Bistability and regular spatial patterns in arid ecosystems

Abstract

A variety of patterns observed in ecosystems can be explained by resource-concentration mechanisms. A resource-concentration mechanism occurs when organisms increase the lateral flow of a resource toward them, leading to a local concentration of this resource and to its depletion from areas farther away. In resource-concentration systems, it has been proposed that certain spatial patterns could indicate proximity to discontinuous transitions where an ecosystem abruptly shifts from one stable state to another. Here, we test this hypothesis using a model of vegetation dynamics in arid ecosystems. In this model, a resourceconcentration mechanism drives a positive feedback between vegetation and soil water availability. We derived the conditions leading to bistability and pattern formation. Our analysis revealed that bistability and regular pattern formation are linked in our model. This means that, when regular vegetation patterns occur, they indicate that the system is along a discontinuous transition to desertification. Yet, in real systems, only observing regular vegetation patterns without identifying the pattern-driving mechanism might not be enough to conclude that an ecosystem is along a discontinuous transition because similar patterns can emerge from different ecological mechanisms.

Biogenic gradients in algal density affect the emergent properties of spatially self-organized mussel beds

“…Interface 11: 20140089 transition when environmental stress reaches a critical threshold or 'tipping point' [14,26,27]. Under homogeneous conditions, this property also holds for the model in the absence of gradients in algal availability [23] (figure 5b).…”

Forest patch symmetry depends on direction of limiting resource delivery

“…Vegetation patches can also arise by self-organization through local facilitation. For example, Klausmeier (1999) showed theoretically that forest patches can arise from directional surface-runoff in semi-arid ecosystems, and similar patterns have been empirically been demonstrated to occur in a wide range of ecosystems, from fog-fed bromeliad fields in the Atacama (Borthagaray et al 2010) through semiarid shrublands (Klausmeier 1999, Van De Koppel and Rietkerk 2004, Saco et al 2007, Kéfi et al 2010 to Sphagnum aggregations in fens (Eppinga et al 2008, Manor and Shnerb 2008 and tree islands in the Everglades (Wetzel et al 2008). In all of these cases limiting resources such as water and nutrients are delivered in a horizontally asymmetric manner (Fig.…”

“…In such cases feedbacks from the surrounding matrix (e.g., fire, competition with shrubs or grasses, different water and nutrient availability, soil microbial communities) may act to stabilize patches. In yet other ecosystems the driver of asymmetries may be seed rain, nutrient deposition (Weathers 1999, Ewing et al 2009), runoff (Klausmeier 1999, Van De Koppel and Rietkerk 2004, Saco et al 2007, Kéfi et al 2010 or frost damage (Watt 1947, Sprugel and Bormann 1981, Satō and Iwasa 1993. The conceptual framework and empirical confirmation presented here are a step towards a more inclusive understanding of forest patches and their internal and external dynamics.…”

Using wavelength and slope to infer the historical origin of semiarid vegetation bands

“…A central concept in the understanding of desertification is the bistability between vegetated states and desert (15,16,55). As rainfall is decreased, a loss in stability of a vegetated state causes a sudden transition to desert, but if rainfall is subsequently increased back above the tipping point the desert state remains, and reestablishment of vegetation requires much wetter conditions (3,56,57).…”