Doctoral Dissertations

Date of Award

8-1993

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Major

Mathematics

Major Professor

T.G Hallam

Committee Members

Louis Gross, Ben Fitzpatrick, Walker Smith

Abstract

The purpose of this study is to model the dynamics of phytoplankton by including the aggregation process. Aggregation, the formation of large particles from the collisions of smaller ones, is fundamental to many biological processes in the ocean. Because larger particles tend to sink faster than smaller ones, coagulation can be important in accelerating the export of organic matter from the ocean's surface to the deep sea and, consequently, it has the potential to limit phytoplankton populations on seasonal time scales. A fundamental but unresolved problem associated with aggregation processes is the determination of the "stickiness function", a measure of the ability of particles to adhere to other particles. This leads to an inverse problem associated with a class of nonlinear integro-differential equations. In this dissertation we develop convergence theory for this algal coagulation model utilizing a spline-based collocation scheme within the context of the parameter identification problem. Even though algal species are most directly affected by coagulation, the oceanographic food web is also impacted, at least indirectly, by the aggregation process. To better understand the role of the coagulation process in oceanographic processes, in this dissertation we investigate the dynamics of a structured algal population in the context of a food chain model setting. While our efforts are generic in character, we focus specifically upon diatoms for parameterization. The food chain model incorporates nutrient dynamics as well as the dynamics of grazing. The algal species is modeled according to individual life history describing cell growth and the reproductive process. The estimation of the "stickiness function" using the inverse method yielded remarkable results under ideal conditions (the observed data is identical to the model output). The model simulations demonstrate that the presence of grazers influence algal population dynamics by generating cyclic behavior of aggregate densities and changing the length of the bloom period. The number of living cells in aggregates is also fundamental to the food chain dynamics as increasing numbers of live cells can enhance coagulation.

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