Mathematical elements of attack risk analysis for mountain pine beetles

Three different mathematical approaches are combined to develop a spatial f ramework in which risk of mountain pine beetle (MPB) attack on individual h osts may be assessed. A density-based partial differential equation model d escribes the dispersal and focusing behavior of MPB. A local projection ont o a system of ordinary differential equations predicts the consequences of the density equations at individual hosts. The bifurcation diagram of these equations provides a natural division into categories of risk for each hos t, A stem-competition model links host vigor to stand age and demographics. Coupled together, these models illuminate spatial risk structures which ma y also shed light on the role of climatic variables in population outbreaks . Preliminary results suggest that stand microclimate has much greater infl uence on risk of attack than host vigor and stand age. (C) 2000 Academic Pr ess.