Bulletin of Mathematical Biology

, Volume 76, Issue 11, pp 2866–2883

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 Giannino
Original Article

Abstract

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.

Keywords

Turing pattern Negative feedback Bifurcation analysis  Numerical simulations 

Supplementary material

11538_2014_36_MOESM1_ESM.avi (3 mb)
ESM 1 (AVI 3104 kb)
11538_2014_36_MOESM2_ESM.avi (4.1 mb)
ESM 1 (AVI 4205 kb)
11538_2014_36_MOESM3_ESM.avi (4.2 mb)
ESM 1 (AVI 4306 kb)
11538_2014_36_MOESM4_ESM.avi (7.8 mb)
ESM 1 (AVI 8035 kb)

References

  1. Banerjee M, Petrovskii S (2011) Self-organised spatial patterns and chaos in a ratio-dependent predator-prey system. Theor Ecol 4(1):37–53CrossRefGoogle Scholar
  2. Boale SB, Hodge CAH (1964) Observations on vegetation arcs in the Northern region, Somali republic. J Ecol 52:511–544CrossRefGoogle Scholar
  3. Bonanomi G, Incerti G, Allegrezza M (2013) Assessing the impact of land abandonment, nitrogen enrichment and fairy-ring fungi on plant diversity of Mediterranean grasslands. Biodivers Conserv 22:2285–2304CrossRefGoogle Scholar
  4. Bonanomi G, Incerti G, Barile E, Capodilupo M, Antignani V, Mingo A, Lanzotti V, Scala F, Mazzoleni S (2011) Phytotoxicity, not nitrogen immobilization, explains plant litter inhibitory effects: evidence from solid-state 13C NMR spectroscopy. New Phytol 191:1018–1030Google Scholar
  5. Bonanomi G, Incerti G, Stinca A, Cartenì F, Giannino F, Mazzoleni S (2014) Ring formation in clonal plants. Community Ecol 15:77–86Google Scholar
  6. Bonanomi G, Mingo A, Incerti G, Mazzoleni S, Allegrezza M (2012) Fairy rings caused by a killer fungus foster plant diversity in species-rich grassland. J Veg Sci 23:236–248CrossRefGoogle Scholar
  7. Cartení F, Marasco A, Bonanomi G, Mazzoleni S, Rietkerk M, Giannino F (2012) Negative plant soil feedback and ring formation in clonal plants. J Theor Biol 313:153–161CrossRefGoogle Scholar
  8. Coullet P, Riera C (2000) Stable static localized structures in one dimension. Phys Rev Lett 84:3069–3072CrossRefGoogle Scholar
  9. Deblauwe V, Barbier N, Couteron P, Lejeune O, Bogaert J (2008) The global biogeography of semi-arid periodic vegetation patterns. Global Ecol Biogeogr 17(6):715–723CrossRefGoogle Scholar
  10. Dekker SC, de Boer HJ, Brovkin V, Fraedrich K, Wassen MJ, Rietkerk M (2009) Biogeophysical feedbacks trigger shifts in the modelled climate system at multiple scales. Biogeosciences Discuss 6:10983–11004CrossRefGoogle Scholar
  11. Flach EH, Schnell S (2006) Use and abuse of the quasi-steady-state approximation. Syst Biol (Stevenage) 153(4):187–191CrossRefGoogle Scholar
  12. Gilad E, Yihzaq H, Meron E (2007a) Localized structures in dryland vegetation: forms and functions. Chaos 17:037109CrossRefGoogle Scholar
  13. Gilad E, von Hardenberg J, Provenzale A, Shachak M, Meron E (2007b) A mathematical model of plants as ecosystem engineers. J Theor Biol 244:680–691CrossRefGoogle Scholar
  14. HilleRisLambers R, Rietkerk M, van den Bosch F, Prins HHT, de Kroon H (2001) Vegetation pattern formation in semi-arid grazing systems. Ecology 82:50–61CrossRefGoogle Scholar
  15. Jensen O, Pannbacker VO, Mosekilde E, Dewel G, Borckmans P (1994) Localized structures and front propagation in the Lengyel–Epstein model. Phys Rev. E 50:736–749CrossRefGoogle Scholar
  16. Kealy BJ, Wollkind DJ (2012) A nonlinear stability analysis of vegetative turing pattern formation for an interaction diffusion plant-surface water model system in an arid flat environment. Bull Math Biol 74(4):803–833MathSciNetCrossRefMATHGoogle Scholar
  17. Kéfi S, Eppinga MB, de Ruiter PC (2010) Bistability and regular spatial patterns in arid ecosystems. Theor Ecol 3:257–269CrossRefGoogle Scholar
  18. Kessler MA, Werner BT (2003) Self-organization of sorted patterned ground. Science 299:380–383CrossRefGoogle Scholar
  19. Klausmeier CA (1999) Regular and irregular patterns in semiarid vegetation. Science 284:1826–1828CrossRefGoogle Scholar
  20. Kulmatisky A, Beard KH, Stevens JR, Cobbold SM (2008) Plant-soil feedbacks: a meta-analytical review. Ecol Lett 11:980–992CrossRefGoogle Scholar
  21. Lefever R, Lejeune O (1997) On the origin of tiger bush. Bull Math Biol 59:263–294CrossRefMATHGoogle Scholar
  22. Lejeune O, Couteron P, Lefever R (1999) Short range co-operativity competing with long range inhibition explains vegetation patterns. Acta Oecol 20:171–183CrossRefGoogle Scholar
  23. Lejeune O, Tlidi M, Couteron P (2002) Localized vegetation patches: a self-organized response to resource scarcity. Phys Rev EGoogle Scholar
  24. Leprun JC (1999) The influences of ecological factors on tiger bush and dotted bush patterns along a gradient from Mali to northern Burkina faso. Catena 37:25–44CrossRefGoogle Scholar
  25. Marasco A, Iuorio A, Cartení F, Bonanomi G, Giannino F, Mazzoleni S (2013) Water limitation and negative plant-soil feedback explain vegetation patterns along rainfall gradient. Procedia Environ Sci 19:139–147CrossRefGoogle Scholar
  26. Mazzoleni S, Bonanomi G, Giannino F, Rietkerk M, Dekker SC, Zucconi F (2007) Is plant biodiversity driven by decomposition processes? An emerging new theory on plant diversity. Community Ecol 8:103–109CrossRefGoogle Scholar
  27. Mazzoleni S, Bonanomi G, Giannino F, Incerti G, Dekker SC, Rietkerk M (2010) Modelling the effects of litter decomposition on tree diversity patterns. Ecol Model 221:2784–2792CrossRefGoogle Scholar
  28. Mazzoleni S, Bonanomi G, Incerti G, Chiusano ML, Termolino P, Mingo A, Senatore M, Giannino F, Cartení F, Rietkerk M, Lanzotti V (2014) Inhibitory and toxic effects of extracellular self-DNA in litter: a mechanism for negative plant-soil feedbacks? New Phytol. doi:10.1111/nph.13121
  29. Meinhardt H (1995) The Algorithmic Beauty of Sea Shells. Springer, New YorkCrossRefGoogle Scholar
  30. Meron E (2011) Modeling dryland landscapes. Math Model Nat Phenom 6(1):163–187MathSciNetCrossRefGoogle Scholar
  31. Meron E, Gilad E, von Hardenberg J, Shachak M, Zarmi Y (2004) Vegetation patterns along a rainfall gradient. Chaos Solitons Fract 19:367–376CrossRefMATHGoogle Scholar
  32. Murray JD (1988) Mathematical biology. Springer, New YorkGoogle Scholar
  33. Nathan J, von Hardenberg J, Meron E (2013) Spatial instabilities untie the exclusion-principle constraint on species coexistence. J Theor Biol 335:198–204CrossRefGoogle Scholar
  34. Okayasu T, Aizawa Y (2001) Systematic analysis of periodic vegetation patterns. Prog Theor Phys 106:705–720CrossRefMATHGoogle Scholar
  35. Petrovskii S, Kawasaki K, Takasu F, Shigesada N (2001) Diffusive waves, dynamical stabilization and spatio-temporal chaos in a community of three competitive species. Jpn J Ind Appl Math 18:459–481MathSciNetCrossRefMATHGoogle Scholar
  36. Rietkerk M, van de Koppel J (2008) Regular pattern formation in real ecosystems. Trends Ecol Evol 23(3):169–175CrossRefGoogle Scholar
  37. Rietkerk M, van den Bosch F, van de Koppel J (1997) Site-specific properties and irreversible vegetation changes in semi-arid grazing systems. Oikos 80:241–252CrossRefGoogle Scholar
  38. Rietkerk M, Boerlijst MC, van Langevelde F, HilleRisLambers R, van de Koppel J, Kumar L, Prins HHT (2002) Self-organization of vegetation in arid ecosystems. Am Nat 160:524–530Google Scholar
  39. Rietkerk M, Dekker SC, de Ruiter PC, van de Koppel J (2004) Self-organized patchiness and catastrophic shifts in ecosystems. Science 305:1926–1929CrossRefGoogle Scholar
  40. Rovinsky AB, Menzinger M (1993) Self-organization induced by the differential ow of activator and inhibitor. Phys Rev Lett 70:778–781CrossRefGoogle Scholar
  41. Scheffer M, Bascompte J, Brock WA, Brovkin V, Carpenter SR, Dakos V, Held H, van Nes EH, Rietkerk M, Sugihara G (2009) Early-warning signals for critical transitions. Nature 461(3):53–59CrossRefGoogle Scholar
  42. Sherratt JA (2005) An analysis of vegetation stripe formation in semi-arid landscapes. J Math Biol 51:183–197MathSciNetCrossRefMATHGoogle Scholar
  43. Sherratt JA (2010) Pattern solutions of the Klausmeier model for banded vegetation in semi-arid environments. I. Nonlinearity 23(10):2657–2675MathSciNetCrossRefMATHGoogle Scholar
  44. Sherratt JA, Lord GJ (2007) Nonlinear dynamics and pattern bifurcations in a model for vegetation stripes in semi-arid environments. Theor Popul Biol 71:1–11CrossRefMATHGoogle Scholar
  45. Sherratt JA, Dagbovie AS, Hilker FM (2014) A mathematical biologist’s guide to absolute and convective instability. Bull Math Biol 76:1–26MathSciNetCrossRefMATHGoogle Scholar
  46. Tlidi M, Mandel P, Lefever R (1994) Localized structures and localized patterns in optical bistability. Phys Rev Lett 73:640–643CrossRefGoogle Scholar
  47. Turing AM (1952) The chemical basis of morphogenesis. Bull Math Biol 52:153–197CrossRefGoogle Scholar
  48. Ursino N, Contarini S (2006) Stability of banded vegetation patterns under seasonal rainfall and limited soil moisture storage capacity. Adv Water Resour 29(10):1556–1564CrossRefGoogle Scholar
  49. Valentin C, d’Herbes JM, Poesen J (1999) Soil and water components of banded vegetation patterns. Catena 37:1–24CrossRefGoogle Scholar
  50. van de Koppel J, Rietkerk M, Weissing FJ (1997) Catastrophic vegetation shifts and soil degradation in terrestrial grazing systems. Tree 12(9):352–356Google Scholar
  51. Volpert V, Petrovskii S (2009) Reaction-diffusion waves in biology. Phys Life Rev 6:267–310CrossRefGoogle Scholar
  52. von Hardenberg J, Meron E, Shachak M, Zarmi Y (2001) Diversity of vegetation patterns and desertification. Phys Rev Lett 87(19):198101CrossRefGoogle Scholar
  53. Watt AS (1947) Pattern and process in the plant community. J Ecol 35:1–22CrossRefGoogle Scholar
  54. White LP (1971) Vegetation stripes on sheet wash surfaces. J Ecol 59(2):615–622CrossRefGoogle Scholar
  55. Wickens GE, Collier FW (1971) Some vegetation patterns in the republic of the Sudan. Geoderma 6:43–59CrossRefGoogle Scholar

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
  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

Personalised recommendations