Pair Approximation for Lattice Models with Multiple Interaction Scales
β Scribed by STEPHEN P. ELLNER
- Publisher
- Elsevier Science
- Year
- 2001
- Tongue
- English
- Weight
- 336 KB
- Volume
- 210
- Category
- Article
- ISSN
- 0022-5193
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β¦ Synopsis
Pair approximation has frequently proved e!ective for deriving qualitative information about lattice-based stochastic spatial models for population, epidemic and evolutionary dynamics. Pair approximation is a moment closure method in which the mean-"eld description is supplemented by approximate equations for the frequencies of neighbor-site pairs of each possible type. A limitation of pair approximation relative to moment closure for continuous space models is that all modes of interaction between individuals (e.g., dispersal of o!spring, competition, or disease transmission) are assumed to operate over a single spatial scale determined by the size of the interaction neighborhood. In this paper I present a multiscale pair approximation which allows di!erent sized neighborhoods for each type of interaction. To illustrate and test the approximation I consider a spatial single-species logistic model in which o!spring are dispersed across a birth neighborhood and established individuals have a death rate depending on the population density in a competition neighborhood, with one of these neighborhoods nested inside the other. Analysis of the steady-state equations yields several qualitative predictions that are con"rmed by simulations of the model, and numerical solutions of the dynamic equations provide a close approximation to the transient behavior of the stochastic model on a large lattice. The multiscale pair approximation thus provides a useful intermediate between the standard pair approximation for a single interaction neighborhood, and a complete set of moment equations for more spatially detailed models.
π SIMILAR VOLUMES
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