Theoretical Analysis of ‘Switching’ in a LocalizedModel for Mountain Pine Beetle Mass Attack

The dynamic interaction between mountain pine beetles (MPB) and hosts (generally lodgepole pine) is reviewed briefly. In particular, successful “switching” from initial foci of attack to nearby hosts which may be higher-quality resources is a potentially critical element initiating the transition from endemic to epidemic population levels. A coupled partial differential equation model for MPB dispersal and host response is reviewed. The equations are decoupled making an adiabatic assumption for MPB chemotaxis, and a “local” projection is made using the leading eigenfunction for the MPB density equation. This projection yields a system of ordinary differential equations for the spatio-temporal responses at individual trees. These equations are analysed to determine what factors control successful “switching” in a two-tree model. The results suggest that stand thinning ameliorates outbreaks mainly through interference with the chemical ecology via a change in micro-climate rather than by altering host vigor