TY - JOUR

T1 - A spatial model of range-dependent succession

AU - Krone, Stephen M.

AU - Neuhauser, Claudia

PY - 2000/12

Y1 - 2000/12

N2 - 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.

AB - 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.

KW - Coexistence

KW - Interacting particle systems

KW - Range-dependent dispersal

KW - Spatial patterns

KW - Succession

KW - Turing instabilities

UR - http://www.scopus.com/inward/record.url?scp=0034336854&partnerID=8YFLogxK

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U2 - 10.1017/S0021900200018210

DO - 10.1017/S0021900200018210

M3 - Article

AN - SCOPUS:0034336854

VL - 37

SP - 1044

EP - 1060

JO - Journal of Applied Probability

JF - Journal of Applied Probability

SN - 0021-9002

IS - 4

ER -