Periodic versus scale-free patterns in dryland vegetation

Hardenberg, Jost von; Kletter, Assaf Y.; Yizhaq, Hezi; Nathan, Jonathan; Meron, Ehud

doi:10.1098/rspb.2009.2208

Cited by 96 publications

(94 citation statements)

References 28 publications

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“…Patterns with no characteristic scales [37,36] are obtainable in the model under conditions of global competition. Such conditions can be realized when the time scale associated with water transport is much shorter than the time scales associated with water exploitation or absorption [38].…”

Section: Resultsmentioning

confidence: 99%

“…One realization of this limit is fast surface-water flow (large D H ) relative to the infiltration into vegetated soil (small A). Under this condition surface water can flow over long distances before infiltrating significantly into the soil, allowing for large vegetation patches whose size scales like √ D H P /A [38]. This limit may not be attainable in practice but may be approached to the extent that it yields wide patch size distributions as observed in field studies [36,37].…”

Section: Plane Topographymentioning

confidence: 99%

“…This limit may not be attainable in practice but may be approached to the extent that it yields wide patch size distributions as observed in field studies [36,37]. For more details about this limit and various realizations thereof the reader is referred to von Hardenberg et al [38].…”

Section: Plane Topographymentioning

confidence: 99%

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Modeling Dryland Landscapes

Meron

2010

Math. Model. Nat. Phenom.

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Abstract. The discovery of nearly periodic vegetation patterns in arid and semi-arid regions motivated numerous model studies in the past decade. Most studies have focused on vegetation pattern formation, and on the response of vegetation patterns to gradients of the limiting water resource. The reciprocal question, what resource modifications are induced by vegetation pattern formation, which is essential to the understanding of dryland landscapes, has hardly been addressed. This paper is a synthetic review of model studies that address this question and the consequent implications for inter-specific plant interactions and species diversity. It focuses both on patch and landscape scales, highlighting bottom-up processes, where plant interactions at the patch scale give rise to spatial patterns at the landscape scale, and top-down processes, where pattern transitions at the landscape scale affect inter-specific interactions at the patch scale.

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Section: Resultsmentioning

confidence: 99%

Section: Plane Topographymentioning

confidence: 99%

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Modeling Dryland Landscapes

Meron

2010

Math. Model. Nat. Phenom.

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“…Intermediate cases such as power-law (scale-free) clustering [14][15][16], and dendritic structures in which vegetation concentrates along drainage lines [17,18] are also observed. All of these morphologies can be related to the presence, strength and directionality of positive feedbacks that concentrate resources (such as nutrients, soil carbon and water) that sustain plant life in a localized region near the plants [19][20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Local properties of patterned vegetation: quantifying endogenous and exogenous effects

Penny

Daniels

Thompson

2013

Phil. Trans. R. Soc. A.

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Dryland ecosystems commonly exhibit periodic bands of vegetation, thought to form due to competition between individual plants for heterogeneously distributed water. In this paper, we develop a Fourier method for locally identifying the pattern wavenumber and orientation, and apply it to aerial images from a region of vegetation patterning near Fort Stockton, TX, USA. We find that the local pattern wavelength and orientation are typically coherent, but exhibit both rapid and gradual variation driven by changes in hillslope gradient and orientation, the potential for water accumulation, or soil type. Endogenous pattern dynamics, when simulated for spatially homogeneous topographic and vegetation conditions, predict pattern properties that are much less variable than the orientation and wavelength observed in natural systems. Our local pattern analysis, combined with ancillary datasets describing soil and topographic variation, highlights a largely unexplored correlation between soil depth, pattern coherence, vegetation cover and pattern wavelength. It also, surprisingly, suggests that downslope accumulation of water may play a role in changing vegetation pattern properties.

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“…Mathematical models play a key role in understanding arid ecosystems, and a wide variety of models have been proposed over the last two decades, ranging from detailed multiscale representations of soil-water dynamics (13) to simple models of key underlying mechanisms (14)(15)(16)(17)(18). I will investigate the extent to which qualitative trends in wavelength apply irrespective of parameter values.…”

Section: Mathematical Modeling Of Semiarid Vegetationmentioning

confidence: 99%

Using wavelength and slope to infer the historical origin of semiarid vegetation bands

Sherratt

2015

Proc. Natl. Acad. Sci. U.S.A.

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Landscape-scale patterns of vegetation occur worldwide at interfaces between semiarid and arid climates. They are important as potential indicators of climate change and imminent regime shifts and are widely thought to arise from positive feedback between vegetation and infiltration of rainwater. On gentle slopes the typical pattern form is bands (stripes), oriented parallel to the contours, and their wavelength is probably the most accessible statistic for vegetation patterns. Recent field studies have found an inverse correlation between pattern wavelength and slope, in apparent contradiction with the predictions of mathematical models. Here I show that this “contradiction” is based on a flawed approach to calculating the wavelength in models. When pattern generation is considered in detail, the theory is fully consistent with empirical results. For realistic parameters, degradation of uniform vegetation generates patterns whose wavelength increases with slope, whereas colonization of bare ground gives the opposite trend. Therefore, the empirical finding of an inverse relationship can be used, in conjunction with climate records, to infer the historical origin of the patterns. Specifically, for the African Sahel my results suggest that banded vegetation originated by the colonization of bare ground during circa 1760–1790 or since circa 1850.

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Periodic versus scale-free patterns in dryland vegetation

Cited by 96 publications

References 28 publications

Modeling Dryland Landscapes

Modeling Dryland Landscapes

Local properties of patterned vegetation: quantifying endogenous and exogenous effects

Using wavelength and slope to infer the historical origin of semiarid vegetation bands

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