Spatial Invasion of Pine Beetles into Lodgepole Forests: A Numerical Approach

We discuss a procedure for numerically approximating solutions to a system of nonlinear partial diierential equations which describe mountain pine beetles attacking lodgepole pine en masse. A centered spatial dicretization which yields a system of ordinary diierential equations is presented, including a method for generating`trans-parent' spatial boundary conditions. A ux-based model estimates the phase speed of pheromone isoclines at the boundary, providing an overestimate of the ux of beetles across the boundaries and giving nearly transparent boundary conditions. An Adams variable-step predictor-corrector approach is applied to the the discretized system. The numerical method and model are tested in both one and two space dimensions. In one space dimension a comparison of the solution using the ux estimates at the boundary is compared with a solution generated on a larger space domain. A spatially complicated example then is given to test the methodology in two dimensions.parent boundary.