Article

Self-Organization of Vegetation in Arid Ecosystems

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Abstract

Vegetation in arid regions of Africa, America, Australia, and Asia reveals remarkable patterns, such as spotted vegetation, labyrinths, gap patterns, and regular bands (Brom-ley et al. 1997; Aguiar and Sala 1999; Klausmeier 1999; Leprun 1999; Couteron and Lejeune 2001; Von Hardenberg et al. 2001). Here, the term “arid” refers to environments characterized by an extended dry season, where yearly potential evaporation exceeds yearly rainfall, and where plant growth is limited by water availability. The two-phase mosaics of vegetation alternating with bare soil as observed in arid ecosystems differ in scale and shape, depending on slope gradient and rainfall. When slope gradient is !0.2% and mean annual rainfall ranges from 200 to 550 mm yr 1, observed vegetation patterns include spots with a diameter of 5–20 m, labyrinths with a vegetated band width of 10–50 m (fig. 1a), and gap patterns with bare spots in the vegetation with a diameter of 5–20 m (fig. 1b; Bromley et al. 1997; Aguiar and Sala 1999; Ludwig et al. 1999b; Valentin et al. 1999; Couteron and Lejeune 2001). On slopes steeper than 0.2% in arid regions, typical regular-banded vegetation patterns with a band width in the range of a few tens of meters are observed (Klausmeier 1999; Leprun 1999; Valentin et al. 1999; d’Herbes et al. 2001). Scientists are still searching for possible unifying mechanisms to explain this range of spatial patterns (Tongway and Ludwig 2001), and an important question of this research is whether this range is the result of preexisting environmental heterogeneity, the result of spatial selforganization, or both (Klausmeier 1999; Couteron and Lejeune 2001; HilleRisLambers et al. 2001; Von Hardenberg et al. 2001). Here, we contribute to the ongoing debate about vegetation pattern formation in arid ecosystems by presenting novel, spatially explicit model analyses and results, extending on the work of HilleRisLambers et al. (2001). Our results show that these different vegetation patterns observed in arid ecosystems might all be the result of spatial self-organization, caused by one single mechanism: water infiltrates faster into vegetated ground than into bare soil, leading to net displacement of surface water to vegetated patches. This model differs from earlier model results (Klausmeier 1999; Couteron and Lejeune 2001; HilleRisLambers et al. 2001; Von Hardenberg et al. 2001)primarily in two ways: it is fully mechanistic, and it treats the lateral flow of water above and below the soil as separate, not independent, variables. Although the current model greatly simplifies the biophysics of arid systems, it can reproduce the whole range of distinctive vegetation patterns as observed in arid ecosystems, indicating that the proposed mechanism might be generally applicable. We further show that self-organized vegetation patterns can persist far into regions of high aridity, where plants would become extinct if homogeneously distributed, pointing to the importance of this mechanism for maintaining productivity of arid ecosystems (Noy-Meir 1973) Our analyses are based on the model first developed in HilleRisLambers et al. (2001), which we now briefly review. Vegetation patterning is generally linked to the mechanism by which plants increase surface-water infiltration into the soil, in combination with low annual rainfall conditions (Bromley et al. 1997; Klausmeier 1999; Leprun 1999; Ludwig et al. 1999a; HilleRisLambers et al. 2001). During rain showers, some rainwater will infiltrate into the soil, while the remainder will run off as surface water to other areas. With increasing plant density, the rate of infiltration of surface water into the soil will asymptotically approach a maximum (Rietkerk and van de Koppel 1997). Lateral flow of surface water is due to pressure differences measured by the slope of the thickness of the surface-water layer and can be described with a single diffusion term (Bear and Verruyt 1990; HilleRisLambers et al. 2001). Part of the infiltrated soil water subsequently evaporates or moves out of reach of plant roots by drainage and lateral subsurface flow due to capillary forces (Hills 1971; Lawrence Dingman 1994). Soil water uptake and plant growth are both assumed to be saturation functions of soil-water availability (de Wit 1958; Rietkerk et al. 1997). Plant dispersal, through seed or vegetative propagation, is approximated by a diffusion term (Okubo 1989; Cain 1990; HilleRisLambers et al. 2001).

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... These range from regular bands of vegetation alternating with bare ground, to vegetated spots and labyrinths, to regular gaps of bare ground within an otherwise continuous expanse of vegetation. These patterns can be observed in satellite imagery (figure 1a; [2][3][4][5]), and can be produced by activation–inhibition systems in computational models (see [6] for a review) (figure 1b; [2,[7][8][9][10][11]). The development of spatial vegetation patterns in simulations follows a well-established sequence that is related to the amount of rainfall supplied to the land surface. ...
... The development of spatial vegetation patterns in simulations follows a well-established sequence that is related to the amount of rainfall supplied to the land surface. At relatively high rainfall levels, the entire land surface is covered with vegetation, and as the rainfall progressively decreases vegetation patterns change from gaps (near continuous vegetation cover with small openings) to labyrinths (reticulate networks of vegetation) to spots (small patches of vegetation), and finally to bare ground (figure 1b; [10,12]). It is thought that these spatial vegetation patterns result from the enhanced infiltration of water into vegetated ground compared with bare ground, and/or extensive lateral root networks, both of ...
... which promote the growth of vegetation at very local scales but inhibit vegetation growth over a larger area because of competition for water [10,12]. Additionally, fast soil-water diffusion in porous sand results in an uptake–diffusion feedback, which requires only confined and not extensive lateral roots. ...
Article
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Vegetation in dryland ecosystems often forms remarkable spatial patterns. These range from regular bands of vegetation alternating with bare ground, to vegetated spots and labyrinths, to regular gaps of bare ground within an otherwise continuous expanse of vegetation. It has been suggested that spotted vegetation patterns could indicate that collapse into a bare ground state is imminent, and the morphology of spatial vegetation patterns, therefore, represents a potentially valuable source of information on the proximity of regime shifts in dryland ecosystems. In this paper, we have developed quantitative methods to characterize the morphology of spatial patterns in dryland vegetation. Our approach is based on algorithmic techniques that have been used to classify pollen grains on the basis of textural patterning, and involves constructing feature vectors to quantify the shapes formed by vegetation patterns. We have analysed images of patterned vegetation produced by a computational model and a small set of satellite images from South Kordofan (South Sudan), which illustrates that our methods are applicable to both simulated and real-world data. Our approach provides a means of quantifying patterns that are frequently described using qualitative terminology, and could be used to classify vegetation patterns in large-scale satellite surveys of dryland ecosystems.
... The vegetation of dryland ecosystems is typically distributed in patches interspersed within a matrix of bare ground and low vegetation (Aguiar and Sala 1999; Deblauwe et al. 2008). A number of ecosystem models considering spatial interactions (so-called spatiallyexplicit models) have successfully described the wide variety of vegetation patterns observed in dryland landscapes worldwide (e.g., von Hardenberg et al. 2001; Kéfi et al. 2007a; Manor and Shnerb 2008; von Hardenberg et al. 2010; Rietkerk et al. 2002). Aside from studying the origin of the patterns, several of these modelling works have explored the impacts of changing climatic conditions and disturbance on vegetation cover and pattern with the aim to derive predictive models for critical transitions from vegetated to degraded states. ...
... So far, the main mechanisms considered in dryland vegetation models are resource-concentration (i.e., resource concentration near the plants and depletion further away leading to long-distance negative plant– plant interactions) and local facilitation (i.e., positive plant–plant interaction due to environment amelioration near the plants). Most of the models including resource concentration as a pattern-driving mechanism account explicitly for feedbacks between vegetation and water availability at the local scale, such as the positive feedback between plant biomass and increased soil infiltration capacity (e.g., von Hardenberg et al. 2001; Rietkerk et al. 2002). In addition to the internal redistribution of resources, the degree of conservation or loss of resources by the landscape (i.e., resource leakiness) is also considered to be crucial in dryland ecosystem dynamics (e.g. ...
... In addition to the internal redistribution of resources, the degree of conservation or loss of resources by the landscape (i.e., resource leakiness) is also considered to be crucial in dryland ecosystem dynamics (e.g. Hillerislambers et al. 2001; Rietkerk et al. 2002; Scanlon et al. 2007; Okin et al. 2009). Both vegetation cover and vegetation pattern greatly impact the potential of the ecosystem to conserve key resources such as water, soil, and nutrients (Abrahams et al. 1995; Ludwig and Tongway 1995; Cammeraat and Imeson 1999; Wilcox et al. 2003; Puigdefábregas 2005; Bautista et al. 2007; King et al. 2011). ...
Article
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Conceptual frameworks of dryland degradation commonly include ecohydrological feedbacks between landscape spatial organization and resource loss, so that decreasing cover and size of vegetation patches result in higher water and soil losses, which lead to further vegetation loss. However, the impacts of these feedbacks on dryland dynamics in response to external stress have barely been tested. Using a spatially-explicit model, we represented feedbacks between vegetation pattern and landscape resource loss by establishing a negative dependence of plant establishment on the connectivity of runoff-source areas (e.g., bare soils). We assessed the impact of various feedback strengths on the response of dryland ecosystems to changing external conditions. In general, for a given external pressure, these connectivity-mediated feedbacks decrease vegetation cover at equilibrium, which indicates a decrease in ecosystem resistance. Along a gradient of gradual increase of environmental pressure (e.g., aridity), the connectivity-mediated feedbacks decrease the amount of pressure required to cause a critical shift to a degraded state (ecosystem resilience). If environmental conditions improve, these feedbacks increase the pressure release needed to achieve the ecosystem recovery (restoration potential). The impact of these feedbacks on dryland response to external stress is markedly non-linear, which relies on the non-linear negative relationship between bare-soil connectivity and vegetation cover. Modelling studies on dryland vegetation dynamics not accounting for the connectivity-mediated feedbacks studied here may overestimate the resistance, resilience and restoration potential of drylands in response to environmental and human pressures. Our results also suggest that changes in vegetation pattern and associated hydrological connectivity may be more informative early-warning indicators of dryland degradation than changes in vegetation cover.
... We are particularly interested in how the interplay between these mechanisms governs the spatial arrangement of trees in mesic savannas, where both mechanisms may operate. On the other side, it has frequently been claimed that pattern formation in arid systems can be explained by a combination of long-distance competition and short-distance facil- itation22232425262728. This combination of mechanisms is also known to produce spatial structures in many other natural systems [29]. ...
... Specifically, the interaction between long-range competition and short-range facilitation might still play a role in pattern formation in savanna tree populations, but only for a limited range of parameter values and possibly modulated by demographic stochasticity. Although the facilitation component has often been thought to be a key component in previous vegetation models [9, 26, 28, 30], Rietkerk and Van de Koppel [31] , speculated, but did not show, that pattern formation could occur without short-range facilitation in the particular example of tidal freshwater marsh. In the case of savannas, as stated before, the presence of adult trees favors the establishment of new trees in the area, protecting the juveniles against fires. ...
... (15) with ρ 0 = 0.8) and α = 1. Similarly to what has been observed in studies of semiarid water limited systems [26, 28], different structures, including gaps, stripes, and tree spots, are obtained in the stationary state as we increase the strength of competition for a fixed value of the fire parameter. On the other hand, if we fix the competition parameter, decreasing the parameter σ makes the local facilitation stronger. ...
Article
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We propose a model equation for the dynamics of tree density in mesic savannas which considers long-range competition among trees and the effect of fire indirectly acting as a local facilitation mechanism. Despite the fact that we take short-range facilitation to the local-range limit, the standard full spectrum of spatial structures already obtained in self-organization models of vegetation is recovered. Nonlocal competition, in the limit of infinitesimally short facilitation, promotes the clustering of trees. The long time coexistence between trees and grass, and how fires affect the survival of trees as well as the maintenance of the patterns is studied. The influence of demographic noise is analyzed. The stochastic system, under the parameter constraints typical of mesic savannas, shows non-homogeneous patterns characteristics of realistic situations. The coexistence of trees and grass still remains at reasonable noise intensities.
... We used a model developed for arid ecosystems, where the dynamics of vegetation and of the main limiting resource, water, were modelled based on the observation that water infiltrates better under vegetation (Rietkerk et al. 2000), which in turn favours vegetation growth. Concentration of water in vegetation patches leads to its depletion farther away (Rietkerk et al. 2002). This model successfully reproduced some of the observed vegetation patterns (i.e. ...
... labyrinth, spot and banded vegetation patterns), but did not include important seed dispersal characteristics. Dispersal was included in the model of Rietkerk et al. (2002) as a diffusion term. This might be appropriate for vegetative growth, but a model of seed dispersed plants needs to include important dispersal traits (quantity of seeds falling in non-suitable places, ability to germinate, reproductive effort, and so on). ...
... Besides the above mentioned seed dispersal traits, the model followed HilleRisLambers et al. (2001) and Rietkerk et al. (2002) in order to be able to attribute the model behaviour to the added effects of seed dispersal traits. The equations then read: ...
Article
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.
... At the same time, these models typically consider external pressures, e.g. mortality by consumption or disease (Rietkerk et al. 2002; Kéfi et al. 2007b, 2011 Manor and Shnerb 2008; von Hardenberg et al. 2010 ), to be homogeneous in space, meaning that they are affecting all individuals equally. However, many types of pressures are likely to include positive local feedback mechanisms that render the pressure spatially heterogeneous, i.e. cases where the intensity of the pressure depends on the local density of individuals. ...
... First, the range of pressure levels at which both desert and vegetated landscapes were simultaneously stable (i.e. the socalled bistability area) increased as spatially explicit grazing became more intense. This is consistent with previous modelling studies of spatially homogeneous grazing pressure (Rietkerk et al. 2002; Kéfi et al. 2007a, 2007b). Second, under high grazing pressure, state transitions from a vegetated to a bare landscape were more sudden and unexpected. ...
Article
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Ecosystems may exhibit catastrophic shifts, i.e. abrupt and irreversible responses of ecosystem functions and services to continuous changes in external conditions. The search for early warning signs of approaching shifts has so far mainly been conducted on theoretical models assuming spatially-homogeneous external pressures (e.g. climatic). Here, we investigate how a spatially explicit pressure may affect ecosystems’ risk of catastrophic shifts and the associated spatial early-warning signs. As a case study, we studied a dryland vegetation model assuming ‘associational resistance’, i.e. the mutual reduction of local grazing impact by neighboring plants sharing the investment in defensive traits. Consequently, grazing pressure depends on the local density of plants and is thus spatially-explicit. We focus on the distribution of vegetation patch sizes, which can be assessed using remote sensing and are candidate early warning signs of catastrophic shifts in drylands. We found that spatially explicit grazing affected both the resilience and the spatial patterns of the landscape. Grazing impact became self-enhancing in more fragmented landscapes, disrupted patch growth and put apparently ‘healthy’ drylands under high risks of catastrophic shifts. Our study highlights that a spatially explicit pressure may affect the nature of the spatial pattern observed and thereby change the interpretation of the early warning signs. This may generalize to other ecosystems exhibiting self-organized spatial patterns, where a spatially-explicit pressure may interfere with pattern formation.
... However, the striking vegetation patterns found in arid and semiarid ecosystems are primarily a result of spatial selforganization , caused by the mechanism of positive feedback loops between plant cover and water infiltration: water infiltrates faster into vegetated ground than into bare soil surface or surfaces with low vegetation cover, leading to net displacement of surface water to vegetated patches. Through this feedback, dryland plants tend to create more favorable conditions for their own survival (Barbier et al., 2006; Rietkerk and Boerlijst, 2002; Rietkerk et al., 2004; Wilcox et al., 2003). The existence of patterned vegetation changes the energy and water balance at a small scale, and exerts a major influence on geomorphic features and hydrological processes at a larger spatial scale (Zeng et al., 2007). ...
... The existence of patterned vegetation changes the energy and water balance at a small scale, and exerts a major influence on geomorphic features and hydrological processes at a larger spatial scale (Zeng et al., 2007). Understanding why and how the self-organized vegetation patterns form is a problem of great general interest (Kumar and Ruddell, 2010; Rietkerk and Boerlijst, 2002; van der Heide et al., 2010 ). Landscapes of the alpine ecosystems in arid northwest China represent a very special and unique self-organized spatial pattern of vegetation, consisting of grassland matrices and shrubforest mosaics (e.g. ...
Article
A tension infiltrometer technique was used to determine the effects of vegetation patterning on the hydraulic properties of surface soils in an alpine catchment unit previously used as rain-fed agricultural land but now exhibiting a significantly self-organized vegetation pattern, with a shrub-covered surface on the north-facing slope and a grass-covered surface on the south-facing slope. We hypothesized that the surface soils in the catchment unit had a random pattern with relatively uniform variance before the fencing program began in 2000, because of long-term tillage and crop production, and we found a slightly organized and apparently heterogeneous pattern of Ks after the recovery period. While a relatively higher average Ks was observed on the north-facing slope than on the south-facing slope, the difference was not statistically significant. The surface soil hydraulic pattern in the catchment unit was controlled mainly by terrain-related processes such as runoff sealing and compaction, and vegetation patterning did not contribute as much as we expected to its development. Although the positive feedbacks between vegetation and soil we postulated in this work were not observed, such a positive feedback may exist in the root-zone soil profile, as indicated by the significant differences in physical and chemical parameters of soil profiles on different slope positions, e.g. bulk density, field capacity, total C, N and available P, etc. Assertion of the statement, however, is still subject to debate because of the limited data, and deserves much more detailed research and investigation in the future.
... Endogenous patterning mechanisms have recently been recognized in arid and semiarid landscapes, leading to the emergence of conspicuous banded, labyrinthine, and spotted patterns (Figure 1) of dense vegetation alternating with bare soil. These landscape-scale, spatially periodic [Couteron and Lejeune, 2001] patterns are explained via classic theories of deterministic pattern formation [e.g., Murray, 1989] through the interplay of local resource availability enhancement (facilitation) and resource consumption by plants (competition) [Lefever and Lejeune, 1997; Klausmeier, 1999; von Hardenberg et al., 2001; Rietkerk et al., 2002]. These patterns are observed to be in a stable equilibrium with environmental constraints [Barbier et al., 2006] and are seldom concerned with fire dynamics [Tongway et al., 2001] . ...
... Thus we follow D'Odorico et al. [2006a] and model vegetation dynamics using only one equation. The temporal variability of V is expressed as a growth-death process, while tree encroachment is modeled as a (deterministic ) diffusion process [von Hardenberg et al., 2001; Rietkerk et al., 2002; Murray, 1989; Okubo, 1989], ...
Article
1] The high degree of spatial organization of dryland vegetation has been often explained invoking a number of different deterministic mechanisms without ever explicitly addressing the role of noise in the process of pattern formation. Noise is usually believed to act on ecosystems as a source of disorganized random fluctuations. However, noise is also known for its ability to induce ordered states in nonlinear systems. An alternative mechanism is here proposed, which explains vegetation pattern formation in mesic and subhumid savannas as the joint effect of fire randomness and fire-vegetation feedbacks. This mechanism is purely noise-induced and has no deterministic counterpart.
... There is a growing body of literature emphasizing the importance of self-organization in determining the spatial complexity of ecosystems. Localized ecological interactions can generate striking large-scale spatial patterns in ecosystems through self-organization [4] [5] [6] [7]. In recent decades, regular spatial patterning, which is common in ecosystems, has been a dominant topic in the study of spatial self-organization [8] [9]. ...
Article
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A wetland ecosystem is studied theoretically and numerically to reveal the rules of dynamics which can be quite accurate to better describe the observed spatial regularity of tussock vegetation. Mathematical theoretical works mainly investigate the stability of constant steady states, the existence of nonconstant steady states, and bifurcation, which can deduce a standard parameter control relation and in return can provide a theoretical basis for the numerical simulation. Numerical analysis indicates that the theoretical works are correct and the wetland ecosystem can show rich dynamical behaviors not only regular spatial patterns. Our results further deepen and expand the study of dynamics in the wetland ecosystem. In addition, it is successful to display tussock formation in the wetland ecosystem may have important consequences for aquatic community structure, especially for species interactions and biodiversity. All these results are expected to be useful in the study of the dynamic complexity of wetland ecosystems.
... Notwithstanding, Wilkinson (2005) and Montgomery (2007) demonstrate that anthropogenic factors, in general, and agricultural practices, in particular, are of the most dominant drivers accelerating erosion rates. Partial differential equations are frequently used to describe soil erosion (Laguna and Giráldez 1993; Hairsine et al. 1999; Smets et al. 2011) and vegetation dynamics (Rietkerk et al. 2002; Collins et al. 2004 ). Models based on ordinary differential equations are more convenient when describing the global properties of the system and have been applied to modeling various aspects of ecological systems including: the effects of water on soil transport (Parsons et al. 2006), as well as grazing (Van Langevelde et al. 2003), human stress (Chen et al. 2011), and global climate change (Nearing et al. 2004). ...
Article
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Wildfire events and anthropogenic activities such as agriculture and livestock grazing may denude the landscape from vegetation cover, resulting in systems prone to soil loss and degradation. Soil dynamics is an intricate process balanced between pedogenesis, which is a relatively slow process, and erosion which depends on many inert (e.g., soil texture, slope, precipitation, and wind) and biological factors such as vegetation properties, grazing intensity, and human disturbance. We develop here a theoretical model of the global dynamics of the interactions between vegetation and soil. Assuming a double feedback between them—plants control erosion, and soil availability facilitates plants growth—a system of nonlinear differential equations is derived, and the outcomes are investigated. The range of realistic parameter values were taken from the literature. Complex properties emerge from this model. For some ranges of parameter values, the model predicts one of two types of steady states—full recovery of vegetation cover or a degraded barren system. For another range of parameter values, bistability appears. We identify the parameter combinations which determine the qualitative behavior of the system and the threshold values beyond which the system becomes bistable. The model predicts that certain ecosystems are highly stable. Others might be bistable transitioning between these two states through perturbations. Therefore, the possibly of hysteresis as parameters vary arises, as well as the ability of the system to shift between steady states, possibly leading to sudden and dramatic changes.
... The model has been used to study vegetation patterns along a rainfall gradient, and to shed new light on desertification phenomena and on the concept of aridity. A few other models have recently been introduced [10] [11] [12] [13] [14] [15] [16] [17]. These studies, however, mostly focused on pattern formation phenomena rather than on their ecological implications. ...
Chapter
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A large-scale view of arid regions often shows that the vegetation grows in patterns. These are related to the amount of precipitation as well as to the topography. A model is presented that reproduces the wide range of patterns observed in water-limited regions, from bare soil at very low precipitation to uniform cover at high precipitation, through intermediate states of spot-, stripe-and hole-patterns. The model pre-dicts the coexistence of more than one stable state in a given range of precipitation. The results of the model lead to an understanding of
... These studies propose that a scale-dependent feedback between localized facilitation and large-scale inhibition induces spatial self-organization, and explains the observed spatial structure. In arid systems, for example, infiltration of water is locally enhanced by plant presence, while on landscape scales competition for water between plants is the dominant process explaining observed vegetation patterns (Couteron and Lejeune 2001, Rietkerk et al. 2002). So far, scale-dependent feedback mechanisms have mostly been linked to coherent patterns, such as banded, spotted or labyrinth structures (Rietkerk et al. 2004a). ...
... For example, effects of vegetation on the geomorphic processes of sediment entrainment and deposition create platforms and drainage networks in tidal marshes (Kirwan and Murray, 2007; van Hulzen et al., 2007), and bank stability that constrains braiding and affects fluvial landform in meandering rivers (Corenblit et al., 2009; Smith, 1976). Likewise, vegetation in arid areas can induce pattern formation in response to the local feedbacks between vegetation density and infiltration, and the distal feedbacks between infiltration hotspots and water limitation that generate interpatch impervious areas (HilleRisLambers et al., 2001; Rietkerk et al., 2002). Among the most important attributes of patterned landscapes is the possibility that patterned and unpatterned configurations of the landscape are themselves bistable at some range of environmental condition; that is, both configurations are resilient over some range of global bistability (see Reitkerk et al., 2004a). ...
Article
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Restoration can be viewed as the process of reestablishing both exogenous drivers and internal feedbacks that maintain ecosystems in a desirable state. Correcting exogenous and abiotic drivers is clearly necessary, but may be insufficient to achieve desired outcomes in systems with self-organizing biotic feedbacks that substantially influence ecological stability and timing of responses. Evidence from a broad suite of systems demonstrates the prevalence of biotic control over key ecosystem attributes such as hydroperiod, nutrient gradients, and landform that are most commonly conceived of as exogenously controlled. While a general theory to predict conditions under which biotic controls exert such strong feedbacks is still nascent, it appears clear that the Greater Everglades/South Florida landscape has a high density of such effects. The authors focus on three examples of biotic control over abiotic processes: hydroperiod and discharge controls exerted by peat accretion in the ridge-slough landscape; phosphorus (P) gradients that emerge, at least in part, from interactions between accelerated peat accretion rates, vegetation structure and fauna; and reinforcing feedbacks among land elevation, aquatic respiration, and carbonate dissolution that produce local and landscape basin structure. The authors propose that the unifying theme of biogeomorphic landforms in South Florida is low extant topographic variability, which allows reciprocal biotic modification of local site conditions via mechanisms of peat accretion (including via effects of landscape P redistribution on primary production) or limestone dissolution. Coupling these local positive feedbacks, which drive patch expansion, with inhibitory or negative feedbacks on site suitability at distance, which serve to constrain patch expansion, provide the mechanistic basis for landscape pattern formation. The spatial attributes (range and isotropy) of the distal negative feedback, in particular, control pattern geometry; elucidating the mechanisms and properties of these distal feedbacks is critical to restoration planning.
... The second group of studies investigated the physical mechanisms of pattern formation in vegetation and their response to changes in environmental conditions and disturbance regime. These studies related vegetation patterns to underlying ecohydrological processes, mechanisms of spatial redistribution of resources [e.g., Klausmeier, 1999; Barbier et al., 2008; Ridolfi et al., 2008], the nature of the spatial interactions existing among plant individuals [e.g., Lefever and Lejeune, 1997; Zeng and Zeng, 2007; Barbier et al., 2008], the stability and resilience of dryland ecosystems [Rietkerk et al., 2002; van de Koppel and Rietkerk, 2004], and the landscape's susceptibility to desertification under different climate drivers and management conditions [e.g., von Hardenberg et al., 2001; D'Odorico et al., 2006c]. Because vegetation patterns are observed even when topography and soils do not exhibit any heterogeneity, their formation represents an intriguing case of self-organized biological systems, which results from completely intrinsic vegetation dynamics [Lejeune et al., 1999]. ...
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Highly organized vegetation patterns can be found in a number of landscapes around the world. In recent years, several authors have investigated the processes underlying vegetation pattern formation. Patterns that are induced neither by heterogeneity in soil properties nor by the local topography are generally explained as the result of spatial self-organization resulting from “symmetry-breaking instability” in nonlinear systems. In this case, the spatial dynamics are able to destabilize the homogeneous state of the system, leading to the emergence of stable heterogeneous configurations. Both deterministic and stochastic mechanisms may explain the self-organized vegetation patterns observed in nature. After an extensive analysis of deterministic theories, we review noise-induced mechanisms of pattern formation and provide some examples of applications relevant to the environmental sciences.
... Simple mechanistic spatial models have an important potential for studying the effect of local interactions on emergent spatio-temporal patterns (Rietkerk et al., 2002). Previous treeline models of this type have focused on coniferous species in temperate regions (Malanson, 1997, 2001; Alftine and Malanson, 2004; Wiegand et al., 2006), and the results probably cannot be extrapolated to tropical treelines, or even to many other temperate treelines. ...
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Climate change could cause alpine treelines to shift in altitude or to change their spatial pattern, but little is known about the drivers of treeline dynamics and patterning. The position and patterns of tropical alpine treelines are generally attributed to land use, especially burning. Species interactions, in particular facilitation through shading, may also be important for treeline patterning and dynamics. We studied how fire in alpine vegetation and shade dependence of trees may affect the position and spatial pattern of tropical alpine treelines and their response to climatic warming, using a spatial minimal model of tree growth at treeline. Neighboring trees provided shade and protection from fire. The positive feedback that resulted from these neighbor interactions strongly affected the emergent treelines and always reduced the distance and speed of treeline advance after a temperature increase. Our model demonstrated that next to fire, shade dependence of trees can also lead to abrupt treelines and relatively low treeline positions. This implies that these patterns do not necessarily indicate human disturbance. Strong abruptness of a treeline may indicate that it will respond slowly to climatic changes.
... Neave & Rayburg, 2007). Resulting concentration of runoff and capture of associated nutrients by vegetated patches are one mechanism sustaining the self-organized patchiness of the shrubland state (Ludwig, Wiens & Tongway, 2000; Rietkerk et al., 2002). Given the strong interrelationships among hydrological and geomorphic processes, alterations of subsystem interactions may be a common feature of ecosystems subject to biogeomorphic regime shifts. ...
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1. Feedbacks between vegetation and geomorphic processes can generate alternative stable states and other nonlinear behaviours in ecological systems, but the consequences of these biogeomorphic interactions for other ecosystem processes are poorly understood. In this study, we describe the changes in the hydrological, geomorphic and biogeochemical characteristics of the hyporheic zone of a Sonoran desert stream (Sycamore Creek, Arizona, U.S.A.) in response to a transition from an unvegetated gravel‐bed state to densely vegetated wetlands (ciénegas). 2. A survey of the entire length of Sycamore Creek indicated that ciénegas occupied c. 18% of the stream, and were disproportionately represented in constrained canyons rather than wide, unconstrained valleys. 3. Vegetated patches were characterized by low concentrations of dissolved oxygen (DO) and nitrate and high concentrations of carbon dioxide and methane in the hyporheic zone. In contrast to unvegetated areas, hyporheic DO in ciénegas exhibited no relationship with vertical hydraulic gradients. 4. Increases in hyporheic DO following removal of vegetation by floods supports the hypothesis that these reduced conditions were the result of biogeochemical and geomorphic changes associated with vegetation establishment. In locations where vegetation persisted, hyporheic DO exhibited no response to flooding; in sections where vegetation was removed hyporheic DO closely tracked post‐flood increases in surface stream DO. 5. Shallow sediments in vegetated patches were finer and more organic‐rich than in unvegetated patches, due to increased deposition during floods. Conservative tracer additions indicated that hydrological exchange between the surface stream and hyporheic zone was much lower in ciénegas than in gravel‐bed reaches. 6. Vegetation establishment in desert streams not only alters the physical and chemical characteristics of the hyporheic zone, but also the nature of interactions between surface and hyporheic subsystems.
... Positive feedbacks are self-reinforcing changes, independent of the direction of change and are particularly pronounced in ecosystems where water stress is important for limiting plant growth. For instance, in arid ecosystems, positive feedbacks operate between increased vegetation biomass, rainwater infiltration into the soil and increased lateral root spread, leading to more vegetation biomass and thus alternate stable vegetated and desert states (Rietkerk et al. 2002Rietkerk et al. , 2004a von Hardenberg et al. 2001). While the dynamics of threshold behavior and regime shifts within ecohydrology are only beginning to be investigated , such research may have far-reaching implications for managing and restoring watersheds (Briggs et al. 2005; Contamin and Ellison 2009; Mayer and Rietkerk 2004), especially when threshold responses are influenced by disturbances or extreme climate events to create unexpected surprises (e.g. Gordon et al. 2008; Mulholland et al. 2009). ...
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Aims The field of ecohydrology is providing new theoretical frameworks and methodological approaches for understanding the complex interactions and feedbacks between vegetation and hydrologic flows at multiple scales. Here we review some of the major scientific and technological advances in ecohydrology as related to understanding the mechanisms by which plant–water relations influence water fluxes at ecosystem, watershed and landscape scales. Important Findings We identify several cross-cutting themes related to the role of plant–water relations in the ecohydrological literature, including the contrasting dynamics of water-limited and water-abundant ecosystems, transferring information about water fluxes across scales, understanding spatiotemporal heterogeneity and complexity, ecohydrological triggers associated with threshold behavior and shifts between alternative stable states and the need for long-term data sets at multiple scales. We then show how these themes are embedded within three key research areas where improved understanding of the linkages between plant–water relations and the hydrologic cycle have led to important advances in the field of ecohydrology: upscaling water fluxes from the leaf to the watershed and landscape, effects of plant–soil interactions on soil moisture dynamics and controls exerted by plant water use patterns and mechanisms on streamflow regime. In particular, we highlight several pressing environmental challenges facing society today where ecohydrology can contribute to the scientific knowledge for developing sound management and policy solutions. We conclude by identifying key challenges and opportunities for advancing contributions of plant–water relations research to ecohydrology in the future.
... In particular we do see small islands of tree species developing from initial establishment events (Resler, Butler, and Malanson 2005), the development of linear forms that later coalesce (Bekker 2005), and the eventual envelopment of these patterns by forest. These conclusions might apply to other cases where endogenous processes have been used to explain nonrandom patterns of vegetation (e.g., Watts 1947; Billings 1969; Valentin, d'Herbès, and Poesen 1999; Rietkerk et al. 2002). That a significant linear correlation between landscape pattern and process emerges from dispersed, nonlinear, localized interactions may explain why many seemingly linear relations are found in a complex world with so many nonlinear processes. ...
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Author's personal copy some general conclusions that are in full agreement with everyday observations and general systems knowledge: • Generalists have a better survival chance than others if moved to an environment of greater variety. • Cautious types have a better survival chance than others if moved to a less reliable environment. • Training in more unreliable and/or more diverse environments increases satisfaction of the security and/or freedom of action orientors at the cost of the effectiveness orientor. • Training in an uncertain environment teaches caution and improves fitness in a different environment. • Learning caution (better satisfaction of the security orientor) takes time and decreases effectiveness, but increases overall fitness. • Investment in learning (exergy cost of learning in the animat) pays off in better fitness; the learning investment is (usually) much smaller than the pay-off gain. Animat individuals not only develop behavior that can be interpreted as intelligent, they also develop a complex goal function (balanced attention to basic orientors), or value orientation. Serious attention to basic values (basic orien-tors: existence, effectiveness, freedom, security, adaptability, coexistence) is therefore an objective requirement emerging in, and characterizing self-organizing systems. These basic values are not subjective human inventions; they are objective consequences of the process of self-organization in response to normal environmental properties.
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In the present paper, numerically robust, unconditionally positive and conservative schemes for the discretisation of stiff systems of production–destruction equations are designed. Such model systems do typically arise in geobiochemical modelling where the reproduction of these properties is vital. We suggest modified Patankar-type methods of first- and second-order in time and compare their performance by means of approximating simple linear and non-linear model problems. For the non-linear model problem, a hybrid method combining the classical Runge–Kutta scheme with a modified Patankar-type scheme gives the best numerical approximation. The classical Robertson test problem for chemical reactions which is known for its stiffness is excellently approximated with the modified Patankar-type scheme. The procedure with respect to the derivation and analysis of the modified Patankar-type schemes can be used as a guideline to develop even unconditionally positive, conservative and third-order as well as higher order methods.
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Ecological research on organism-environment interactions has developed asymmetrically. Modulation of organisms by the environment has received much attention, while theoretical studies on the environmental impact of organisms have until recently been limited. We propose a theoretical framework for studying the environmental impacts of woody plants in order to understand their effects on biodiversity. We adopt pattern formation theory to discuss how woody plants organize ecological systems on the patch and landscape levels through patch formation, and how organism patchiness creates resource patchiness that affects biodiversity. We suggest an integrative model that links organisms as landscape modulators through resource distribution and species filtering from larger to smaller spatial scales. Our “biodiversity cycling hypothesis” states that in organism-modulated landscapes, disturbance enables the coexistence of different developmental stages of vegetation patches, thereby increasing biodiversity. This hypothesis emphasizes that species and landscape diversity vary with the development, renewal, maturation, and decay of biotically induced patches.
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In this paper, we investigate which factors determine tree clustering in Southern African savannas. This was tested by measuring clustering of trees using the T-squared sampling method in plots of the Kruger National Park experimental burning programme in South Africa. Fire return interval is the main treatment in these plots, but also several auxiliary determining parameters like clay content in the soil, diameter of tree canopies, understorey composition, tree species diversity and average annual rainfall were measured while sampling. In the Kruger National Park 48 plots distributed over four different landscape types and with three different burning treatments (never, once every 3 y and annually) were sampled. First, we related the clustering of trees to these environmental variables. When looking at the most abundant species in each plot, the analysis revealed that clustering is mainly correlated with clay content in the soil. This analysis also showed that fire frequency had a positive effect on the clustering of tree species that are not very abundant. We suggest that less abundant species might be less resistant to fire and therefore adopt a mechanism of clustering to exclude grass fires under their canopy. Finally, we tested the effect of clustering on the impact of fire on trees by analysing the relationship between the distance of a tree to its nearest neighbour and its canopy diameter. We found that clustering reduces the damaging effect of fire on trees. Our study contributes to understanding of savanna functioning by showing which processes are relevant in the distribution of savanna trees.
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A new model for vegetation patterns is introduced. The model reproduces a wide range of patterns observed in water-limited regions, including drifting bands, spots, and labyrinths. It predicts transitions from bare soil at low precipitation to homogeneous vegetation at high precipitation, through intermediate states of spot, stripe, and hole patterns. It also predicts wide precipitation ranges where different stable states coexist. Using these predictions we propose a novel explanation of desertification phenomena and a new approach to classifying aridity.
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