Bistability and regular spatial patterns in arid ecosystems

S. Kefi, M.B. Eppinga, P.C. de Ruiter, M.G. Rietkerk

Research output: Contribution to journalArticleAcademicpeer-review


A variety of patterns observed in ecosystems can be explained by resource–concentration mechanisms. A resource–concentration mechanism occurs when organisms increase the lateral flow of a resource toward them, leading to a local concentration of this resource and to its depletion from areas farther away. In resource–concentration systems, it has been proposed that certain spatial patterns could indicate proximity to discontinuous transitions where an ecosystem abruptly shifts from one stable state to another. Here, we test this hypothesis using a model of vegetation dynamics in arid ecosystems. In this model, a resource– concentration mechanism drives a positive feedback between vegetation and soil water availability. We derived the conditions leading to bistability and pattern formation. Our analysis revealed that bistability and regular pattern formation are linked in our model. This means that, when regular vegetation patterns occur, they indicate that the system is along a discontinuous transition to desertification. Yet, in real systems, only observing regular vegetation patterns without identifying the pattern-driving mechanism might not be enough to conclude that an ecosystem is along a discontinuous transition because similar patterns can emerge from different ecological mechanisms.
Original languageEnglish
Pages (from-to)257-269
Number of pages13
JournalTheoretical Ecology
Issue number4
Publication statusPublished - 2010


  • Resource-concentration
  • Scale-dependent feedback
  • Desertification
  • Spatial organization


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