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1 results

  • A spatial model of range-dependent succession

  • Part of
  • Stephen M. Krone, Claudia Neuhauser
  • Journal:
    Journal of Applied Probability / Volume 37 / Issue 4 / December 2000
    Published online by Cambridge University Press:
    14 July 2016, pp. 1044-1060
    Print publication:
    December 2000

  • We consider an interacting particle system in which each site of the d-dimensional integer lattice can be in state 0, 1, or 2. Our aim is to model the spread of disease in plant populations, so think of 0 = vacant, 1 = healthy plant, 2 = infected plant. A vacant site becomes occupied by a plant at a rate which increases linearly with the number of plants within range R, up to some saturation level, F1, above which the rate is constant. Similarly, a plant becomes infected at a rate which increases linearly with the number of infected plants within range M, up to some saturation level, F2. An infected plant dies (and the site becomes vacant) at constant rate δ. We discuss coexistence results in one and two dimensions. These results depend on the relative dispersal ranges for plants and disease.