Edaphic properties enable facilitative and competitive interactions resulting in fairy circle formation

Millions of generally regularly spaced, roughly circular barren patches called fairy circles occur in a narrow band ca 100 km inland of the south‐west African coast. These generally have conspicuously taller peripheral grasses in a shorter grass matrix. The origins of these fairy circles are controversial, but one possibility is that they are self‐organizing emergent vegetation patterns that are the consequence of interplay between positive (facilitative) and negative (competitive) interactions between grasses. We hypothesized that the coarse textured sand on which fairy circles occur creates a hydraulically and nutritionally connected landscape, in which neighbouring fairy circles competitively influence each other over several metres, while providing opportunity for focusing of resources around the peripheral grasses. To test our hypotheses we conducted three main groups of analyses: 1) we measured grass biomass to assess facilitative and competitive effects of the component grasses; 2) across a region with fairy circles we measured the size and density of fairy circles and correlated that with water infiltration rates into soil; 3) we measured the capacity of soil to conduct water pulses and ¹⁵N tracers. We found evidence of facilitative interactions in the periphery of the fairy circles and competitive suppression of the matrix grass proximal to the periphery. Across the region, fairy circle size was positively correlated with soil infiltration rates and negatively with precipitation. This suggests that fairy circles emerge in soils with high capacity for water flux that enables landscape hydraulic connectivity. Water‐ and ¹⁵N‐pulse experiments showed that edaphic resources were highly mobile, moving up to 7.5 m over a period of 1–3 weeks. We concluded that the evidence is consistent with an emergent vegetation pattern explanation for the origins of fairy circles and that the circles are more closely associated with a highly connective edaphic environment, rather than with particular biota.     

Experiments Testing the Causes of Namibian Fairy Circles

The grasslands on the sandy soils of the eastern edge of the Namib Desert of Namibia are strikingly punctuated by millions of mostly regularly-spaced circular bare spots 2 to 10 m or more in diameter, generally with a margin of taller grasses. The causes of these so called fairy circles are unknown, but several hypotheses have been advanced. In October 2009, we set up experiments that specifically tested four hypothesized causes, and monitored these 5 times between 2009 and 2015. Grass exclusion in circles due to seepage of subterranean vapors or gases was tested by burying an impermeable barrier beneath fairy circles, but seedling density and growth did not differ from barrier-less controls. Plant germination and growth inhibition by allelochemicals or nutrient deficiencies in fairy circle soils were tested by transferring fairy circle soil to artificially cleared circles in the grassy matrix, and matrix soil to fairy circles (along with circle to circle and matrix to matrix controls). None of the transfers changed the seedling density and growth from the control reference conditions. Limitation of plant growth due to micronutrient depletion within fairy circles was tested by supplementing circles with a micronutrient mixture, but did not result in differences in plant seedling density and growth. Short-range vegetation competitive feedbacks were tested by creating artificially-cleared circles of 2 or 4 m diameter located 2 or 6 m from a natural fairy circle. The natural circles remained bare and the artificial circles revegetated. These four experiments provided evidence that fairy circles were not caused by subterranean vapors, that fairy circle soil per se did not inhibit plant growth, and that the circles were not caused by micronutrient deficiency. There was also no evidence that vegetative feedbacks affected fairy circles on a 2 to 10 m scale. Landscape-scale vegetative self-organization is discussed as a more likely cause of fairy circles.     

Are Namibian “Fairy Circles” the Consequence of Self-Organizing Spatial Vegetation Patterning?

Causes of over-dispersed barren “fairy circles” that are often surrounded by ca. 0.5 m tall peripheral grasses in a matrix of shorter (ca. 0.2 m tall) grasses in Namibian grasslands remain mysterious. It was hypothesized that the fairy circles are the consequence of self-organizing spatial vegetation patterning arising from resource competition and facilitation. We examined the edaphic properties of fairy circles and variation in fairy circle size, density and landscape occupancy (% land surface) with edaphic properties and water availability at a local scale (<50 km) and with climate and vegetation characteristics at a regional scale. Soil moisture in the barren fairy circles declines from the center towards the periphery and is inversely correlated with soil organic carbon, possibly indicating that the peripheral grass roots access soil moisture that persists into the dry season within fairy circles. Fairy circle landscape occupancy is negatively correlated with precipitation and soil [N], consistent with fairy circles being the product of resource-competition. Regional fairy circle presence/absence is highly predictable using an empirical model that includes narrow ranges of vegetation biomass, precipitation and temperature seasonality as predictor variables, indicating that fairy circles are likely a climate-dependent emergent phenomenon. This dependence of fairy circle occurrence on climate explains why fairy circles in some locations may appear and disappear over time. Fairy circles are only over-dispersed at high landscape occupancies, indicating that inter-circle competition may determine their spacing. We conclude that fairy circles are likely to be an emergent arid-grassland phenomenon that forms as a consequence of peripheral grass resource-competition and that the consequent barren circle may provide a resource-reservoir essential for the survival of the larger peripheral grasses and provides a habitat for fossicking fauna.     

Dispersal strategies and spatial organization of vegetation in arid ecosystems

Seed dispersal and establishment are critical stages for plants in arid environments, where vegetation is spatially organized in patches with suitable and unsuitable sites for establishment. Theoretical studies suggest that the ability of vegetation to self‐organize in patchy spatial patterns is a critical property for plant survival in arid environments, and is a consequence of a scale‐dependent feedback between plants and resource availability. Field observations show that plants of arid environments evolved towards short dispersal distance (proxichory) and that the investment in reproduction increases along an aridity gradient. Here, we investigated how plant dispersal strategies affect spatial organization and associated scale‐dependent feedback in arid ecosystems. We addressed this research question using a model where the spatio‐temporal vegetation patterns were driven by scale‐dependent feedbacks between plants and soil water availability. In the model, water availability limited vegetation growth, seed production and establishment ability. Seed dispersal was modelled with an integrodifferential equation that mimicked important plant dispersal characteristics (i.e. fecundity, mean dispersal distance and establishment ability). Results showed that, when the investment in fecundity was relatively high, short seed dispersal helped maintaining higher mean biomass in the system, improving the vegetation efficiency in water use. However, higher fecundity induced a large cost, and high mean biomass could be sustained only with high establishment ability. Considering low establishment ability, intermediate fecundity was more efficient than low fecundity in maintaining high plant biomass under the most arid conditions. Consistently, plant dispersal strategies that maintained more biomass were related to a vegetation spatial organization that allowed the most efficient soil water redistribution, through the strengthening of the scale‐dependent feedback. The efficient dispersal strategies and spatial patterns in the model are commonly observed in plants of arid environments. Thus, dispersal strategies in arid environments might contribute to a favourable spatial organization and associated scale‐dependent feedback.     

Self‐organised patchiness and scale‐dependent bio‐geomorphic feedbacks in aquatic river vegetation

Spatial self‐organisation of ecosystems is the process by which large‐scale ordered spatial patterns emerge from disordered initial conditions through local feedbacks between organisms and their environment. Such process is considered important for ecosystem functioning, providing increased productivity, resistance and resilience against environmental change. Although spatial self‐organisation has been found for an increasing number of ecosystems, it has never been shown so far for aquatic river vegetation. Here we explore the existence of spatial self‐organisation of freshwater macrophyte patches in a typical lowland river (Belgium), showing that the underlying mechanisms for pattern formation are scale‐dependent feedbacks between plant growth, water flow and local river bed erosion and sedimentation. The mapping of vegetation patches showed that the frequency distribution of patch sizes is governed by a power‐law function, suggesting that the patches are self‐organised. Scale‐dependent feedbacks, likely to lead to this self‐organised pattern, were demonstrated with a mimic experiment. Both positive and negative feedbacks on plants were confirmed by a transplantation experiment. Placing vegetation patch mimics in the river showed experimentally that on a short range (within and behind the mimics) flow reduction and increased sedimentation occurred, while on a larger range (next to patches) the flow was accelerated and decreased sedimentation took place. By transplanting macrophytes within, next to and further away from existing patches, it was proven that the conditions within the patches favoured the survival and growth of transplants (i.e. short‐range positive feedback), while the conditions just next to patches led to decreased survival and growth (i.e. long‐range negative feedback).     

Spiral vegetation patterns in high-altitude wetlands

When plant communities suffer the stress of limited resources, for instance adverse environmental conditions such as extreme aridity, the spatial homogeneity of the biomass is lost and self-organized patterns may arise. Here, we report the observation of spiral-shaped patterns in the biomass of grass (genus deyeuxia), under highland arid conditions in the north of Chile. The spiral arms are a few meters long and a few centimeters wide. These dynamic structures are observed in the grazing area of an herbivore member of the South American camelids, the vicuna, on the border of highland wetlands. These spirals cannot be explained by the well-established mathematical models which describe other vegetation patterns (that emerge from a Turing-type of instability) such as stripes, rings, or fairy circles. We attribute the formation of spirals to the coupling between the growth of vegetation in semiarid regions and the grazing of vicunas. The mathematical analysis of this coupling reveals an excitable behavior, i.e. small perturbations of the equilibrium generate large trajectories before coming back, that is the origin of the spirals.     

Complexity and coexistence in a simple spatial model for arid savanna ecosystems

Tree–grass coexistence is broadly observed in tropical savannas. Recent studies indicate that, in arid savannas, such coexistence is stable and related to water availability. The role of different factors (from niche separation to demographic structure) has been explored. Nevertheless, spatial mechanisms of water–vegetation interactions have been rarely taken into account, despite their well-known importance for vegetation distribution. Here, we introduce a spatial model including tree and grass biomass dynamics, together with soil and surface water dynamics. We consider two water–vegetation feedbacks. Grasses increase water infiltration into the soil, while tree shadow limits evaporation, and both mechanisms increase soil water availability, leading to positive feedbacks. The infiltration feedback can also lead to spatial pattern formation. Despite the fact that trees and grasses compete for the same resource, namely water, we observe stable coexistence as a possible model outcome. The system displays a complex behavior, with multiple stable states and possible catastrophic shifts between states, e.g., patterned grassland, bare soil and forest. In our model, coexistence is always linked with multi-stability and spatial pattern formation, driven by grass infiltration feedback. Given such complex model solutions, we expect that, under real conditions, heterogeneities and disturbances, acting on the multi-stable states, may further foster coexistence.     

Scale matters: fire–vegetation feedbacks are needed to explain tropical tree cover at the local scale

At a broad (regional to global) spatial scale, tropical vegetation is controlled by climate; at the local scale, it is believed to be determined by interactions between disturbance, vegetation and local conditions (soil and topography) through feedback processes. It has recently been suggested that strong fire–vegetation feedback processes may not be needed to explain tree‐cover patterns in tropical ecosystems and that climate–fire determinism is an alternative possibility. This conclusion was based on the fact that it is possible to reproduce observed patterns in tropical regions (e.g. a trimodal frequency distribution of tree cover) using a simple model that does not explicitly incorporate fire–vegetation feedback processes. We argue that these two mechanisms (feedbacks versus fire–climate control) operate at different spatial and temporal scales; it is not possible to evaluate the role of a process acting at fine scales (e.g. fire–vegetation feedbacks) using a model designed to reproduce regional‐scale pattern (scale mismatch). While the distributions of forest and savannas are partially determined by climate, many studies are providing evidence that the most parsimonious explanation for their environmental overlaps is the existence of feedback processes. Climate is unlikely to be an alternative to feedback processes; rather, climate and fire–vegetation feedbacks are complementary processes at different spatial and temporal scales.     

Namibian fairy circles and epithelial cells share emergent geometric order

Fairy circles are enigmatic features of the Namib desert landscape. They are large, almost perfectly circular patches of barren soil in sparse grassland. Although a matter of continuing debate, we make no attempt to explain their origin. The focus of our approach is a statistical analysis of the spatial patterns. These are easily accessible via aerial and satellite imagery. Observations over extended periods of time have revealed that they have a life-cycle of birth, growth and death. It has also been known for some time that the fairy circles are not randomly distributed. Our novel finding is that the connectivity patterns of fairy circles and metazoan epithelial cells are statistically indistinguishable, while remaining clearly distinct from other commonly observed polygonal patternings. This result identifies an analogy between the microscopic world of epithelial cells and the macroscopic realm of the Namib, suggesting that approaches developed specifically for the analysis of microscopic structures may extend into ecologically relevant, macroscopic dimensions.     

The global biogeography of semi‐arid periodic vegetation patterns

Aim Vegetation exhibiting landscape‐scale regular spatial patterns has been reported for arid and semi‐arid areas world‐wide. Recent theories state that such structures are bound to low‐productivity environments and result from a self‐organization process. Our objective was to test this relationship between periodic pattern occurrence and environmental factors at a global scale and to parametrize a predictive distribution model. Location Arid and semi‐arid areas world‐wide. Methods We trained an empirical predictive model (Maxent) for the occurrence of periodic vegetation patterns, based on environmental predictors and known occurrences verified on Landsat satellite images. Results This model allowed us to discover previously unreported pattern locations, and to report the first ever examples of spotted patterns in natural systems. Relationships to the main environmental drivers are discussed. Main conclusions These results confirm that periodic patterned vegetations are ubiquitous at the interface between arid and semi‐arid regions. Self‐organized patterning appears therefore to be a biome‐scale response to environmental conditions, including soil and topography. The set of correlations between vegetation patterns and their environmental conditions presented in this study will need to be reproduced in future modelling attempts.     

Ants and the enigmatic Namibian fairy circles – cause and effect?

1. Parts of the Namibian landscape show extensive surface perturbation in the form of long‐lived, yet dynamic ‘fairy circles'. While exerting profound ecological effects on 7.3% of the land surface, the origin and nature of these large bare discs embedded in an arid grassland matrix remains unresolved. 2. We found no evidence to support the current hypothesis of a termite origin for fairy circles but instead observed a strong spatial association between fairy circles and large nests of the ant Black pugnacious ant Anoplolepis steingroeveri Forel, with much higher ant abundances on the circles compared with the matrix. 3. Aggression trials showed that different colonies of A. steingroeveri were located on different circles, and that the species was polydomous. 4. Fairy circles and Pogonomyrmex ant nests both have a bare disc surrounding the nest, are overdispersed (evenly spaced), and are associated with elevated soil moisture. Fairy circle soils exhibited a five‐fold increase in soil moisture when compared with the matrix. 5. Senescent Stipagrostis obtusa (Delile) Nees seedlings were only observed on the circles and not in the matrix, and were found to have a reduction in both root length and number of roots. 6. Anoplolepis steingroeveri excavated the root system of both S. obtusa seedlings on the disc and Stipagrostis ciliata (Desf.) de Winter grasses on the perimeter of the circles, where they tended honeydew‐secreting Meenoplidae bugs that fed on grass roots and culms. The bugs occurred almost exclusively on grasses associated with the circles. This ant–bug interaction is a possible mechanism for the observed reduction in root length and number of senescent grass seedlings on the circles.     

Temporal control of self‐organized pattern formation without morphogen gradients in bacteria

Diverse mechanisms have been proposed to explain biological pattern formation. Regardless of their specific molecular interactions, the majority of these mechanisms require morphogen gradients as the spatial cue, which are either predefined or generated as a part of the patterning process. However, using Escherichia coli programmed by a synthetic gene circuit, we demonstrate here the generation of robust, self‐organized ring patterns of gene expression in the absence of an apparent morphogen gradient. Instead of being a spatial cue, the morphogen serves as a timing cue to trigger the formation and maintenance of the ring patterns. The timing mechanism enables the system to sense the domain size of the environment and generate patterns that scale accordingly. Our work defines a novel mechanism of pattern formation that has implications for understanding natural developmental processes.     

Multifractal growth in periphyton communities

Periphyton is an aquatic community composed by algae, bacteria, fungi, and other microorganisms that can develop a complex architecture comparable to tropical forests. We analyzed the spatial pattern of a periphyton community along a succession developed in experimental tanks. Our aim was to identify regularities that may help us to explain the patchiness of this community. Therefore, we estimated the spatial pattern of periphyton biomass using a non‐destructive image analysis technique to obtain a temporal series of the spatial distribution. These were analyzed using multifractal techniques. Multifractals are analogous to fractals but they look at the geometry of quantities instead of the geometry of pattern. To use these techniques the object of study must show scale invariance and then can be characterized by a spectra of fractal dimensions. Self‐organization describes the evolution of complex structures that emerge spontaneously driven internally by variations of the system itself. The spatial distribution of biomass showed scale invariance at all stages of succession and as the periphyton developed in a homogeneous landscape, in a demonstration of self‐organized behavior. Self‐organization to a critical state (SOC) is presented in the complex systems literature as a general explanation for scale invariance in nature. SOC requires a mechanism where the history of past events in a place influence the actual dynamics, this was termed ecological memory. The scale invariance was found from the very beginning of the succession thus self‐organized criticality is a very improbable explanation for the pattern because there would be not enough time for the build‐up of ecological memory. Positive interactions between algae and bacteria, and the existence of different spatial scales of colonization and growth are the likely causes of this pattern. Our work is a demonstration of how large scale patterns emerge from local biotic interactions.     

Putting self‐organization to the test: labyrinthine patterns as optimal solution for persistence

Spatial patterns formed through the process of self‐organization are found in nature across a variety of ecosystems. Pattern formation may reduce the costs of competition while maximizing the benefits of group living, and thus promote ecosystem persistence. This leads to the prediction that self‐organizing to obtain locally intermediate densities will be the optimal solution to balance costs and benefits. However, despite much evidence documenting pattern formation in natural ecosystems, there is limited empirical evidence of how these patterns both influence and are influenced by tradeoffs between costs and benefits. Using mussels as a model system, we coupled field observations in mussel‐culture plots with manipulative laboratory experiments to address the following hypotheses: 1) labyrinthine spatial patterns, characteristically found at intermediate to high patch densities, are the most persistent over time; this is because labyrinthine patterns 2) result in adequately heavy patches that can maximize resistance to dislodgement while 3) increasing water turbulence with spacing, which will maximize food delivery processes. In the field, we observed that labyrinthine ‘stripes’ patterns are indeed the most persistent over time, confirming our first hypothesis. Furthermore, with laboratory experiments, we found the ‘stripes’ pattern to be highly resistant to dislodgement, confirming the second hypothesis. Finally, with regards to the third hypothesis, we found positive effects of this pattern on local turbulence. These results suggest that the mechanisms of intraspecific facilitation not only depend on initial organism densities, but may also be influenced by spatial patterning. We hence recommend taking into account spatial patterns to maximize productivity and persistence in shellfish‐cultivation practices and to increase the restoration success of ecosystems with self‐organizing properties.     

干旱半干旱区斑块状植被格局形成模拟研究进展

斑块状植被格局是世界上干旱半干旱区常见的景观类型,它们的形成、组成结构和演替过程研究,对于揭示区域生态系统变化的关键过程具有重要意义。鉴于基于地面调查和遥感技术的方法难以全面刻画斑块状植被格局的形成过程及机制,借助于模型模拟成为解决这一问题的有效方法。自20世纪90年代初至今,斑块状植被格局形成的连续和离散模拟研究不断涌现,然而,连续模拟侧重于植被格局形成的一般机理,缺乏与现实格局的对比和验证,离散模拟单元选择与规则制定等仍需不断研究。在简要回顾斑块状格局形成的反馈机制基础上,重点综述了斑块状植被格局形成的连续和离散模拟的最新研究进展,并指出了现有研究的不足。干旱半干旱区小尺度上植物和水的反馈作用决定了大尺度的斑块状植被格局,充分揭示植被-土壤水分相互作用机理是模型模拟研究的关键,放牧强度和降水格局等外部环境对干旱半干旱区斑块状植被格局特征具有重要影响。在未来研究中,应加强模型模拟结果与实际观测的植被格局比较和验证,重视局域环境条件、生态系统功能在模型中的表达,构建综合连续和离散模型各自优点的混合模型,注重斑块状植被格局形成过程中的标准子模型及模型开发和集成平台的研发,同时强调面向格局模拟和构建空间显式的斑块状植被格局形成模型。     

Vegetation Pattern Formation Due to Interactions Between Water Availability and Toxicity in Plant–Soil Feedback

Development of a comprehensive theory of the formation of vegetation patterns is still in progress. A prevailing view is to treat water availability as the main causal factor for the emergence of vegetation patterns. While successful in capturing the occurrence of multiple vegetation patterns in arid and semiarid regions, this hypothesis fails to explain the presence of vegetation patterns in humid environments. We explore the rich structure of a toxicity-mediated model of the vegetation pattern formation. This model consists of three PDEs accounting for a dynamic balance between biomass, water, and toxic compounds. Different (ecologically feasible) regions of the model’s parameter space give rise to stable spatial vegetation patterns in Turing and non-Turing regimes. Strong negative feedback gives rise to dynamic spatial patterns that continuously move in space while retaining their stable topology.     

A mathematical model of plants as ecosystem engineers

Understanding the structure and dynamics of plant communities in water-limited systems often calls for the identification of ecosystem engineers--key species that modify the landscape, redistribute resources and facilitate the growth of other species. Shrubs are excellent examples; they self-organize to form patterns of mesic patches which provide habitats for herbaceous species. In this paper we present a mathematical model for studying ecosystem engineering by woody plant species in drylands. The model captures various feedbacks between biomass and water including water uptake by plants' roots and increased water infiltration at vegetation patches. Both the uptake and the infiltration feedbacks act as mechanisms for vegetation pattern formation, but have opposite effects on the water resource; the former depletes the soil-water content under a vegetation patch, whereas the latter acts to increase it. Varying the relative strength of the two feedbacks we find a trade-off between the engineering capacity of a plant species and its resilience to disturbances. We further identify two basic soil-water distributions associated with engineering at the single patch level, hump-shaped and ring-shaped, and discuss the niches they form for herbaceous species. Finally, we study how pattern transitions at the landscape level feedback to the single patch level by affecting engineering strength.     

Spatial heterogeneity of tundra vegetation response to recent temperature changes

The spatial heterogeneity of recent decadal dynamics in vegetation greenness and biomass in response to changes in summer warmth index (SWI) was investigated along spatial gradients on the Arctic Slope of Alaska. Image spatial analysis was used to examine the spatial pattern of greenness dynamics from 1991 to 2000 as indicated by variations of the maximum normalized difference vegetation index (Peak NDVI) and time‐integrated NDVI (TI‐NDVI) along latitudinal gradients. Spatial gradients for both the means and temporal variances of the NDVI indices for 0.1° latitude intervals crossing three bioclimate subzones were analyzed along two north–south Arctic transects. NDVI indices were generally highly variable over the decade, with great heterogeneity across the transects. The greatest variance in TI‐NDVI was found in low shrub vegetation to the south (68.7–68.8°N) and corresponded to high fractional cover of shrub tundra and moist acidic tundra (MAT), while the greatest variance in Peak‐NDVI predominately occurred in areas dominated by wet tundra (WT) and moist nonacidic tundra (MNT). Relatively high NDVI temporal variances were also related to specific transitional areas between dominant vegetation types. The regional temporal variances of NDVI from 1991 to 2000 were largely driven by meso‐scale climate dynamics. The spatial heterogeneity of the NDVI variance was mostly explained by the fractional land cover composition, different responses of each vegetation type to climate change, and patterned ground features. Aboveground plant biomass exhibited similar spatial heterogeneity as TI‐NDVI; however, spatial patterns are slightly different from NDVI because of their nonlinear relationship.     

Assessing long‐term hydrological and ecological responses to drainage in a raised bog using paleoecology and a hydrosequence

Question: We studied vegetation succession after drainage in a bog, as an analogue for potential persistent water table drawdown due to climate change. We asked: (1) how does bog vegetation change following a long‐term water table lowering and (2) how are effects of drainage on hydrology and vegetation distributed temporally and spatially? Location: Mer Bleue peatland, Ontario, Canada (45.41°N, 75.48°W). Methods: Analyses of changes in vegetation and hydrology associated with drainage were examined spatially along a hydrosequence and temporally using paleoecological reconstructions from peat cores (testate amoebae, pollen) in a drained portion of a peatland untouched for 85 years following drainage. Relationships between modern vegetation and water table were assessed through clustering and ordination analyses of vegetation relevés. Results: Post‐drainage increases in tree cover, especially Betula and Larix, decreases in Sphagnum cover and shifts in species composition of dominant shrubs were observed. Present‐day vegetation patterns along the hydrosequence were primarily related to seasonal variability of water table depth. Paleoecological records reveal that where the present‐day vegetation has been impacted by drainage, persistent water table lowering occurred in response to drainage. However, in an area with relatively natural vegetation, a transient drop in water table depth occurred at the time of drainage. Conclusions: Temporal and spatial patterns revealed that the bog response to drainage was spatially and temporally heterogeneous, and probably mediated by feedbacks among vegetation, peat structure and hydrology. Spatial patterns along the hydrosequence were similar to those observed in paleoecological reconstructions, but the use of the two complementary techniques provides additional insights.