IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v428y2022ics0096300322001473.html

Nonlocal interactions between vegetation induce spatial patterning

Author

Listed:
  • Liang, Juan
  • Liu, Chen
  • Sun, Gui-Quan
  • Li, Li
  • Zhang, Lai
  • Hou, Meiting
  • Wang, Hao
  • Wang, Zhen

Abstract

Vegetation pattern provides useful signals for vegetation protection and can be identified as an early warning of desertification. In some arid or semi-arid regions, vegetation absorbs water through nonlocal interaction of roots. In this study, we present a vegetation model with nonlocal interaction which is characterized by an integral term with a kernel function. Mathematical analysis provides the conditions for the generation of stationary pattern. Numerical simulations exhibit different spatial distributions of vegetation. Densities of vegetation and water show an inverse relationship at same spatial locations due to water transport mechanism. The results reveal that the interaction intensity and the shape of the kernel function can cause the transition of vegetation pattern. Specifically, the vegetation biomass increases as the interaction intensity decreases or as the nonlocal interaction distance increases. We demonstrate that the nonlocal interactions between roots of vegetation is a key mechanism for the formation of vegetation pattern, which provides a theoretical basis for the preservation and restoration of vegetation.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:apmaco:v:428:y:2022:i:c:s0096300322001473
    DOI: 10.1016/j.amc.2022.127061
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300322001473
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2022.127061?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Cisternas, Jaime & Escaff, Daniel & Clerc, Marcel G. & Lefever, René & Tlidi, Mustapha, 2020. "Gapped vegetation patterns: Crown/root allometry and snaking bifurcation," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    2. Mark Pagani & Ken Caldeira & Robert Berner & David J. Beerling, 2009. "The role of terrestrial plants in limiting atmospheric CO2 decline over the past 24 million years," Nature, Nature, vol. 460(7251), pages 85-88, July.
    3. Kefi, Sonia & Rietkerk, Max & Katul, Gabriel G., 2008. "Vegetation pattern shift as a result of rising atmospheric CO2 in arid ecosystems," Theoretical Population Biology, Elsevier, vol. 74(4), pages 332-344.
    4. 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.
    5. Consolo, Giancarlo & Valenti, Giovanna, 2019. "Secondary seed dispersal in the Klausmeier model of vegetation for sloped semi-arid environments," Ecological Modelling, Elsevier, vol. 402(C), pages 66-75.
    6. Shushi Peng & Shilong Piao & Philippe Ciais & Ranga B. Myneni & Anping Chen & Frédéric Chevallier & Albertus J. Dolman & Ivan A. Janssens & Josep Peñuelas & Gengxin Zhang & Sara Vicca & Shiqiang Wan &, 2013. "Asymmetric effects of daytime and night-time warming on Northern Hemisphere vegetation," Nature, Nature, vol. 501(7465), pages 88-92, September.
    7. Pessa, Arthur A.B. & Zola, Rafael S. & Perc, Matjaž & Ribeiro, Haroldo V., 2022. "Determining liquid crystal properties with ordinal networks and machine learning," Chaos, Solitons & Fractals, Elsevier, vol. 154(C).
    8. Corina E. Tarnita & Juan A. Bonachela & Efrat Sheffer & Jennifer A. Guyton & Tyler C. Coverdale & Ryan A. Long & Robert M. Pringle, 2017. "A theoretical foundation for multi-scale regular vegetation patterns," Nature, Nature, vol. 541(7637), pages 398-401, January.
    9. Meron, Ehud, 2012. "Pattern-formation approach to modelling spatially extended ecosystems," Ecological Modelling, Elsevier, vol. 234(C), pages 70-82.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Guo, Gaihui & Qin, Qijing & Cao, Hui & Jia, Yunfeng & Pang, Danfeng, 2024. "Pattern formation of a spatial vegetation system with cross-diffusion and nonlocal delay," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    2. Liu, Chen & Pang, Yi-Zhi & Xue, Qiang & Li, Li & Luo, Xiaofeng, 2025. "Exploring the regime shifts of dryland vegetation under climate change: A case study of the Altay, Xinjiang," Chaos, Solitons & Fractals, Elsevier, vol. 191(C).
    3. Shi, Yu & Luo, Xiao-Feng & Zhang, Yong-Xin & Sun, Gui-Quan, 2023. "An indicator of Crohn’s disease severity based on Turing patterns," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    4. Jiaming Guo & Xiaofeng Luo & Juan Zhang & Mingtao Li, 2022. "A Mathematical Model for Ovine Brucellosis during Dynamic Transportation of Sheep, and Its Applications in Jalaid Banner and Ulanhot City," Mathematics, MDPI, vol. 10(19), pages 1-26, September.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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).
    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. Liu, Chen & Pang, Yi-Zhi & Xue, Qiang & Li, Li & Luo, Xiaofeng, 2025. "Exploring the regime shifts of dryland vegetation under climate change: A case study of the Altay, Xinjiang," Chaos, Solitons & Fractals, Elsevier, vol. 191(C).
    4. Chen, Zheng & Liu, Jieyu & Li, Li & Wu, Yongping & Feng, Guolin & Qian, Zhonghua & Sun, Gui-Quan, 2022. "Effects of climate change on vegetation patterns in Hulun Buir Grassland," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 597(C).
    5. 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).
    6. 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).
    7. Ferreira, A.S. & Raposo, E.P. & Viswanathan, G.M. & da Luz, M.G.E., 2012. "The influence of the environment on Lévy random search efficiency: Fractality and memory effects," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(11), pages 3234-3246.
    8. Yang, Junxiang & Kim, Junseok, 2023. "Computer simulation of the nonhomogeneous zebra pattern formation using a mathematical model with space-dependent parameters," Chaos, Solitons & Fractals, Elsevier, vol. 169(C).
    9. Hezi Yizhaq & Constantin Rein & Lior Saban & Noa Cohen & Klaus Kroy & Itzhak Katra, 2024. "Aeolian Sand Sorting and Soil Moisture in Arid Namibian Fairy Circles," Land, MDPI, vol. 13(2), pages 1-14, February.
    10. Han, Bingtao & Jiang, Daqing, 2023. "Coexistence and extinction for a stochastic vegetation-water model motivated by Black–Karasinski process," Chaos, Solitons & Fractals, Elsevier, vol. 175(P2).
    11. Fei Zhang & Mathieu Dellinger & Robert G. Hilton & Jimin Yu & Mark B. Allen & Alexander L. Densmore & Hui Sun & Zhangdong Jin, 2022. "Hydrological control of river and seawater lithium isotopes," Nature Communications, Nature, vol. 13(1), pages 1-10, December.
    12. Piva, G.G. & Anteneodo, C., 2025. "Influence of density-dependent diffusion on pattern formation in a refuge," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 658(C).
    13. Marina E Wosniack & Marcos C Santos & Ernesto P Raposo & Gandhi M Viswanathan & Marcos G E da Luz, 2017. "The evolutionary origins of Lévy walk foraging," PLOS Computational Biology, Public Library of Science, vol. 13(10), pages 1-31, October.
    14. Tobias Brett & Marco Ajelli & Quan-Hui Liu & Mary G Krauland & John J Grefenstette & Willem G van Panhuis & Alessandro Vespignani & John M Drake & Pejman Rohani, 2020. "Detecting critical slowing down in high-dimensional epidemiological systems," PLOS Computational Biology, Public Library of Science, vol. 16(3), pages 1-19, March.
    15. Consolo, Giancarlo & Grifó, Gabriele & Valenti, Giovanna, 2022. "Dryland vegetation pattern dynamics driven by inertial effects and secondary seed dispersal," Ecological Modelling, Elsevier, vol. 474(C).
    16. van den Berg, J. & Björnberg, J.E. & Heydenreich, M., 2015. "Sharpness versus robustness of the percolation transition in 2d contact processes," Stochastic Processes and their Applications, Elsevier, vol. 125(2), pages 513-537.
    17. Min Cheng & Ying Liang & Canying Zeng & Yi Pan & Jinxia Zhu & Jingyi Wang, 2023. "Economic Growth Does Not Mitigate Its Decoupling Relationship with Urban Greenness in China," Land, MDPI, vol. 12(3), pages 1-14, March.
    18. van de Koppel, Johan & Gupta, Rohit & Vuik, Cornelis, 2011. "Scaling-up spatially-explicit ecological models using graphics processors," Ecological Modelling, Elsevier, vol. 222(17), pages 3011-3019.
    19. Li, Feiran & Yang, Ruizhi & Liu, Liqin, 2025. "Synergistic effects of feedback regulation and vegetation internal competition on vegetation patterns in semi-arid environments," Chaos, Solitons & Fractals, Elsevier, vol. 199(P3).
    20. Salvati, Luca & Carlucci, Margherita, 2015. "Towards sustainability in agro-forest systems? Grazing intensity, soil degradation and the socioeconomic profile of rural communities in Italy," Ecological Economics, Elsevier, vol. 112(C), pages 1-13.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:apmaco:v:428:y:2022:i:c:s0096300322001473. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.