A mathematical model of plants as ecosystem engineers

Gilad, Erez; Hardenberg, Jost von; Provenzale, A.; Shachak, Moshe; Meron, Ehud

doi:10.1016/j.jtbi.2006.08.006

Cited by 214 publications

(245 citation statements)

References 38 publications

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“…A similar transition can be induced without a strong disturbance by a precipitation down shift to the monostability range of the spot pattern [30]. From [15].…”

Section: Ecosystem Engineering and Spatial Patterningmentioning

confidence: 72%

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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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“…A similar transition can be induced without a strong disturbance by a precipitation down shift to the monostability range of the spot pattern [30]. From [15].…”

Section: Ecosystem Engineering and Spatial Patterningmentioning

confidence: 72%

“…2. The linear stability analysis leading to this diagram is described in [15]. The parameters used describe woody vegetation.…”

Section: Plane Topographymentioning

confidence: 99%

Modeling Dryland Landscapes

Meron

2010

Math. Model. Nat. Phenom.

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“…A central concept in the understanding of desertification is the bistability between vegetated states and desert (15,16,55). As rainfall is decreased, a loss in stability of a vegetated state causes a sudden transition to desert, but if rainfall is subsequently increased back above the tipping point the desert state remains, and reestablishment of vegetation requires much wetter conditions (3,56,57).…”

Section: Discussionmentioning

confidence: 99%

“…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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“…Here, X ¼ ðX; Y Þ are the spatial coordinates, T is time and r 2 ¼ @ X 2 þ @ Y 2 is the Laplacian operator. We refer the reader to Gilad et al (2004Gilad et al ( , 2007a for a detailed presentation of the model. Here, we focus on the quantities and terms that are most relevant to the present study.…”

Section: The Modelmentioning

confidence: 99%

Periodic versus scale-free patterns in dryland vegetation

et al. 2010

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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.

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A mathematical model of plants as ecosystem engineers

Cited by 214 publications

References 38 publications

Modeling Dryland Landscapes

Modeling Dryland Landscapes

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

Periodic versus scale-free patterns in dryland vegetation

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