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An Analysis of Vegetation Stripe Formation in Semi-Arid Landscapes

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Abstract.

Vegetation stripes (“tiger bush”) are a characteristic feature of semi-arid environments. The stripes typically lie along the contours of gentle slopes, and some authors report a gradual uphill migration. A previous mathematical model (Klausmeier, Science, 284:1826, 1999) has shown that this phenomenon can be explained relatively simply by the downhill flow of rainwater coupled with the diffusive spread of the plant population. This paper presents a detailed analysis of pattern formation in the Klausmeier model. The author derives formulae for the wavelength and migration speed of the predicted patterns, and systematically investigates how these depend on model parameters. The results make new predictions and suggest possible approaches to testing the model.

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References

  1. Couteron, P., Lejeune, O.: Periodic spotted patterns in semi-arid vegetation explained by a propagation-inhibition model. J. Ecol. 89, 616–628 (2001)

    Article  Google Scholar 

  2. Dunkerley, D.L.: Banded vegetation: development under uniform rainfall from a simple cellular automaton model. Plant Ecol 129, 103–111 (1997)

    Article  Google Scholar 

  3. Dunkerley, D.L., Brown, K.J.: Oblique vegetation banding in the Australian arid zone: implications for theories of pattern evolution and maintenance. J. Arid Environments 52, 163–181 (2002)

    Article  Google Scholar 

  4. Hemming, C.F.: Vegetation arcs in Somaliland. J. Ecol. 53, 57–67 (1965)

    Google Scholar 

  5. HilleRisLambers, R., Rietkerk, M., van de Bosch, F., Prins, H.H.T., de Kroon, H.: Vegetation pattern formation in semi-arid grazing systems. Ecology 82, 50–61 (2001)

    Google Scholar 

  6. Jorné, J.: The effects of ionic migration on oscillations and pattern formation in chemical systems. J. Theor. Biol. 43, 375–380 (1974)

    PubMed  Google Scholar 

  7. Klausmeier, C.A.: Regular and irregular patterns in semiarid vegetation. Science 284, 1826–1828 (1999)

    Article  PubMed  Google Scholar 

  8. Lefever, R., Lejeune, O.: On the origin of tiger bush. Bull. Math. Biol. 59, 263–294 (1997)

    Article  Google Scholar 

  9. Lejeune, O., Tlidi, M.: A model for the explanation of vegetation stripes (tiger bush). J. Vegetation Science 10, 201–208 (1999)

    Google Scholar 

  10. Mabbutt, J.A., Fanning, P.C.: Vegetation banding in arid Western Australia. J. Arid Environments 12, 41–59 (1987)

    Google Scholar 

  11. MacFadyen, W.: Vegetation patterns in the semi-desert plains of British Somaliland. Geographical J. 115, 199–211 (1950)

    Google Scholar 

  12. Mauchamp, A., Rambal, S., Lepart, J.: Simulating the dynamics of a vegetation mosaic: a spatialized functional model. Ecological Modelling 71, 107–130 (1994)

    Article  Google Scholar 

  13. Meron, E., Gilad, E., von Hardenberg, J., Shachak, M., Zarmi, Y.: Vegetation patterns along a rainfall gradient. Chaos, Solitons and Fractals 19, 367–376 (2004)

    Google Scholar 

  14. Montaña, C., Lopez-Portillo, J., Mauchamp, A.: The response of two woody species to the conditions created by a shifting ecotone in an arid ecosystem. J. Ecol. 78, 789–798 (1990)

    Google Scholar 

  15. Montaña, C.: The colonization of bare areas in two-phase mosaics of an arid ecosystem. J. Ecol. 80, 315–327 (1992)

    Google Scholar 

  16. Perumpanani, A.J., Sherratt, J.A., Maini, P.K.: Phase differences in reaction-diffusion-advection systems and applications to morphogenesis. IMA J. Appl. Math. 55, 19–33 (1995)

    MathSciNet  Google Scholar 

  17. Rietkerk, M., Boerlijst, M.C., van Langevelde, F., HilleRisLambers, R., van de Koppel, J., Prins, H.H.T., de Roos, A.: Self-organisation of vegetation in arid ecosystems. Am. Nat. 160, 524–530 (2002)

    Article  Google Scholar 

  18. Rovinsky, A.B., Menzinger, M.: Self-organization induced by the differential flow of activator and inhibitor. Phys. Rev. Lett. 70, 778–781 (1993)

    Article  PubMed  Google Scholar 

  19. Satnoianu, R.A., Maini, P.K., Menzinger, M.: Parameter space analysis, pattern sensitivity and model comparison for Turing and stationary flow-distributed waves. Physica D 160, 79–102 (2001)

    Google Scholar 

  20. Thiéry, J.M., D’Herbès, J.-M., Valentin, C.: A model simulating the genesis of banded vegetation patterns in Niger. J. Ecol. 83, 497–507 (1995)

    Google Scholar 

  21. van de Koppel, J., Rietkerk, M., van Langevelde, F., Kumar, L., Klausmeier, C.A., Fryxell, J.M., Hearne, J.W., van Andel, J., de Ridder, N., Skidmore, M.A., Stroosnijder, L., Prins, H.H.T.: Spatial heterogeneity and irreversible vegetation change in semiarid grazing systems. Am. Nat. 159, 209–218 (2002)

    Article  Google Scholar 

  22. von Hardenberg, J., Meron, E., Shachak, M., Zarmi, Y. Diversity of vegetation patterns and desertification. Phys. Rev. Lett. 87, art. no. 198101 (2001)

    Google Scholar 

  23. White, L.P.: Vegetation stripes on sheet wash surfaces. J. Ecol. 59, 615–622 (1971)

    Google Scholar 

  24. Wickens, G.E., Collier, F.W.: Some vegetation patterns in the Republic of Sudan. Geoderma 6, 43–59 (1971)

    Article  Google Scholar 

  25. Worrall, G.A.: The Butana grass patterns. J. Soil Sci. 10, 34–53 (1959)

    Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Heriot-Watt University, Edinburgh, EH14 4AS, UK

    Jonathan A. Sherratt

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  1. Jonathan A. Sherratt
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Correspondence to Jonathan A. Sherratt.

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Sherratt, J. An Analysis of Vegetation Stripe Formation in Semi-Arid Landscapes. J. Math. Biol. 51, 183–197 (2005). https://doi.org/10.1007/s00285-005-0319-5

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  • DOI: https://doi.org/10.1007/s00285-005-0319-5

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