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Generic Modelling of Vegetation Patterns. A Case Study of Tiger Bush in Sub-Saharian Sahel

  • R. Lefever
  • O. Lejeune
  • P. Couteron
Part of the The IMA Volumes in Mathematics and its Applications book series (IMA, volume 121)

Abstract

The conditions underlying the mean field description of vegetation patterns are reviewed. A generic partial differential equation model describing vegetation propagation over space by reproduction under isotropic as well as anisotropic environmental conditions is discussed. An example of Tiger Bush in Burkina Faso is analyzed on the basis of this model.

Keywords

Vegetation Density Unstable Mode Vegetation Pattern Ground Slope Nonlocal Interaction 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. [1]
    For reviews, see e.g., J.D. Gunton, M. San Miguel and P.S. Sahni, in: Phase Transitions and Critical Phenomena, Vol. 8, edited by C. Domb and J.L. Lebowitz (Academic Press 1983). K. Binder, in: Phase Transformations of Materials (Material Science and Technology 5), edited by P. Haasen (Weinheim: VCH 1991).Google Scholar
  2. [2]
    cf. the numerous examples described in, e.g., J.D. Murray (1989). Mathematical Biology. Biomathematics Texts 19. Berlin/New York: Springer-Verlag. H. Meinhardt (1982). Models of Biological Pattern Formation. New York: Academic Press.MATHGoogle Scholar
  3. [3]
    H. Othmer (1969). Interactions of reaction and diffusion in open systems. Doctoral Thesis, University of Minnesota (USA).Google Scholar
  4. [4]
    D.S. Cohen and J.D. Murray (1981). A generalized diffusion model for growth and dispersal in a population. J. Math. Biol. 12, 237–249.MathSciNetMATHCrossRefGoogle Scholar
  5. [5]
    L.A. Segel (1985). Pattern generation in space and aspect. SIAM Rev. 27, 45–67.MathSciNetMATHCrossRefGoogle Scholar
  6. [6]
    W.A. Macfadyen (1950a). Soil and vegetation in British Somaliland. Nature 165, p. 121.CrossRefGoogle Scholar
  7. [7]
    W.A. Macfadyen (1950b). Vegetation patterns in the semi-desert plains of British Somaliland. Geogr. J. 116, 199–211.CrossRefGoogle Scholar
  8. [8]
    G.A. Worrall (1959). The Butana grass patterns. J. Soil Sci. 10 n °1, 34–53.CrossRefGoogle Scholar
  9. [9]
    P. Couteron (1998). Relations spatiales entre individus et structure d’ensemble dans des peuplements ligneux soudano-sahéliens au nord-ouest du Burkina Faso. Doctoral Thesis, University of Toulouse (France).Google Scholar
  10. [10]
    G.E. Wickens and F.W. Collier (1971). Some vegetation patterns in the Republic of the Sudan. Geoderma 6, 43–59.CrossRefGoogle Scholar
  11. [11]
    F. Van Der Meulen and J.W. Morris (1979). Striped vegetation patterns in a Transvaal savanna. Geo-Eco-Trop 3(4), 253–266.Google Scholar
  12. [12]
    L.P. White (1970). Brousses Tigrées Patterns in Southern Niger. J. Ecol. 58, 549–553.CrossRefGoogle Scholar
  13. [13]
    M. Gavaud (1966). Etude pédologique du Niger Occidental. Editions de l’ORSTOM de Dakkar-Hann.Google Scholar
  14. [14]
    J.-M. d’Herbès, C. Valentin, and J.M. Thiéry (1997). La brousse tigrée au Niger: Synthèse des connaissances acquises. Hypothèse sur la génèse et les facteurs déterminant les différentes structures contractées. In Fonctionnement et gestion des écosystèmes contractés sahéliens (J.-M. d’Herbes, J.M.K. Ambouta and R. Peltier, eds.), 131–152. John Libbey Eurotext, Paris.Google Scholar
  15. [15]
    S.B. Boaler and C.A.H. Hodge (1964). Observations on vegetation arcs in the northern region, Somali Republic. J. Ecol. 52, 511–544.CrossRefGoogle Scholar
  16. [16]
    J.A. Mabbutt and P.C. Fanning (1987). Vegetation banding in arid Western Australia. J. Arid Env. 12, 41–59.Google Scholar
  17. [17]
    C. Montaña, J. Lopez-Portillo, and A. Mauchamp (1990). The response of two woody species to the conditions created by a shifting ecotone in an arid ecosystem. J. Ecol. 78, 789–798.CrossRefGoogle Scholar
  18. [18]
    C. Montaña (1992). The colonization of bare areas in two-phase mosaics of an arid ecosystem. J. Ecol. 80, 315–327.CrossRefGoogle Scholar
  19. [19]
    A.F. Cornet, J.P. Delhoume, and C. Montaña (1988). Dynamics of striped vegetation patterns and water balance in the Chihuahuan desert. In Diversity and Pattern in Plant Communities (H.J. During, M.J.A. Werger, and J.H. Willems, eds.), 221–231. SPB Academic Publishing: The Hague.Google Scholar
  20. [20]
    D.J. Tongway and J.A. Ludwig (1990). Vegetation and soil patterning in semi-arid mulga lands of Eastern Australia. Aust. J. Ecol. 15, 23–34.CrossRefGoogle Scholar
  21. [21]
    R. Lefever and O. Lejeune (1997). On the origin of tiger bush. Bull. Math. Biol. 59, 263–294.MATHCrossRefGoogle Scholar
  22. [22]
    O. Lejeune, P. Couteron, and R. Lefever (1999). Short range cooperativity competing with long range inhibition explains vegetation patterns. Acta Oeco-logica 20, 171–183.CrossRefGoogle Scholar
  23. [23]
    P. Greig-smith (1979). Pattern in vegetation. J. Ecology 67, 755–779.CrossRefGoogle Scholar
  24. [24]
    O. Lejeune, June 1999. Une théorie champ moyen de l’organisation spatiotemporelle des écosystmes végétaux. Doctoral Thesis, University of Brussels (Belgium).Google Scholar
  25. [25]
    O. Lejeune and R. Lefever. Propagator-inhibitor model of vegetal ecosystems: amplitude equations in the isotropic case. In preparation.Google Scholar
  26. [26]
    P. Couteron and K. Kokou (1997). Woody vegetation spatial patterns in a semi-arid savanna of Burkina Faso, West Africa. Plant Ecol. 132, 211–227.CrossRefGoogle Scholar
  27. [27]
    F. White (1983). The vegetation of Africa. A descriptive memoir to accompany the UNESCO/AEFTAT/UNSO vegetation map. (UNESCO/AEFTAT/UNSO. Paris), p. 356.Google Scholar
  28. [28]
    H.N. le Houerou (1989). The grazing land ecosystems of the African Sahel. (Springer-Verlag. Berlin), p. 282.CrossRefGoogle Scholar
  29. [29]
    O.R. Vetaas (1992). Micro-site effects of trees and shrubs in dry savannas. J. Veg. Sci. 3, 337–344.CrossRefGoogle Scholar
  30. [30]
    P.E. Glover (1951). The root systems of some British-Somaliland plants-IV. East Afr. Agr. J. 17, 38–50.Google Scholar
  31. [31]
    H. Poupon (1980). Structure et dynamique de la strate ligneuse d’une steppe sahélienne au nord du Sénégal. (ORSTOM. Paris), p. 351.Google Scholar
  32. [32]
    A.J. Belsky (1994). Influence of trees on savanna productivity: tests of shade, nutrients, and tree-grass competition. Ecol. 75, 922–932.CrossRefGoogle Scholar
  33. [33]
    J.E.G.W. Greenwood (1957). The development of vegetation in Somaliland Protectorate. Geogr. J. 123, 465–473.CrossRefGoogle Scholar
  34. [34]
    A. Clos-Arceduc (1964). La géométrie des associations végétales en zone aride. Act. Conf. UNESCO: Explorations aériennes et études intégrées, Toulouse, 419–421.Google Scholar
  35. [35]
    S.B. Boaler and C.A.H. Hodge (1962). Vegetation stripes in Somaliland. J. Ecol. 50, 465–474.CrossRefGoogle Scholar
  36. [36]
    O. Lejeune and M. Tlidi (1999). A model for the explanation of vegetation stripes (tiger bush). J. Veg. Sci. 10, 201–208.CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • R. Lefever
    • 1
  • O. Lejeune
    • 1
  • P. Couteron
    • 2
  1. 1.Faculté des Sciences, CP 231Université Libre de BruxellesBruxellesBelgium
  2. 2.Ecole Nationale du Génie Rural des Eaux et ForêtsMontpellier Cedex 01France

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