Interactions of predator-prey ecological processes and advective movement in a spatially heterogeneous environment

Spatial models have been developed based on predator-prey ecological interactions and on a prey-gradient driven movement of the predator. Moreover, the prey species is assumed to be immobile.

We begin by establishing the existence of traveling wave solutions for an aggregated model in which the predator and prey interactions are based on a modified Lotka-Volterra model with logistic growth of the prey. Each predator responds identically to changes in the prey density. The traveling wave solutions discussed here are waves that travel without change in shape and are not necessarily monotone. We find that traveling wave solutions can evolve from asymptotic initial conditions. We also find that steep waves that correspond to slow moving waves, eventually "break".

We numerically investigate the dynamics of an aquatic predator-prey system in a bounded linear habitat. The predator species is physiologically structured according to the age, lipid, and structure (protein and carbohydrates) of an individual. The response of the predator to changes in the prey density depends on physiological char acteristics of the individual. The dynamics of the predator population are compared using two movement behaviors, one in which individuals move continuously in the direction of increasing prey and another in which energetic constraints are imposed. The model has been developed for a rainbow trout, Oncorhynchus mykiss, population feeding on a Daphnia population.

The model has been used to study the effects of nonpolar narcotic toxicants on the fish population which is exposed to a spatially varying toxicant and a dynamic resource. The exposure might occur through the environmental and/or the food pathways.