Regime shifts in models of dryland vegetation

Abstract

Drylands are pattern-forming systems showing self-organized vegetation patchiness, multiplicity of stable states and fronts separating domains of alternative stable states. Pattern dynamics, induced by droughts or disturbances, can result in desertification shifts from patterned vegetation to bare soil. Pattern formation theory suggests various scenarios for such dynamics: an abrupt global shift involving a fast collapse to bare soil, a gradual global shift involving the expansion and coalescence of bare-soil domains and an incipient shift to a hybrid state consisting of stationary bare-soil domains in an otherwise periodic pattern. Using models of dryland vegetation, we address the question of which of these scenarios can be realized. We found that the models can be split into two groups: models that exhibit multiplicity of periodic-pattern and bare-soil states, and models that exhibit, in addition, multiplicity of hybrid states. Furthermore, in all models, we could not identify parameter regimes in which bare-soil domains expand into vegetated domains. The significance of these findings is that, while models belonging to the first group can only exhibit abrupt shifts, models belonging to the second group can also exhibit gradual and incipient shifts. A discussion of open problems concludes the paper.

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

“…Diffusion is used to model plant dispersal in the interests of mathematical simplicity; some subsequent models have used instead a nonlocal dispersal term (30,31). Klausmeier's original formulation (14) did not include water diffusion but this has been added by a number of subsequent authors (20)(21)(22)(23). Because D will typically be much larger than the (dimensionless) plant dispersal coefficient of 1, this additional term tends to enhance the pattern forming potential of the model.…”

“…Eq. 1 is one of the earliest and simplest models for vegetation patterning, and remains in widespread use (19)(20)(21)(22)(23). Crucially, there are only four dimensionless parameters, which makes comprehensive scans of parameter space feasible.…”

Pattern formation in the geosciences

“…Prediction, and in some cases even control, of geophysical patterns is an area where future developments can be expected to be particularly influential. Pattern-forming systems can be susceptible to catastrophic regime changes [22], such as the desertification process studied by Zelnik et al [14], when a bifurcation point is reached. Alternatively, the approaches of Murray & Ashton [21] to coastline migration, or Da Lio et al [16] to wetland development use nonlinear feedback to make explicit testable predictions, which will be important in attempts to minimize disruption of coastal regions by changing climates.…”

“…The interacting variables can, however, be more subtle. Zelnik et al [14] study the process of desertification in a series of models of dry-land vegetation, where moisture and biomass interact to give rise either to patterns of vegetative spots or bare soil. Penny et al [15] share an observational study of a similar pattern, where symmetry is broken by hills, and the downslope drainage of the water leads to oriented stripes.…”

“…[22]). Zelnik et al [14] survey a broad range of the models that have developed to describe the interaction of vegetative spots with water, given a limiting precipitation rate. In particular, they study the process of desertification, which in these models results from multiple stable states, and hysteresis, in the vegetative cover.…”