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Pattern-formation approach to modelling spatially extended ecosystems

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  • Meron, Ehud

Abstract

Self-organization processes leading to pattern formation phenomena are ubiquitous in nature. Intensive theoretical and experimental research efforts during the past few decades have resulted in a mathematical theory of pattern formation whose predictions are well confirmed by controlled laboratory experiments. There is an increasing observational evidence that pattern formation plays a significant role in shaping dryland landscapes. Supporting these observations are studies of continuum vegetation models that have reproduced many of the observed patterns. Such continuum models consist of partial differential equations and lend themselves to the powerful methods of pattern formation theory. Indeed, vegetation pattern formation has been identified with mathematical instabilities of uniform vegetation states, occurring at threshold degrees of aridity. This paper describes applications of this modelling approach to problems in landscape, community, ecosystem and restoration ecology, highlighting new open questions and research directions that are motivated by pattern formation theory. Three added values of this approach are emphasized: (i) the approach reveals universal nonlinear elements for which a great deal of knowledge is already available, (ii) it captures important aspects of ecosystem complexity, and (iii) it provides an integrative framework for studying problems in spatial ecology.

Suggested Citation

  • Meron, Ehud, 2012. "Pattern-formation approach to modelling spatially extended ecosystems," Ecological Modelling, Elsevier, vol. 234(C), pages 70-82.
    • Handle: RePEc:eee:ecomod:v:234:y:2012:i:c:p:70-82
    DOI: 10.1016/j.ecolmodel.2011.05.035
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    1. Todd M. Scanlon & Kelly K. Caylor & Simon A. Levin & Ignacio Rodriguez-Iturbe, 2007. "Positive feedbacks promote power-law clustering of Kalahari vegetation," Nature, Nature, vol. 449(7159), pages 209-212, September.
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    3. Sonia Kéfi & Max Rietkerk & Concepción L. Alados & Yolanda Pueyo & Vasilios P. Papanastasis & Ahmed ElAich & Peter C. de Ruiter, 2007. "Spatial vegetation patterns and imminent desertification in Mediterranean arid ecosystems," Nature, Nature, vol. 449(7159), pages 213-217, September.
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    Cited by:

    1. Li, Jing & Sun, Gui-Quan & Li, Li & Jin, Zhen & Yuan, Yuan, 2023. "The effect of grazing intensity on pattern dynamics of the vegetation system," Chaos, Solitons & Fractals, Elsevier, vol. 175(P2).
    2. King, Elizabeth G. & Franz, Trenton E., 2016. "Combining ecohydrologic and transition probability-based modeling to simulate vegetation dynamics in a semi-arid rangeland," Ecological Modelling, Elsevier, vol. 329(C), pages 41-63.
    3. Franco, Rebeca & Morales, Marco A. & Rodríguez-Mora, J.Isrrael & Agustín-Serrano, Ricardo, 2024. "A new reaction-diffusion-advection model with long-range inhibition for vegetation-desertification pattern-formation as a unified approach," Ecological Modelling, Elsevier, vol. 492(C).
    4. Martinez-Garcia, Ricardo & Cabal, Ciro & Calabrese, Justin M. & Hernández-García, Emilio & Tarnita, Corina E. & López, Cristóbal & Bonachela, Juan A., 2023. "Integrating theory and experiments to link local mechanisms and ecosystem-level consequences of vegetation patterns in drylands," Chaos, Solitons & Fractals, Elsevier, vol. 166(C).
    5. Oborny, B. & Mony, C. & Herben, T., 2012. "From virtual plants to real communities: A review of modelling clonal growth," Ecological Modelling, Elsevier, vol. 234(C), pages 3-19.
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    7. Ding, Zhen-Wei & Zhang, Ji-Qiang & Zheng, Guo-Zhong & Cai, Wei-Ran & Cai, Chao-Ran & Chen, Li & Wang, Xu-Ming, 2024. "Emergence of anti-coordinated patterns in snowdrift game by reinforcement learning," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    8. Liang, Juan & Liu, Chen & Sun, Gui-Quan & Li, Li & Zhang, Lai & Hou, Meiting & Wang, Hao & Wang, Zhen, 2022. "Nonlocal interactions between vegetation induce spatial patterning," Applied Mathematics and Computation, Elsevier, vol. 428(C).
    9. El-Nabulsi, Rami Ahmad, 2024. "Transition from circular to spiral waves and from Mexican hat to upside-down Mexican hat-solutions: The cases of local and nonlocal λ−ω reaction-diffusion-convection fractal systems with variable coef," Chaos, Solitons & Fractals, Elsevier, vol. 189(P2).

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