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Spatial vegetation patterns and imminent desertification in Mediterranean arid ecosystems


Humans and climate affect ecosystems and their services1, which may involve continuous and discontinuous transitions from one stable state to another2. Discontinuous transitions are abrupt, irreversible and among the most catastrophic changes of ecosystems identified1. For terrestrial ecosystems, it has been hypothesized that vegetation patchiness could be used as a signature of imminent transitions3,4. Here, we analyse how vegetation patchiness changes in arid ecosystems with different grazing pressures, using both field data and a modelling approach. In the modelling approach, we extrapolated our analysis to even higher grazing pressures to investigate the vegetation patchiness when desertification is imminent. In three arid Mediterranean ecosystems in Spain, Greece and Morocco, we found that the patch-size distribution of the vegetation follows a power law. Using a stochastic cellular automaton model, we show that local positive interactions among plants can explain such power-law distributions. Furthermore, with increasing grazing pressure, the field data revealed consistent deviations from power laws. Increased grazing pressure leads to similar deviations in the model. When grazing was further increased in the model, we found that these deviations always and only occurred close to transition to desert, independent of the type of transition, and regardless of the vegetation cover. Therefore, we propose that patch-size distributions may be a warning signal for the onset of desertification.

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Figure 1: Effect of grazing on the patch-size distribution of vegetation in three Mediterranean ecosystems.
Figure 2: Effect of local positive interactions and grazing pressure on the patch-size distribution in the model.
Figure 3: Localization of the deviation to a power law along transitions in the model.

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  1. Millennium Ecosystem Assessment. Ecosystems and Human Well-Being: Desertification Synthesis (World Resources Institute, Washington DC, 2005)

  2. Scheffer, M., Carpenter, S., Foley, J. A., Folke, C. & Walker, B. Catastrophic shifts in ecosystems. Nature 413, 591–596 (2001)

    Article  ADS  CAS  Google Scholar 

  3. Kéfi, S., Rietkerk, M., van Baalen, M. & Loreau, M. Local facilitation, bistability and transitions in arid ecosystems. Theor. Popul. Biol. 71, 367–379 (2007)

    Article  Google Scholar 

  4. Rietkerk, M., Dekker, S. C., de Ruiter, P. C. & van de Koppel, J. Self-organized patchiness and catastrophic shifts in ecosystems. Science 305, 1926–1929 (2004)

    Article  ADS  CAS  Google Scholar 

  5. Reynolds, J. F. et al. Global desertification: Building a science for dryland development. Science 316, 847–851 (2007)

    Article  ADS  CAS  Google Scholar 

  6. Aguiar, M. R. & Sala, O. E. Patch structure, dynamics and implications for the functioning of arid ecosystems. Trends Ecol. Evol. 14, 273–277 (1999)

    Article  CAS  Google Scholar 

  7. Alados, C. L. et al. Association between competition and facilitation processes and vegetation spatial patterns in alpha steppes. Biol. J. Linn. Soc. 87, 103–113 (2006)

    Article  Google Scholar 

  8. Callaway, R. M. & Walker, L. R. Competition and facilitation: a synthetic approach to interactions in plant communities. Ecology 78, 1958–1965 (1997)

    Article  Google Scholar 

  9. Schlesinger, W. H. et al. Biological feedbacks in global desertification. Science 247, 1043–1048 (1990)

    Article  ADS  CAS  Google Scholar 

  10. Pugnaire, F. I., Haase, P. & Puigdefabregas, J. Facilitation between higher plant species in a semiarid environment. Ecology 77, 1420–1426 (1996)

    Article  Google Scholar 

  11. Jordano, P., Bascompte, J. & Olesen, J. M. Invariant properties in coevolutionary networks of plant–animal interactions. Ecol. Lett. 6, 69–81 (2003)

    Article  Google Scholar 

  12. Solé, R. V. & Bascompte, J. in Self-organization in Complex Ecosystems Ch. 6 215–262 (Princeton Univ. Press, Princeton, 2006)

    Book  Google Scholar 

  13. Iwasa, Y. in The Geometry of Ecological Interactions. Simplify Ecological Complexity (eds Dieckmann, U., Law, R. & Metz, J. A. J.) 227–251 (Cambridge Univ. Press, Cambridge, 2000)

    Book  Google Scholar 

  14. Noy-Meir, I. Stability of grazing systems: an application of predator–prey graphs. J. Ecol. 63, 459–481 (1975)

    Article  Google Scholar 

  15. Brown, J. H. et al. The fractal nature of nature: power laws, ecological complexity and biodiversity. Phil. Trans. R. Soc. Lond. B 357, 619–626 (2002)

    Article  Google Scholar 

  16. Guichard, F., Halpin, P. M., Allison, G. W., Lubchenco, J. & Menge, B. A. Mussel disturbance dynamics: signatures of oceanographic forcing from local interactions. Am. Nat. 161, 889–904 (2003)

    Article  Google Scholar 

  17. Malamud, B. D., Morein, G. & Turcotte, D. L. Forest fires: an example of self-organized critical behavior. Science 281, 1840–1842 (1998)

    Article  ADS  CAS  Google Scholar 

  18. Vandermeer, J. & Perfecto, I. A keystone mutualism drives pattern in a power function. Science 311, 1000–1002 (2006)

    Article  ADS  CAS  Google Scholar 

  19. Venegas, J. G. et al. Self-organized patchiness in asthma as a prelude to catastrophic shifts. Nature 434, 777–782 (2005)

    Article  ADS  CAS  Google Scholar 

  20. Bak, P., Tang, C. & Wiesenfeld, K. Self-organized criticality. Phys. Rev. A. 38, 364–374 (1988)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  21. Sornette, D. Critical Phenomena in Natural Sciences: Chaos, Fractals, Selforganization and Disorder: Concepts and Tools (Springer, Berlin/Heidelberg, 2004)

    MATH  Google Scholar 

  22. Pascual, M. & Guichard, F. Criticality and disturbance in spatial ecological systems. Trends Ecol. Evol. 20, 88–95 (2005)

    Article  Google Scholar 

  23. Schröter, D. et al. Ecosystem service supply and vulnerability to global change in Europe. Science 310, 1333–1337 (2005)

    Article  ADS  Google Scholar 

  24. Schabenberger, O. & Pierce, F. J. Contemporary Statistical Models for the Plant and Soil Sciences Ch. 1 1–34 (CRC Press, Boca Raton, 2002)

    MATH  Google Scholar 

  25. Ingerson, T. E. & Buvel, R. L. Structure in asynchronous cellular automata. Physica D 10, 59–68 (1984)

    Article  ADS  MathSciNet  Google Scholar 

  26. Matsuda, H., Ogita, N., Sasaki, A. & Sato, K. Statistical mechanics of population—the lattice Lotka–Volterra model. Prog. Theor. Phys. 88, 1035–1049 (1992)

    Article  ADS  Google Scholar 

  27. Kutznetsov, Y. A. & Levitin, V. V. CONTENT: a Multiplatform Environment for Continuation and Bifurcation Analysis of Dynamical Systems (Centrum voor Wiskunde en Informatica, Amsterdam, 1997)

    Google Scholar 

  28. Alados, C. L. et al. Change in plant spatial patterns and diversity along the successional gradient of Mediterranean grazing ecosystems. Ecol. Modell. 180, 523–535 (2004)

    Article  Google Scholar 

  29. Pueyo, Y. & Alados, C. L. Effects of fragmentation, abiotic factors and land use on vegetation recovery in a semi-arid Mediterranean area. Basic Appl. Ecol. 8, 158–170 (2007)

    Article  Google Scholar 

  30. Pascual, M., Roy, M., Guichard, F. & Flierl, G. Cluster size distributions: signatures of self-organization in spatial ecologies. Phil. Trans. R. Soc. Lond. B 357, 657–666 (2002)

    Article  Google Scholar 

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The data collection was part of the DRASME (Desertification Risk Assessment in Silvopastoral Mediterranean Ecosystems) Collaborative Research Project. DRASME is funded by the EU under the INCO-DC Program. We acknowledge the assistance of M. Vrachnakis, D. Sirkou and K. Iovi in collecting the field data in Greece. The research of S.K. and M.R. is supported by a personal VIDI grant from the Netherlands Organization of Scientific Research/Earth and Life Sciences (NWO-ALW) to M.R. The research of Y.P. is funded by the Secretaría de Estado de Universidades e Investigación of Ministerio de Educación y Ciencia (Spain). The research of P.C.d.R. is supported by the LNV-NL Strategic Research Program “Sustainable spatial development of ecosystems, landscapes and regions”. We are grateful to M. Kéfi for his help with the figures, and to R. C. G. Chaves for commenting on the manuscript.

Author Contributions The data collection was organized and carried out by C.L.A. (Spanish, Greek and Moroccan sites), V.P.P. (Greek site) and A.E. (Moroccan site). Y.P. participated in the data collection in Spain. S.K. conducted the data analyses with help from C.L.A. and Y.P. S.K. performed the numerical simulations and analysis of the model in collaboration with M.R. and P.C.d.R., and wrote the manuscript. M.R. and P.C.d.R. supervised this work and were involved in the writing. All authors discussed the results and commented on the manuscript.

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Correspondence to Sonia Kéfi.

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Kéfi, S., Rietkerk, M., Alados, C. et al. Spatial vegetation patterns and imminent desertification in Mediterranean arid ecosystems. Nature 449, 213–217 (2007).

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