Masters Theses

Date of Award

8-1997

Degree Type

Thesis

Degree Name

Master of Science

Major

Mathematics

Major Professor

Thomas G. Hallam

Committee Members

Louis J. Gross, Mark Kot, Walker O. Smith Jr.

Abstract

In this study a mathematical model for phytoplankton assemblages is developed. A detailed physiological model on the individual cell level focuses on nutrient and energy flows in the system. Flows of nutrients, production of storage, and growth are modeled independently. This allows uncoupled dynamics of storage and structure pools in a cell. A population of zooplankton grazing on the phytoplankton cells is part of the model. Grazing and sinking determine the losses of phytoplankton cells. Euler’s and Runge-Kutta’s Method for numer-ical solutions of systems of ordinary differential equations were implemented in a computer code written in C. The code was used to perform simulations of a population of the diatom Skeletonema costatum under various environmental conditions. Simulations were usually performed for 5-25 days in a homogeneous environment with equally distributed cells. Ad-ditional simulations included two species simulations to investigate species competition and dominance. Dynamical behavior of the system showed realistic patterns. Growth of cells was either limited through nutrient or energy shortage. The uncoupling of storage and structure production resulted in changes in cell composition, and allowed to detect indirect effects of nutrient or energy limitations. In simulations of two competing species the model showed effects of cell growth and composition that cannot be explained with less detailed models.

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