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Waves of desertification in a competitive ecosystem

Author

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  • Daza C., Y.C.
  • Laguna, M.F.
  • Monjeau, J.A.
  • Abramson, G.

Abstract

We study a mathematical model inspired by a common scenario in northern Patagonia consisting of humans and their livestock living together with native wildlife. The main production system in this area is sheep farming, which due to wrong historical management has led to desertification of the habitat, with impact on both native wildlife and livestock. Particularly the largest native herbivore, the guanaco, has reflected in their numbers this alteration induced in the environment. We analyze a mathematical model that captures the main characteristics of the interaction between sheep and guanaco: the hierarchical competition and the advantage granted by humans to the herds, and also incorporates a dynamic for the habitat. Using the metapopulation formalism, the trophic web of two herbivores is extended over a patchy landscape that considers two characteristic times for the dynamics of the resource. Our study stresses the dependence of the metapopulations dynamics on the recovery time of the resource. These results are backed up by a deterministic mean field model which shares some similarities with the stochastic and spatially extended one. We find different regimes depending on the parameters considered: coexistence of both species, survival of a single species and extinction of the other, and extinction of both. Remarkably, in some regions of parameters space we detect the presence of periodical spatio-temporal patterns, with persistent oscillations of constant amplitude. Based on these results, we perform a characterization of the observed scenarios in order to gain insight about the system.

Suggested Citation

  • Daza C., Y.C. & Laguna, M.F. & Monjeau, J.A. & Abramson, G., 2019. "Waves of desertification in a competitive ecosystem," Ecological Modelling, Elsevier, vol. 396(C), pages 42-49.
    • Handle: RePEc:eee:ecomod:v:396:y:2019:i:c:p:42-49
    DOI: 10.1016/j.ecolmodel.2019.01.018
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    References listed on IDEAS

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    1. Laguna, M.F. & Abramson, G. & Kuperman, M.N. & Lanata, J.L. & Monjeau, J.A., 2015. "Mathematical model of livestock and wildlife: Predation and competition under environmental disturbances," Ecological Modelling, Elsevier, vol. 309, pages 110-117.
    2. Ilkka Hanski & Torsti Schulz & Swee Chong Wong & Virpi Ahola & Annukka Ruokolainen & Sami P. Ojanen, 2017. "Ecological and genetic basis of metapopulation persistence of the Glanville fritillary butterfly in fragmented landscapes," Nature Communications, Nature, vol. 8(1), pages 1-11, April.
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    Cited by:

    1. Rares Halbac-Cotoara-Zamfir & Andrea Colantoni & Enrico Maria Mosconi & Stefano Poponi & Simona Fortunati & Luca Salvati & Filippo Gambella, 2020. "From Historical Narratives to Circular Economy: De-Complexifying the “Desertification” Debate," IJERPH, MDPI, vol. 17(15), pages 1-18, July.
    2. Rares Halbac-Cotoara-Zamfir & Daniela Smiraglia & Giovanni Quaranta & Rosanna Salvia & Luca Salvati & Antonio Giménez-Morera, 2020. "Land Degradation and Mitigation Policies in the Mediterranean Region: A Brief Commentary," Sustainability, MDPI, vol. 12(20), pages 1-17, October.
    3. Gianluca Egidi & Luca Salvati & Pavel Cudlin & Rosanna Salvia & Manuela Romagnoli, 2020. "A New ‘Lexicon’ of Land Degradation: Toward a Holistic Thinking for Complex Socioeconomic Issues," Sustainability, MDPI, vol. 12(10), pages 1-19, May.
    4. Jinmeng Lee & Xiaojun Yin & Honghui Zhu & Xin Zheng, 2023. "Geographical Detector-Based Research of Spatiotemporal Evolution and Driving Factors of Oasification and Desertification in Manas River Basin, China," Land, MDPI, vol. 12(8), pages 1-20, July.

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