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A spatial model of range-dependent succession

Part of: Special processes Mathematical biology in general

Published online by Cambridge University Press:  14 July 2016

Stephen M. Krone  and
Claudia Neuhauser
Stephen M. Krone*
Affiliation:
University of Idaho
Claudia Neuhauser*
Affiliation:
University of Minnesota
*
∗ Postal address: Department of Mathematics, University of Idaho, Moscow, ID 83844, USA. Email address: [email protected]
∗∗ Postal address: School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA.
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Abstract

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.

Keywords

Interacting particle systemssuccessionrange-dependent dispersalcoexistencespatial patternsTuring instabilities

MSC classification

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory
Secondary: 92B05: General biology and biomathematics
Type
Research Papers
Information
Journal of Applied Probability , Volume 37 , Issue 4 , December 2000 , pp. 1044 - 1060
Copyright
Copyright © by the Applied Probability Trust 2000 

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