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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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.