The models presented are one and two species models using differential equations. The extensive bibliography at the end of the article provides an excellent reading list for those interested in pursuing other realistic examples of mathematical modeling. The model was developed in Canada to describe infestations observed there, but is certainly relevant to northern Minnesota. Our interest lies in seeing how models can be used to evaluate management decisions in the natural resource realm. The spruce budworm crawls upon and consumes the leaves of coniferous trees.
Excessive consumption can damage and kill the host.
The budworms themselves are eaten primarily by birds, who eat many other insects as well. The budworms prefer larger trees. A key factor in determining the spruce budworm population is the leaf surface area per tree. Larger trees have larger leaf surface areas, resulting in larger spruce budworm populations. The Canadians had observed that the spruce budworm population underwent irruptions approximately every 40 years.