Models For Predator-Prey Systems with Multiple Spatial and Temporal Scales
Friday, January 14, 2000 - 11:15am - 11:55am
Chris Cosner (University of Miami College of Arts and Sciences)
This talk will describe an approach to modeling a predator-prey system which involves multiple spatial and temporal scales. The models describe a natural system where the predators are ladybird beetles and the prey are aphids. The underlying environment consists of a collection of patches of plants which may support colonies of aphids. The beetles disperse through the environment quite rapidly by searching the patches for aphid colonies, but reproduce only once per season. The aphids colonize some of the patches and go through several generations per season, but disperse slowly within each patch. Thus, the predators are assumed to interact with the environment on a large spatial scale and to experience it as a collection of patches, to disperse on a very fast time scale, and to reproduce on a slow time scale. The prey are assumed to interact with the environment on a small spatial scale and to experience each patch as a continuum, and to disperse and reproduce on moderately fast time scales. Structurally the models are a hybrid of patch models (for the predators) and reaction-diffusion models (for the prey). The assumptions about time scales are used to simplify the models. The models can be used to study the effect of patch size on population dynamics. In some parameter ranges the models predict that smaller habitat patches will sustain higher prey densities than larger patches. This phenomenon has been observed in a natural system consisting of aphids and ladybird beetles. It is an emergent propery of the system in the sense that models based on the prey alone typically predict higher population densities on larger patches. Other issues such as comparisons of different foraging strategies which might be used by the predators can also be addressed from the same general modeling viewpoint.