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Resilience of alternative states in spatially extended ecosystems.

van de Leemput IA, van Nes EH, Scheffer M - PLoS ONE (2015)

Bottom Line: 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.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.

View Article: PubMed Central - PubMed

Affiliation: Department of Environmental Sciences, Wageningen University, Wageningen, The Netherlands.

ABSTRACT
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.

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The effect of spatially heterogeneous conditions.A gradual increase in growth conditions in space (e.g. north-south gradient in temperature) results in a distinct shift in space from the low biomass state to the high biomass state (i.e. a stable standing wave) on the location where conditions cross the Maxwell point. Upper panel: The solid black line represents the local growth rate r on the landscape. The solid grey line indicates where the conditions cross the Maxwell point (MP), and the two dashed grey lines indicate where the two fold bifurcations (F) are crossed. Lower panel: The shaded area represents the stable end configuration of biomass for any initial configuration (c = 2.35 g m−1 d−1).
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pone.0116859.g006: The effect of spatially heterogeneous conditions.A gradual increase in growth conditions in space (e.g. north-south gradient in temperature) results in a distinct shift in space from the low biomass state to the high biomass state (i.e. a stable standing wave) on the location where conditions cross the Maxwell point. Upper panel: The solid black line represents the local growth rate r on the landscape. The solid grey line indicates where the conditions cross the Maxwell point (MP), and the two dashed grey lines indicate where the two fold bifurcations (F) are crossed. Lower panel: The shaded area represents the stable end configuration of biomass for any initial configuration (c = 2.35 g m−1 d−1).

Mentions: Next, we simulated heterogeneity in environmental conditions in the most straightforward manner, using a spatial gradient of growth rate r (Fig. 6). One can, for example, imagine a gradient in water availability related to distance to water source, or precipitation and temperature gradients related to latitude. With a smooth spatial gradient in the growth rate, a sharp boundary between two states is formed simply wherever conditions cross the Maxwell point. If both sides of the landscape are connected to an area in which the system has only one stable state, this configuration is completely independent of initial conditions (Fig. 6). As a consequence, as long as diffusion rates are homogeneous, and there is a smooth gradient in environmental conditions, there will be no local nor large-scale hysteresis effects in the response to a changing environmental variable. If global conditions change gradually, the location of the spatial shift will also shift in a gradual manner.


Resilience of alternative states in spatially extended ecosystems.

van de Leemput IA, van Nes EH, Scheffer M - PLoS ONE (2015)

The effect of spatially heterogeneous conditions.A gradual increase in growth conditions in space (e.g. north-south gradient in temperature) results in a distinct shift in space from the low biomass state to the high biomass state (i.e. a stable standing wave) on the location where conditions cross the Maxwell point. Upper panel: The solid black line represents the local growth rate r on the landscape. The solid grey line indicates where the conditions cross the Maxwell point (MP), and the two dashed grey lines indicate where the two fold bifurcations (F) are crossed. Lower panel: The shaded area represents the stable end configuration of biomass for any initial configuration (c = 2.35 g m−1 d−1).
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4340810&req=5

pone.0116859.g006: The effect of spatially heterogeneous conditions.A gradual increase in growth conditions in space (e.g. north-south gradient in temperature) results in a distinct shift in space from the low biomass state to the high biomass state (i.e. a stable standing wave) on the location where conditions cross the Maxwell point. Upper panel: The solid black line represents the local growth rate r on the landscape. The solid grey line indicates where the conditions cross the Maxwell point (MP), and the two dashed grey lines indicate where the two fold bifurcations (F) are crossed. Lower panel: The shaded area represents the stable end configuration of biomass for any initial configuration (c = 2.35 g m−1 d−1).
Mentions: Next, we simulated heterogeneity in environmental conditions in the most straightforward manner, using a spatial gradient of growth rate r (Fig. 6). One can, for example, imagine a gradient in water availability related to distance to water source, or precipitation and temperature gradients related to latitude. With a smooth spatial gradient in the growth rate, a sharp boundary between two states is formed simply wherever conditions cross the Maxwell point. If both sides of the landscape are connected to an area in which the system has only one stable state, this configuration is completely independent of initial conditions (Fig. 6). As a consequence, as long as diffusion rates are homogeneous, and there is a smooth gradient in environmental conditions, there will be no local nor large-scale hysteresis effects in the response to a changing environmental variable. If global conditions change gradually, the location of the spatial shift will also shift in a gradual manner.

Bottom Line: 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.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.

View Article: PubMed Central - PubMed

Affiliation: Department of Environmental Sciences, Wageningen University, Wageningen, The Netherlands.

ABSTRACT
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.

Show MeSH