Date of Award


Degree Type


Degree Name

Departmental Honors


Mathematics and Statistics


The mountain pine beetle (Dendroctonus ponderosae Hopkins) represents a significant threat to ponderosa pine and lodgepole pine stands in the western United States, and has the potential to threaten commercially valuable jack pine in both the United States and Canada. The success of the mountain pine beetle is based on synchronization of developmental events to time cold-hardened life stages for extreme winter temperatures and to facilitate mass attack and overwhelm the defenses of the host. This paper presents a solution methodology for an extended McKendrick - von Foerster model for the development of the mountain pine beetle in varying temperature environments. The model reflects the effect of phenotypic variability on output, and is suitable for determining field distributions of emergence events. An efficient computational method, based on Green's functions, is presented. Results are compared with direct numerical simulation, and the modelling and simulation strategy is applied to determine the distribution of emergence for mountain pine beetles. Eventually these results will be applied to improve forest management strategies in regard to the epidemic outbreak of pine beetles in northwestern North America.

Included in

Mathematics Commons



Faculty Mentor

James Powell

Departmental Honors Advisor

James Powell