Hezi Yizhaq

Periodic versus scale-free patterns in dryland vegetation

Two major forms of vegetation patterns have been observed in drylands: nearly periodic patterns with characteristic length scales, and amorphous, scale-free patterns with wide patch-size distributions. The emergence of scale-free patterns has been attributed to global competition over a limiting resource, but the physical and ecological origin of this phenomenon is not understood. Using a spatially explicit mathematical model for vegetation dynamics in water-limited systems, we unravel a general mechanism for global competition: fast spatial distribution of the water resource relative to processes that exploit or absorb it. We study two possible realizations of this mechanism and identify physical and ecological conditions for scale-free patterns. We conclude by discussing the implications of this study for interpreting signals of imminent desertification.

Localized structures in dryland vegetation: Forms and functions

Vegetation patches in drylands are localized structures of biomass and water. We study these structures using a mathematical modeling approach that captures biomass-water feedbacks. Biomass-water structures are found to differ in their spatial forms and ecological functions, depending on species type, soil conditions, precipitation range, and other environmental factors. Asymptotic spot structures can destabilize to form ring structures, expanding in the radial direction, or crescent structures, migrating uphill. Stable spot structures can differ in their soil-water distributions, forming water-enriched patches or water-deprived patches. The various biomass-water structures are expected to function differently in the context of a plant community, forming landscapes of varying species diversity.

Regime shifts in models of dryland vegetation.

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.

Discovery of fairy circles in Australia supports self-organization theory

Significance Pattern-formation theory predicts that vegetation gap patterns, such as the fairy circles of Namibia, emerge through the action of pattern-forming biomass–water feedbacks and that such patterns should be found elsewhere in water-limited systems around the world. We report here the exciting discovery of fairy-circle patterns in the remote outback of Australia. Using fieldwork, remote sensing, spatial pattern analysis, mathematical modeling, and pattern-formation theory we show that the Australian gap patterns share with their Namibian counterparts the same characteristics but are driven by a different biomass–water feedback. These observations are in line with a central universality principle of pattern-formation theory and support the applicability of this theory to wider contexts of spatial self-organization in ecology. 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.

Emerged or imposed: a theory on the role of physical templates and self-organisation for vegetation patchiness

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.

Mechanisms of vegetation-ring formation in water-limited systems

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).

Dune‐like dynamic of Martian Aeolian large ripples

Martian dunes are sculpted by meter-scale bed forms, which have been interpreted as wind ripples based on orbital data. Because aeolian ripples tend to orient and migrate transversely to the last sand-moving wind, they have been widely used as wind vanes on Earth and Mars. In this report we show that Martian large ripples are dynamically different from Earth’s ripples. By remotely monitoring their evolution within the Mars Science Laboratory landing site, we show that these bed forms evolve longitudinally with minimal lateral migration in a time-span of ~ six terrestrial years. Our observations suggest that the large Martian ripples can record more than one wind direction and that in certain cases they are more similar to linear dunes from a dynamic point of view. Consequently, the assumption of the transverse nature of the large Martian ripples must be used with caution when using these features to derive wind directions. 1. Study Area and Methods In this study, we investigate the meter-scale aeolian bed forms sculpting the slopes of the informally named Bagnold dunes within the NASA Mars Science Laboratory landing site (Figure 1a) in Gale Crater. We will refer to these features as large ripples (LRs) or we will use the more generic term of “bed forms” because we will argue they may have a different dynamic to most known terrestrial aeolian ripples. The Bagnold dunes are elongated barchans and longitudinal dunes, morphologies consistent with a bidirectional wind regime [Hobbs et al., 2010; Silvestro et al., 2013]. These dunes are covered by three overlapping High-Resolution Imaging Science Experiment (HiRISE) images that are suitable for aeolian change detection studies (Figure S1 and Table S1 in the supporting information). We quantified the LR’s migration rate in the T1–T3 time span (ΔT= 2075 Earth days) using the “Co-registration of Optically Sensed Images and Correlation” (COSI-Corr) tool suite [Leprince et al., 2007]. The normalized misregistration error, which resulted from the coregistration and orthorectification process, was 0.03 ± 0.95 and 0.05 ± 1.39 pixels for the T1–T2 and T2–T3 pairs, respectively (more detail is provided in the supporting information). The COSI-Corr displacement maps are further improved by removing jitter artifacts (Figure S2). We then used the Object-based Ripple Analysis technique [Vaz and Silvestro, 2014] to characterize the directional distribution of the LRs, evaluate their spatial distribution and correlate bed form pattern characteristics with migration rates and morphometric settings [Vaz and Silvestro, 2014; Vaz et al., 2015] (Figure S3).

Morphology and dynamics of aeolian mega-ripples in Nahal Kasuy, southern Israel

Yizhaq, H., Isenberg, O., Wenkart, R., Tsoar, H., and Karnieli, A. 2008. Morphology and dynamics of aeolian mega-ripples in Nahal Kasuy, southern Israel. Isr. J. Earth sci. 57: 149–165. Aeolian sand ripples are a common feature on sandy deserts and beaches. Aeolian ripples often have wavelengths of 10–15 cm and amplitudes of a few millimeters. Mega-ripples are bigger than regular ripples and have a mean wavelength of about 70 cm. They are characterized by a bimodal distribution of coarse and fine particle sizes, which is necessary for their formation. We present here the results of a 11⁄2year field study at the Nahal Kasuy mega-ripple field, located in the southern Negev Desert. The regular sand ripples superposed on the mega-ripples were formed by weaker winds blowing from different directions. The time evolution of mega-ripples developing from a flat surface was monitored. They grow due to a sand coarsening mechanism. Initially, regular ripples form, which subsequently undergo coarsening by winnowing of the finer particles, thereby producing a coalescence of the regular ripples. The smaller, faster-moving ripples overtake the larger, slower-moving ripples, resulting in increased size and spacing. This state was analyzed by a new technique we developed, using a digital elevation model (DEM) constructed from stereo digital photographs. Data on the wind power (drift potential) during the fieldwork and grain size of samples taken from the mega-ripple crest and trough are presented. The grainsize characteristics demonstrate that only fine particles saltate, while coarse grains creep due to the low wind power at Nahal Kasuy.

Biogenic crust dynamics on sand dunes.

Sand dunes are often covered by vegetation and biogenic crusts. Despite their significant role in dune stabilization, biogenic crusts have rarely been considered in model 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 crossover between two different forms of desertification.

A Mathematical Model of Segregation Patterns in Residential Neighbourhoods

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.