Diversity of Vegetation Patterns and Desertification

Hardenberg, Jost von; Meron, Ehud; Shachak, Moshe; Zarmi, Yair

doi:10.1103/physrevlett.87.198101

Cited by 543 publications

(589 citation statements)

References 15 publications

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“…Our general model results are in line with those of the models based on scale-dependent feedback in that we obtain bistability (under certain environmental conditions) and spatial self-organization of the vegetation (Lefever and Lejeune, 1997;Lejeune et al, 1999;von Hardenberg et al, 2001;Lejeune and Tlidi, 2002;Rietkerk et al, 2002;Meron et al, 2004). However, the spatial organization is different in our system.…”

Section: Article In Presssupporting

confidence: 76%

“…Note that we reserve the term pattern(s) for regular spatial organization of the vegetation (following Levin and Segel, 1985). Various mathematical models succeed in reproducing these regular patterns (Lejeune et al, 1999;von Hardenberg et al, 2001;Lejeune and Tlidi, 2002;Rietkerk et al, 2002;Meron et al, 2004). These models assume that the driving mechanism of regular vegetation pattern formation is the difference in water infiltration and/or evaporation rates between vegetation and bare sites within the system (von Hardenberg et al, 2001;Rietkerk et al, 2002;Meron et al, 2004).…”

Section: Article In Pressmentioning

confidence: 99%

“…Mortality Just as germination turns an unoccupied site into a vegetation site, mortality turns it back into an unoccupied site again. We assume that mortality is density-independent (e.g., Klausmeier, 1999;von Hardenberg et al, 2001;Rietkerk et al, 2002;Meron et al, 2004) …”

Section: Colonizationmentioning

confidence: 99%

“…Bistable systems potentially undergo sudden, discontinuous transitions, corresponding to switches from one stable state to the other because of small, continuous changes in parameter values (Scheffer et al, 2001). For example, with decreasing rainfall, such a system may shift from a patched vegetation state to a bare state (von Hardenberg et al, 2001;Rietkerk et al, 2002). An increase in rainfall to values for which this shift occurs does not necessarily lead to a recovery of the vegetation state.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Local facilitation, bistability and transitions in arid ecosystems

Kéfi

Rietkerk

Baalen³

et al. 2007

Theoretical Population Biology

172

221

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Arid ecosystems are liable to undergo sudden discontinuous transitions from a vegetated to a desert state as a result of human pressure and climate change. A predictive framework about the conditions under which such transitions occur is lacking. Here, we derive and analyze a general model describing the spatial dynamics of vegetation in arid ecosystems considering local facilitation as an essential process. We investigate the conditions under which continuous or discontinuous transitions from a vegetated to a desert state are likely to occur. We focus on arid ecosystems but our approach is sufficiently general to be applied to other ecosystems with severe environmental conditions. The model exhibits bistability and vegetation patchiness. High local facilitation decreases the risk of discontinuous transitions. Moreover, for arid ecosystems where local facilitation is a driving process, vegetation patchiness indicates proximity to a transition point, but does not allow distinguishing between continuous and discontinuous transitions. r

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Section: Article In Presssupporting

confidence: 76%

Section: Article In Pressmentioning

confidence: 99%

Section: Colonizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Local facilitation, bistability and transitions in arid ecosystems

Kéfi

Rietkerk

Baalen³

et al. 2007

Theoretical Population Biology

172

221

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“…A number of studies of selforganized complexity, in terms of species interaction patterns (De Ruiter et al 1995;Neutel et al 2002) or in terms of spatial complexity (Klausmeier 1999;Von Hardenberg et al 2001;Rietkerk et al 2002;Van de Koppel and Rietkerk 2004), indicate that ecosystem stability and functioning is improved by self-organization. This study shows the opposite: salt marsh ecosystems, as a consequence of local interaction of plants and sediment, develop to a critical state, becoming more vulnerable to disturbances as more clay accumulates.…”

Section: Discussionmentioning

confidence: 99%

Self‐Organization and Vegetation Collapse in Salt Marsh Ecosystems

Koppel¹,

Wal²,

Bakker³

et al. 2005

The American Naturalist

261

103

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Complexity theory predicts that local feedback processes may strongly affect the organization of ecosystems on larger spatial scales. Whether complexity leads to increased resilience and stability or to increased vulnerability and criticality remains one of the dominant questions in ecology. We present a combined theoretical and empirical study of complex dynamics in mineralogenic salt marsh ecosystems that emerge from a positive feedback between clay accumulation and plant growth. Positive feedback induces self-organizing within the ecosystem, which buffers for the strong physical gradient that characterizes the marine-terrestrial boundary, and improves plant growth along the gradient. However, as a consequence of these self-organizing properties, salt marshes approach a critical state as the edge of the salt marsh and the adjacent intertidal flat becomes increasingly steep and vulnerable to wave attack. Disturbance caused, for instance, by a storm may induce a cascade of vegetation collapse and severe erosion on the cliff edge, leading to salt marsh destruction. Our study shows that on short timescales, self-organization improves the functioning of salt marsh ecosystems. On long timescales, however, self-organization may lead to destruction of salt marsh vegetation.

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Multiple hydrological attractors under stochastic daily forcing: 2. Can multiple attractors emerge?

Peterson

Western

Argent

2014

Water Resources Research

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The companion paper showed that multiple steady state groundwater levels can exist within a hill-slope Boussinesq-vegetation model under daily stochastic forcing. Using a numerical limit-cycle continuation algorithm, the steady states (henceforth attractors) and the threshold between them (henceforth repellor) were quantified at a range of saturated lateral conductivity values, k smax . This paper investigates if stochastic daily forcing can switch the catchment between both of the attractors. That is, an attractor may exist under average forcing conditions but can stochastic forcing switch the catchment into and out of each of the attractor basins?; i.e., making the attractor emerge. This was undertaken using the model of the companion paper and by completing daily time-integration simulations at six values of the saturated lateral hydraulic conductivity, k smax ; three having two attractors and three having only a deep water table attractor. By graphically analyzing the simulations, and comparing against simulations from a model modified to have only one attractor, multiple attractors were found to emerge under stochastic daily forcing. However, the emergence of attractors was significantly more subtle and complex than that suggested by the companion paper. That is, an attractor may exist but never emerge; both attractors may exist and both may emerge but identifying the switching between attractors was often ambiguous; and only one attractor may exist and but a second temporary attractor may exist and emerge during periods of high precipitation. This subtle and complex emergence of attractors was explained using continuation analysis of the climate forcing rate, and not a model parameter such as k smax . It showed that the temporary attractor existed over a large range of k smax values and this suggests that more catchments may have multiple attractors than suggested by the companion paper. By combining this continuation analysis with the time-integration simulations, hydrological signatures indicative of a switch of multiple attractors were proposed. These signatures may provide a means for identifying actual catchments that have switched between multiple attractors.

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Diversity of Vegetation Patterns and Desertification

Cited by 543 publications

References 15 publications

Local facilitation, bistability and transitions in arid ecosystems

Local facilitation, bistability and transitions in arid ecosystems

Self‐Organization and Vegetation Collapse in Salt Marsh Ecosystems

Multiple hydrological attractors under stochastic daily forcing: 2. Can multiple attractors emerge?

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