Diffusion models for population dynamics incorporating individual behaviorat boundaries: Applications to refuge design

We construct models for dispersal of a population which incorporate the res ponse of individuals to interfaces between habitat types. The models are ba sed on random walks where there may be a bias in the direction an individua l moves when it encounters an interface. This sort of dispersal process is called skew Brownian motion. Our models take the form of diffusion equation s with matching conditions across the interface between regions for populat ion densities and fluxes, We combine the dispersal models with linear popul ation growth models which assume that the population growth rate differs be tween regions of different habitat types. We use those models to study issu es of refuge design. We specifically consider how the effectiveness of buff er zones depends on their size, quality, and the population's response to t he interface between the buffer zone and the refuge. (C) 1999 Academic Pres s.