Models and methods in analysis problems of Shannon-Wiener diversity index for coral reefs ecosystems

Armando J.Hoare

University of South Florida

St. Petersburg, FL 33701, USA

Chris P.Tsokos

University of South Florida

Tampa, FL, 33620, USA

The objective of the present study is to perform parametric and non-parametric analysis of the Shannon-Wiener diversity index results of actual environmental data collected in the Florida Keys. We used the Jackknifing procedure to increase the information on the Shannon-Wiener diversity index. Previous analysis of the subject data assumed that it followed the Gaussian Probability Distribution when in fact that assumption cannot be justified. In the present study we utilized nonparametric kernel density estimate to analyze the data and compare to the results obtained under the non-justifiable assumption of normality.

Coral reef communities are very important ecosystems of the world. They are home to at least 4,000 species, or almost a third of the world's marine fish species. Paulay, Hinrichsen wrote that the Great Barrier Reef of Australia boasts 400 species of coral providing habitat for more than 1500 species of fish, 4000 different kinds of mollusks, and 400 species of sponges. It is important in maintaining a healthy reef system. This led to creation of the Florida Keys National Marine Sanctuary Protection Act (HR5909) which designated over 2,800 square nautical miles of coastal waters, south of Miami to the Tortugas Banks off the state of Florida, as the Florida Keys National Marine Sanctuary (FKNMS). In an effort to monitor the coral reef system in this sanctuary region, the Coral Reef Evaluation and Monitoring Project (CREMP) was established and supported by U.S. Environmental Protection Agency. Through this project, 40 sites within FKNMS were identified and from these sites 160 stations were established for annual sampling starting in 1996. Presently there are only 37 sites with 103 stations in what we will refer as the sanctuary region. In 1999, three sites with 12 stations were established in what is known as the Dry Tortugas region.

The data we used in this present study are coming from the sanctuary region of this project. Many environmental variables are collected annually from the stations within the sanctuary. The data variable of interest for this study is the stony coral species count. The main purpose of collecting species data is to monitor the status of the reef. One measurement that attempts to quantify the status of the reef is the diversity index of coral species that inhabit it. Many scientists believe diversity is an indicator of the stability of the ecosystem (Xu, Hayek and Buzas, Datta and Jana, Foggo, Jorgensen). The concept of the diversity index is the measurement of the number of species and the spread of these species in their habitat.

We will focus on the Shannon-Wiener diversity index. Shannon-Wiener diversity index is a measure of the uncertainty that an individual in an ecosystem belongs to a certain species.

 

The maximum value of the Shannon-Wiener diversity index for a fixed set of species is obtained whenever each species has the same abundance. This creates the most uncertainty of knowing which species an individual in the habitat belongs to. On the other hand, if a habitat is dominated by a few species, then the uncertainty of knowing which species an individual belongs to becomes low. This means that the higher the number of species and the more evenly distributed their abundance, the higher the Shannon-Wiener diversity index will be. Thus it is very important that a good estimate of the true Shannon-Wiener diversity index is obtained for CREMP and for any environmental system under study. Another important requirement is the ability to statistically analyze the diversity index. This is a difficult task since from each data set we can only calculate one value for the Shannon-Wiener diversity index. For CREMP this meant that there was just one Shannon-Wiener diversity index for the sanctuary region per year. This meant that it was impossible to construct any confidence interval for the true value of the Shannon-Wiener diversity index.

Zahl proposed that the Jackknifing procedure can be applied when calculating the Shannon-Wiener diversity index from sampling frame that records species count per some unit area. This procedure produces as many Shannon-Wiener like diversity index values, as there are unit areas. These values are known as pseudovalues of the index, for which Zahl claims that they are independently and normally distributed.

We have shown that the Gaussian kernel density estimate is clearly a much better fit to the jackknifing pseudovalues compared to the normal probability distribution and other continuous probability distributions. A good estimate of the true probability structure of the pseudovalues data is imperative for sound decision making. The estimates of the statistical properties of the data obtained from the Gaussian kernel density estimate are different than the ones from the normal probability distribution.

The results presented in this paper can help to analyze and interpret the Shannon-Weiner diversity index of the stony coral for CREMP. A better understanding of the underlying probability distribution of the jackknifing pseudovalues can enhance the advantages of using the jackknifing method in obtaining a good estimate of the Shannon-Wiener diversity index and providing data that can be used in the statistical analysis and interpretation of the Shannon-Wiener diversity index. Furthermore, we have shown that one cannot just assume that the pseudovalues obtained from the jackknifing procedure are normally distributed as suggested by Zahl. This assumption can lead to obtaining false information.