Doctoral Dissertations

Date of Award

8-1983

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Major

Mathematics

Major Professor

T. G. Hallam

Committee Members

Charles E. Clark

Abstract

A model of a toxicant-population interaction with variables population biomass, concentration of toxicant in the environment, and concentration of toxicant in the organism are investigated. First order kinetics are assumed for the toxicant while the population is governed by a modified Smith-type equation. Exposure is allowed through both environmental and food chain pathways. The non-additivity of environmental and food chain toxicant inputs is modelled by assuming that there is a coupling between the uptake rates of the different toxicant pathways. This feedback between the toxicant accumulation sources is assumed to depend reciprocally upon the environmental up take parameter a1. The main theoretical results focus on system level effects involving persistence and extinction of the population. Additionally, an approximation to the original model is shown to be adequate since error propagation is uniform in the toxicant components and when appropriate biological conditions hold, the reduced model yields environmentally safe predictions.

Three models of population-toxicant interactions that include an explicit representation for a dynamic resource have been developed and analyzed. Each model contains components representing population-resource subsystem, concentration of the toxicant in the environment, and concentration of the toxicant in the organism. The first resource-consumer-toxicant system includes a resource-consumer subsystem of the Leslie type; the second model uses a resource-consumer subsystem of the Gallopin type; the third deals with a model of the continuous culture type. The reduced model is employed to model the concentration of the toxicant components.

Although the three resource-consumer-toxicant systems studied have modelling features that are different, each exhibits an interesting phenomenon related to ultimate population levels under stressed and unstressed conditions. The presence of toxicant in the system results in higher levels of resource needed to support a lower population level, that is, the equilibrium value of the population with toxicant is less than the population equilibrium without toxicant while the inequality is reversed for the resource equilibrium values. Thus, the presence of toxicant in the resource-consumer-toxicant models could be interpreted as resulting in higher maintenance costs and lower growth rates.

Download
Files over 3MB may be slow to open. For best results, right-click and select "save as..."

Share

COinS