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.

Sand dunes are often covered by vegetation and biogenic crusts. Despite their significant role in dune stabilization, biogenic crusts have rarely been considered in studies of dune dynamics. Using a simple model, we study the existence and stability ranges of different dune-cover states along gradients of rainfall and wind power. Two ranges of alternative stable states are identified: fixed crusted dunes and fixed vegetated dunes at low wind power, and fixed vegetated dunes and active dunes at high wind power. These results suggest a cross-over between two different forms of desertification.Sand dunes have been the subject of active research for many years, largely because of their fascinating shapes and dynamics [1][2][3][4]. Current studies have increasingly addressed the question of sand-dune stability in relation to climate change and anthropogenic disturbances [5][6][7]. Sand dunes are considered "stable" when they are fixed in place or are stationary [31]. Their stability is strongly affected by the degree of vegetation coverage. High coverage reduces the wind power at the dune surface and thereby acts to immobilize the dunes. The remobilization of fixed dunes, either by vegetation mortality or clear-cutting, often has detrimental effects on the unique ecosystems that develop in stable dunes [8,9], leading to alternative ecosystems associated with active sand [10]. Active dunes may also pose a threat to human settlement as they can block roads and cover residential areas and agricultural fields [11,12].Sand dunes are also stabilized by biogenic soil crusts. These crusts comprise a variety of organisms, including cyanobacteria, lichens and mosses, which live at the surface of desert soils [13]. Biogenic crusts enhance the aggregation of sand grains, prevent saltation, and reduce wind erosion. Since most sandy soils are located in drylands where the vegetation is patchy and generally sparse [3], the role of biogenic crusts in stabilizing dunes is important and often crucial [14]. Despite their significance and vast presence in the Kalahari, Australian and Central Asia deserts [15][16][17], soil crusts have rarely been considered in studies of dune dynamics [18,19].Depending on wind power and precipitation level different dune-cover states are observed. Figure 1 shows several typical states from regions of relatively weak winds. At very low precipitation levels (Fig. 1a), dunes are active due to low crust and vegetation coverage. As the precipitation increases, the dunes are gradually stabilized. At low precipitation levels, the dominant stabilizing agent is the soil crust (Fig. 1b,c), while at high levels, the stabilizing agent is predominantly vegetation (Fig. 1d). Although vegetation and biogenic crusts have similar effects in stabilizing dunes, they lead to ecosystems that differ vastly in their bioproductivity.Motivated by these observations, we ask whether the transition from crusted to vegetated dunes along the rainfall gradient is gradual or abrupt, and how it is affected by the wind power. Studying t...

We use the context of dryland vegetation to study a general problem of complex pattern-forming systems: multiple pattern-forming instabilities that are driven by distinct mechanisms but share the same spectral properties. We find that the co-occurrence of two Turing instabilities when the driving mechanisms counteract each other in some region of the parameter space results in the growth of a single mode rather than two interacting modes. The interplay between the two mechanisms compensates for the simpler dynamics of a single mode by inducing a wider variety of patterns, which implies higher biodiversity in dryland ecosystems.

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