Bulletin of Mathematical Biology

, Volume 76, Issue 11, pp 2866–2883 | Cite as

Vegetation Pattern Formation Due to Interactions Between Water Availability and Toxicity in Plant–Soil Feedback

  • Addolorata Marasco
  • Annalisa Iuorio
  • Fabrizio Cartení
  • Giuliano Bonanomi
  • Daniel M. Tartakovsky
  • Stefano Mazzoleni
  • Francesco GianninoEmail author
Original Article


Development of a comprehensive theory of the formation of vegetation patterns is still in progress. A prevailing view is to treat water availability as the main causal factor for the emergence of vegetation patterns. While successful in capturing the occurrence of multiple vegetation patterns in arid and semiarid regions, this hypothesis fails to explain the presence of vegetation patterns in humid environments. We explore the rich structure of a toxicity-mediated model of the vegetation pattern formation. This model consists of three PDEs accounting for a dynamic balance between biomass, water, and toxic compounds. Different (ecologically feasible) regions of the model’s parameter space give rise to stable spatial vegetation patterns in Turing and non-Turing regimes. Strong negative feedback gives rise to dynamic spatial patterns that continuously move in space while retaining their stable topology.


Turing pattern Negative feedback Bifurcation analysis  Numerical simulations 



Max Rietkerk provided useful comments to improve the manuscript. We thank Antonello Migliozzi for photointerpretation. Photographs in Fig. 10 are data available from the U.S. Geological Survey.

Supplementary material

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Copyright information

© Society for Mathematical Biology 2014

Authors and Affiliations

  • Addolorata Marasco
    • 1
  • Annalisa Iuorio
    • 2
  • Fabrizio Cartení
    • 3
  • Giuliano Bonanomi
    • 3
  • Daniel M. Tartakovsky
    • 4
  • Stefano Mazzoleni
    • 3
  • Francesco Giannino
    • 3
    Email author
  1. 1.Department of Mathematics and Applications “R. Caccioppoli”University of Naples Federico IIVia CintiaItaly
  2. 2.Institute for Analysis and Scientific ComputingVienna University of TechnologyViennaAustria
  3. 3.Department of AgricultureUniversity of Naples Federico IIPortici (Na)Italy
  4. 4.Department of Mechanical and Aerospace EngineeringUniversity of California, San DiegoLa JollaUSA

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