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Vegetation and biocrust play crucial roles in dune stability and mobility, and their interaction can lead to bistability, temporal oscillations, and hysteresis. We studied a two-dimensional (2D) mathematical model of vegetation and biogenic crust cover dynamics on sand dunes. Under a certain parameter range, the space-independent version of the model exhibited the bi-stability of an oscillatory state and a steady state, and we studied the 2D dynamics of the model under these parameters. The patterns developed by the 2D model showed a high degree of spatial heterogeneity and complexity depending on the initial conditions and on the state type across the front. The results suggest that spatial heterogeneity and complexity can evolve from the intrinsic dynamics between vegetation and biocrust, even without natural geodiversity and spatiotemporal climate fluctuations. In the real world, these two types of intrinsic and extrinsic heterogeneity processes interact such that it is difficult to distinguish between them. [ABSTRACT FROM AUTHOR]

Vegetation gap patterns in arid grasslands, such as the "fairy circles" of Namibia, are one of nature's greatest mysteries and subject to a lively debate on their origin. They are characterized by small-scale hexagonal ordering of circular bare-soil gaps that persists uniformly in the landscape scale to form a homogeneous distribution. Pattern-formation theory predicts that such highly ordered gap patterns should be found also in other water-limited systems across the globe, even if the mechanisms of their formation are different. Here we report that so far unknown fairy circles with the same spatial structure exist 10,000 km away from Namibia in the remote outback of Australia. Combining fieldwork, remote sensing, spatial pattern analysis, and process-based mathematical modeling, we demonstrate that these patterns emerge by self-organization, with no correlation with termite activity; the driving mechanism is a positive biomass- water feedback associated with water runoff and biomass-dependent infiltration rates. The remarkable match between the patterns of Australian and Namibian fairy circles and model results indicate that both patterns emerge from a nonuniform stationary instability, supporting a central universality principle of pattern-formation theory. Applied to the context of dryland vegetation, this principle predicts that different systems that go through the same instability type will show similar vegetation patterns even if the feedback mechanisms and resulting soil-water distributions are different, as we indeed found by comparing the Australian and the Namibian fairy-circle ecosystems. These results suggest that biomass-water feedbacks and resultant vegetation gap patterns are likely more common in remote drylands than is currently known. [ABSTRACT FROM AUTHOR]

Abstract: Transgressive dune fields, which are active sand areas surrounded by vegetation, exist on many coasts. In some regions like in Fraser Island in Australia, small dunes shrink while large ones grow, although both experience the same climatic conditions. We propose a general mathematical model for the spatiotemporal dynamics of vegetation cover on sand dunes and focus on the dynamics of transgressive dunes. Among other possibilities, the model predicts growth parallel to the wind with shrinkage perpendicular to the wind, where, depending on geometry and size, a transgressive dune can initially grow although eventually shrink. The larger is the initial area the slower its stabilization process. The model’s predictions are supported by field observations from Fraser Island in Australia. [Copyright &y& Elsevier]

In this article, we develop a unifying framework for the understanding of spatial vegetation patterns in heterogeneous landscapes. While much recent research has focused on self-organised vegetation the prevailing view is still that biological patchiness is mostly due to top-down control by the physical landscape template, disturbances or predators. We suggest that vegetation patchiness in real landscapes is controlled both by the physical template and by self-organisation simultaneously, and introduce a conceptual model for the relative roles of the two mechanisms. The model considers four factors that control whether vegetation patchiness is emerged or imposed: soil patch size, plant size, resource input and resource availability. The last three factors determine the plant-patch size, and the plant-to-soil patch size ratio determines the impact of self-organisation, which becomes important when this ratio is sufficiently small. A field study and numerical simulations of a mathematical model support the conceptual model and give further insight by providing examples of self-organised and template-controlled vegetation patterns co-occurring in the same landscape. We conclude that real landscapes are generally mixtures of template-induced and self-organised patchiness. Patchiness variability increases due to source-sink resource relations, and decreases for species of larger patch sizes. [ABSTRACT FROM AUTHOR]

Abstract: A common patch form in dryland landscapes is the vegetation ring. Vegetation patch formation has recently been attributed to self-organization processes that act to increase the availability of water to vegetation patches under conditions of water scarcity. The view of ring formation as a water-limited process, however, has remained largely unexplored. Using laboratory experiments and model studies we identify two distinct mechanisms of ring formation. The first mechanism pertains to conditions of high infiltration contrast between vegetated and bare soil, under which overland water flow is intercepted at the patch periphery. The decreasing amount of water that the patch core receives as the patch expands, leads to central dieback and ring formation. The second mechanism pertains to plants with large lateral root zones, and involves central dieback and ring formation due to increasing water uptake by the newly recruited individuals at the patch periphery. In general the two mechanisms act in concert, but the relative importance of each mechanism depends on environmental conditions. We found that strong seasonal rainfall variability favors ring formation by the overland-flow mechanism, while a uniform rainfall regime favors ring formation by the water-uptake mechanism. Our results explain the formation of rings by fast-growing species with confined root zones in a dry-Mediterranean climate, such as Poa bulbosa. They also explain the formation of rings by slowly growing species with highly extended root zones, such as Larrea tridentata (Creosotebush). [Copyright &y& Elsevier]

Aeolian sand ripples are a common feature on sandy deserts and beaches. Standard aeolian ripples have wavelengths of a few centimeters and amplitudes of a few millimeters. Sometimes, much larger ripples are observed. These are known by different names, such as ridges, granule ripples, gravel ripples, or megaripples. Aeolian megaripples are composed of a mixture of coarse and fine noncohesive material; a bimodal distribution of particle sizes is thought to be necessary for large, ripplelike bed forms to develop. Here, we discuss the extension of a recent model for the dynamics of aeolian megaripples. The model assumes that both the saltation and reptation fluxes are modulated by the emergent bed forms. We present a linear stability analysis of the full model as well as the results of numerical simulations. The modeled megaripples evolve through interactions between ripples of different sizes. The formation of megaripples is therefore another example of a self-organizing geomorphological system. [ABSTRACT FROM AUTHOR]

Abstract: Vegetation band patterns on hill slopes are studied using a mathematical model. The model applies to drylands, where the limiting resource is water, and takes into account positive feedback effects between biomass and water. Multiple band patterns coexisting in wide precipitation ranges are found. For given precipitation and slope conditions band patterns with higher wavenumbers are more biologically productive. High-wavenumber patterns, however, are less resilient to environmental changes. [Copyright &y& Elsevier]

A mathematical model is proposed which describes the dynamics and the spatial distributions of two population groups, where migration is driven by considerations of socioeconomic status. The model associates segregation with instabilities of spatially uniform mixed population states. These instabilities lead to a wide range of segregation forms including: (a) variable (weak) segregation where the population is everywhere mixed and the spatial variability is controlled by a ’status-gap’ parameter, (b)strong segregation, where nearby neighbourhoods consists of pure (unmixed) population groups, and (c) intermediate forms involving enclaves of a pure population group in neighbourhoods of mixed population. The model associates tipping-point phenomena with the existence of an unstable mixed population state which introduces a threshold for population inversion. The model predicts that uneven invasions of one population group into another may result from interface instabilities rather than from urban heterogeneities. [ABSTRACT FROM AUTHOR]

Vegetation rings are a unique vegetation pattern found in drylands. Most examples are found in clonal plants growing in sandy soils with confined root zones. Using field measurements and numerical simulations, we found that water overland flow is a predominant mechanism that drives ring formation in the clonal species Asphodelus ramosus. In these rings, an infiltration contrast develops due to aeolian feedback between vegetation and wind‐induced particle transport. Fine particles settle at the patch's centre, reducing water infiltrability compared with that of its perimeter. In turn, this encourages the development of biological soil crust in the ring's centre, further decreasing water infiltration in this micro‐environment. These processes cause the development of surface run‐off source–sink relations between the ring's centre and perimeter. The outcome of this process is the formation of three different micro‐environments: the centre of the patch, characterized by low soil‐water content; its perimeter, characterized by higher soil‐water content; and the matrix, also characterized by higher soil‐water content. Competition for the water resource between the ramets at the perimeter and the ones at the centre leads to dieback, resulting in ring formation. Measurements of soil‐water content in rings of A. ramosus in the semiarid Negev of Israel throughout 5 years showed that the soil‐water content in the ring's centre is lower than that at its perimeter and matrix. These results are in accord with numerical simulations of a mathematical model for plant species with confined roots grown under highly seasonal rainfalls in water‐limited environments. [ABSTRACT FROM AUTHOR]