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
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U2 - 10.1017/S0021900200018210
DO - 10.1017/S0021900200018210
M3 - Article
AN - SCOPUS:85037782191
SN - 0021-9002
VL - 37
SP - 1044
EP - 1060
JO - Journal of Applied Probability
JF - Journal of Applied Probability
IS - 4
ER -