Math Biology Seminar Abstracts

Wednesday September 25, 2002

Dynamics of a Multi-Patch Herbivory System: Herbivore Enhancement, Adaptive Behavior and (Apparent) Trophic Cascades

Nancy Sundell

Department of Mathematics, University of Utah

Abstract: An ordinary differential equations model is developed of a herbivory system with four main components: herbivores, plants, soil nitrogen and soil salinity. The key properties of the model system are the existence of positive enhancements to the plant population under low to moderate grazing levels (through nitrogen addition), and irreversible plant population declines under conditions of high soil salinity. The motivation for this project comes from ongoing research of Snow Geese and their interactions with the environment in their summer breeding ground near the Hudson Bay in Canada. This system is of environmental concern as a recent increase in the goose population has led to widespread destruction of plant biomass and the desertification of formerly healthy salt marsh. Analysis of the model suggests that a wide variety of factors can contribute to the observed destruction. These include not only the total number of herbivores present, but also the initial distribution of the herbivores on the landscape, the perceived and actual predation risk to the herbivores, and the length of time between the initiation of grazing and the realization of the positive enhancement effects.

For more information contact J. Keener, 1-6089