Diffusion Models for Population Dynamics Incorporating Individual Behavior at Boundaries: Applications to Refuge Design

We construct models for dispersal of a population which incorporate the response of individuals to interfaces between habitat types. The models are based on random walks where there may be a bias in the direction an individual moves when it encounters an interface. This sort of dispersal process is...

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Bibliographic Details
Published in:Theoretical population biology 1999-04, Vol.55 (2), p.189-207
Main Authors: Cantrell, R.S., Cosner, C.
Format: Article
Language:English
Subjects:
Animals
Behavior, Animal
Ecosystem
Environment Design
Humans
Models, Biological
Population Dynamics
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Summary:We construct models for dispersal of a population which incorporate the response of individuals to interfaces between habitat types. The models are based on random walks where there may be a bias in the direction an individual moves when it encounters an interface. This sort of dispersal process is called skew Brownian motion. Our models take the form of diffusion equations with matching conditions across the interface between regions for population densities and fluxes. We combine the dispersal models with linear population growth models which assume that the population growth rate differs between regions of different habitat types. We use those models to study issues of refuge design. We specifically consider how the effectiveness of buffer zones depends on their size, quality, and the population's response to the interface between the buffer zone and the refuge.
ISSN:0040-5809
1096-0325
DOI:10.1006/tpbi.1998.1397