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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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Simulations in a homogeneous landscape with local alternative states and diffusion of the modeled species.Initially, the left side of the landscape is set to the high biomass state, and the right side to the low biomass state. With these initial conditions a moving front establishes, shifting the entire landscape to the state with the highest resilience (a) c = 2.2, (b) c = 2.3487, (c) c = 2.5 (g m−1 d−1). The four figures in each panel represent: 1) snapshots of the moving front with the grey arrows indicating the shifting direction (scale = 30 m), 2) the local change in biomass per day due to growth and mortality (fN), 3) the local change in biomass per day due to diffusion (fD), and 4) the net local change in biomass per day. Note that local dynamics and diffusion precisely cancel out if conditions are such that the modeled system is at the Maxwell point (panel b). The scale of all change-in-biomass plots ranges from -0.5 to 0.5 (g m−1 d−1).
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pone.0116859.g002: Simulations in a homogeneous landscape with local alternative states and diffusion of the modeled species.Initially, the left side of the landscape is set to the high biomass state, and the right side to the low biomass state. With these initial conditions a moving front establishes, shifting the entire landscape to the state with the highest resilience (a) c = 2.2, (b) c = 2.3487, (c) c = 2.5 (g m−1 d−1). The four figures in each panel represent: 1) snapshots of the moving front with the grey arrows indicating the shifting direction (scale = 30 m), 2) the local change in biomass per day due to growth and mortality (fN), 3) the local change in biomass per day due to diffusion (fD), and 4) the net local change in biomass per day. Note that local dynamics and diffusion precisely cancel out if conditions are such that the modeled system is at the Maxwell point (panel b). The scale of all change-in-biomass plots ranges from -0.5 to 0.5 (g m−1 d−1).

Mentions: We first show how the resilience of alternative stable states in homogeneous spatially extended systems differs from the classical well-mixed systems. At first, we initialized the landscape such that the population was in the high biomass state on one half of the landscape, and in the low biomass state on the other half. On either side of the created boundary the local dynamics driven by diffusion (fD) have an equalizing effect, while the growth and mortality dynamics (fN) drive the system back to each equilibrium state. The net effect around the front drives the system locally towards one of the states (Fig. 2). This shift propagates further through the landscape resembling a domino effect. Such moving front is called a ‘travelling wave’ [7].


Resilience of alternative states in spatially extended ecosystems.

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

Simulations in a homogeneous landscape with local alternative states and diffusion of the modeled species.Initially, the left side of the landscape is set to the high biomass state, and the right side to the low biomass state. With these initial conditions a moving front establishes, shifting the entire landscape to the state with the highest resilience (a) c = 2.2, (b) c = 2.3487, (c) c = 2.5 (g m−1 d−1). The four figures in each panel represent: 1) snapshots of the moving front with the grey arrows indicating the shifting direction (scale = 30 m), 2) the local change in biomass per day due to growth and mortality (fN), 3) the local change in biomass per day due to diffusion (fD), and 4) the net local change in biomass per day. Note that local dynamics and diffusion precisely cancel out if conditions are such that the modeled system is at the Maxwell point (panel b). The scale of all change-in-biomass plots ranges from -0.5 to 0.5 (g m−1 d−1).
© Copyright Policy
Related In: Results  -  Collection

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getmorefigures.php?uid=PMC4340810&req=5

pone.0116859.g002: Simulations in a homogeneous landscape with local alternative states and diffusion of the modeled species.Initially, the left side of the landscape is set to the high biomass state, and the right side to the low biomass state. With these initial conditions a moving front establishes, shifting the entire landscape to the state with the highest resilience (a) c = 2.2, (b) c = 2.3487, (c) c = 2.5 (g m−1 d−1). The four figures in each panel represent: 1) snapshots of the moving front with the grey arrows indicating the shifting direction (scale = 30 m), 2) the local change in biomass per day due to growth and mortality (fN), 3) the local change in biomass per day due to diffusion (fD), and 4) the net local change in biomass per day. Note that local dynamics and diffusion precisely cancel out if conditions are such that the modeled system is at the Maxwell point (panel b). The scale of all change-in-biomass plots ranges from -0.5 to 0.5 (g m−1 d−1).
Mentions: We first show how the resilience of alternative stable states in homogeneous spatially extended systems differs from the classical well-mixed systems. At first, we initialized the landscape such that the population was in the high biomass state on one half of the landscape, and in the low biomass state on the other half. On either side of the created boundary the local dynamics driven by diffusion (fD) have an equalizing effect, while the growth and mortality dynamics (fN) drive the system back to each equilibrium state. The net effect around the front drives the system locally towards one of the states (Fig. 2). This shift propagates further through the landscape resembling a domino effect. Such moving front is called a ‘travelling wave’ [7].

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