NRCAN - Canadian Forest Services 1

Insect dispersal is often divided into two classes (perhaps somewhat artificially): local and long distance. Local dispersal is the most common dispersal mode and because many individuals disperse this way, it is well described by dispersal kernels. Long distance dispersal is more stochastic and difficult to model using dispersal kernels because only a small proportion of insects are thought to disperse long distances. For the mountain pine beetle for example, most individuals disperse between five and fifty meters from where they were born. About 0.2 percent of individuals (Safranyik et al, 1991), however end up above tree canopies where they can be pulled upwards by updrafts and then transported laterally by higher wind speeds in the lower atmosphere. Mountain pine beetles that disperse long distances would typically disperse 40 km on average (Ainsley and Jackson, 2011) but specifics may vary depending on where individuals are dispersing from. Long-distance dispersal is risky for mountain pine beetles because if they disperse too far into locations where mountain pine beetles are sparse, they are unable to recruit enough conspecifics to attack new trees and they suffer the consequences of a strong Allee effect. Therefore, although long-distance dispersal is likely the dominant determinant of the speed of mountain pine beetle invasions, estimation of invasion speeds using standard mathematical approaches are impeded by the strong Allee effect (we can no longer rely on the linear conjecture—see Kot and Lewis et all., 1998). In addition, the nature of long distance dispersal, in which individuals that disperse to the invasion front are more likely to have dispersed from dense populations behind the front of the invasion, combined with the Allee effect, implies that traveling waves arising from the dynamics described above will be “pushed waves” rather than “pulled waves”. Using two theoretical dispersal distributions (potentially derived from the literature cited herein) and a population model with a strong Allee effect in discrete time, develop an approach (mathematical and/or simulation/based) for estimating invasion speed. If possible, demonstrate that traveling waves subject to the biology described above are pushed rather than pulled when they exist.