Graduation Year

2008

Document Type

Dissertation

Degree

Ph.D.

Degree Granting Department

Mathematics and Statistics

Major Professor

Chris P. Tsokos, Ph.D.

Committee Member

Marcus McWaters, Ph.D.

Committee Member

Kandethody Ramachandran, Ph.D.

Committee Member

Gangaram S. Ladde, Ph.D.

Committee Member

Pamela Hallock Muller, Ph.D.

Keywords

regression model, stony coral, Shannon-Wiener diversity index, Simpson's diversity index, jackknifing, bootstrap, three-parameter lognormal distribution, kernel density estimate

Abstract

Like coral reefs worldwide, the Florida Reef Tract has dramatically declined within the past two decades. Monitoring of 40 sites throughout the Florida Keys National Marine Sanctuary has undertaken a multiple-parameter approach to assess spatial and temporal changes in the status of the ecosystem. The objectives of the present study consist of the following:

In chapter one, we review past coral reef studies; emphasis is placed on recent studies on the stony corals of reefs in the lower Florida Keys. We also review the economic impact of coral reefs on the state of Florida. In chapter two, we identify the underlying probability distribution function of the stony coral cover proportions and we obtain better estimates of the statistical properties of stony coral cover proportions. Furthermore, we improve present procedures in constructing confidence intervals of the true median and mean for the underlying probability distribution.

In chapter three, we investigate the applicability of the normal probability distribution assumption made on the pseudovalues obtained from the jackknife procedure for the Shannon-Wiener diversity index used in previous studies. We investigate a new and more effective approach to estimating the Shannon-Wiener and Simpson's diversity index.

In chapter four, we develop the best possible estimate of the probability distribution function of the jackknifing pseudovalues, obtained from the jackknife procedure for the Shannon-Wiener diversity index used in previous studies, using the xi nonparametric kernel density estimate method. This nonparametric procedure gives very effective estimates of the statistical measures for the jackknifing pseudovalues.

Lastly, the present study develops a predictive statistical model for stony coral cover. In addition to identifying the attributable variables that influence the stony coral cover data of the lower Florida Keys, we investigate the possible interactions present. The final form of the developed statistical model gives good estimates of the stony coral cover given some information of the attributable variables. Our nonparametric and parametric approach to analyzing coral reef data provides a sound basis for developing efficient ecosystem models that estimate future trends in coral reef diversity. This will give the scientists and managers another tool to help monitor and maintain a healthy ecosystem.

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