wide shift to the alternative state. Close to this Maxwell point the travelling wave moves very slow. Under these conditions both states have a comparable resilience, allowing long transient co-occurrence of alternative states side-by-side, and also permanent co-existence if there are mild spatial barriers. Overall however, hysteresis may mostly disappear in a spatial context as one of both alternative states will always tend to be dominant. Our results imply that local restoration efforts on a homogeneous landscape will typically either fail or trigger a landscape-wide transition. For extensive biomes with alternative stable states, such as tundra, steppe and forest, our results imply that, as climatic change reduces the stability, the effect might be difficult to detect until a point where local disturbances inevitably induce a spatial cascade to the alternative state