Nonlinear Physics of Ecosystems

Meron, Ehud

doi:10.1201/b18360

Cited by 166 publications

(183 citation statements)

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“…This supports the prevailing view of the necessity of improved environmental conditions for the reverse transition (e.g., [5]). The lowest precipitation value leading to pattern formation and the lowest precipitation value preserving existing patterns differ by a factor of 0.7 and are thus in accordance with the factor provided by Sherratt and Lord [51].…”

Section: Influence Of Variable Precipitationsupporting

confidence: 74%

“…It has been reported that periodic patterns at the border between semi-arid and arid climates are even omnipresent [4]. The diversity in patterns makes pattern formation in arid and semi-arid areas an interesting case study for pattern formation in ecology [5]. Furthermore, semi-arid regions are highly dynamic (e.g., [6]), which makes them an intriguing research area in general.…”

Section: Introductionmentioning

confidence: 99%

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Impact of Parameter Variability and Environmental Noise on the Klausmeier Model of Vegetation Pattern Formation

Köhnke

Malchow

2017

Mathematics

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Semi-arid ecosystems made up of patterned vegetation, for instance, are thought to be highly sensitive. This highlights the importance of understanding the dynamics of the formation of vegetation patterns. The most renowned mathematical model describing such pattern formation consists of two partial differential equations and is often referred to as the Klausmeier model. This paper provides analytical and numerical investigations regarding the influence of different parameters, including the so-far not contemplated evaporation, on the long-term model results. Another focus is set on the influence of different initial conditions and on environmental noise, which has been added to the model. It is shown that patterning is beneficial for semi-arid ecosystems, that is, vegetation is present for a broader parameter range. Both parameter variability and environmental noise have only minor impacts on the model results. Increasing mortality has a high, nonlinear impact underlining the importance of further studies in order to gain a sufficient understanding allowing for suitable management strategies of this natural phenomenon.

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Section: Influence Of Variable Precipitationsupporting

confidence: 74%

Section: Introductionmentioning

confidence: 99%

Impact of Parameter Variability and Environmental Noise on the Klausmeier Model of Vegetation Pattern Formation

Köhnke

Malchow

2017

Mathematics

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“…The patterns may emerge on completely flat and homogeneous substrate and are induced by positive feedbacks between local vegetation growth and water transport toward the growth location. The depletion of water in the vicinity of the growing vegetation inhibits the growth there and promotes the development of large-scale patterns with a typical periodicity (5,(7)(8)(9). Spatial self-organization by scale-dependent pattern-forming feedbacks of this kind is a population-level response to water stress that complements phenotype changes at the organism level (10).…”

mentioning

confidence: 99%

“…According to pattern-formation theory, the large-scale order that emerges from a uniform state obeys a universal pattern whose particular form is dictated by the instability that the uniform state undergoes (8,22). The fairy-circle gap pattern observed in Namibia (15) is likely an example of a universal hexagonal pattern that, according to pattern-formation theory, is induced by a nonuniform stationary instability (3,(21)(22)(23)(24).…”

mentioning

confidence: 99%

Discovery of fairy circles in Australia supports self-organization theory

Getzin

Yizhaq

Bell

et al. 2016

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

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Vegetation gap patterns in arid grasslands, such as the "fairy circles" of Namibia, are one of nature's greatest mysteries and subject to a lively debate on their origin. They are characterized by small-scale hexagonal ordering of circular bare-soil gaps that persists uniformly in the landscape scale to form a homogeneous distribution. Pattern-formation theory predicts that such highly ordered gap patterns should be found also in other water-limited systems across the globe, even if the mechanisms of their formation are different. Here we report that so far unknown fairy circles with the same spatial structure exist 10,000 km away from Namibia in the remote outback of Australia. Combining fieldwork, remote sensing, spatial pattern analysis, and process-based mathematical modeling, we demonstrate that these patterns emerge by self-organization, with no correlation with termite activity; the driving mechanism is a positive biomasswater feedback associated with water runoff and biomass-dependent infiltration rates. The remarkable match between the patterns of Australian and Namibian fairy circles and model results indicate that both patterns emerge from a nonuniform stationary instability, supporting a central universality principle of pattern-formation theory. Applied to the context of dryland vegetation, this principle predicts that different systems that go through the same instability type will show similar vegetation patterns even if the feedback mechanisms and resulting soil-water distributions are different, as we indeed found by comparing the Australian and the Namibian fairy-circle ecosystems. These results suggest that biomass-water feedbacks and resultant vegetation gap patterns are likely more common in remote drylands than is currently known.drylands | spatial pattern | Triodia grass | Turing instability | vegetation gap P attern-formation theory (1) and the influence of Alan Turing's work on understanding biological morphogenesis (2) are increasingly recognized in environmental sciences (3). Vegetation patterns resulting from self-organization occur frequently in waterlimited ecosystems and, similar to Turing patterns, show pattern morphologies that change from gaps to stripes (labyrinths) to spots with decreasing plant-available moisture (4-6). The patterns may emerge on completely flat and homogeneous substrate and are induced by positive feedbacks between local vegetation growth and water transport toward the growth location.

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“…To the unfamiliar, it may be difficult to realize that plant populations can organize themselves into geometric order so as to optimize their access to scarce soil water (4)(5)(6). Based on the preliminary data obtained by excavating two gaps from the fairy circle (FC) area near Newman, Walsh et al (7) claim that subterranean termitaria are the sole cause of the Australian FCs (8).…”

mentioning

confidence: 99%