where «, is the number of individuals belonging to the 

 rth of J" species in the sample, and « is the total number 

 of individuals in the sample. Hill's Nl was used 

 because it is units of numbers of species and is 

 therefore easier to interpret than most other diversity 

 indices. 



All statistical analyses were performed using SAS soft- 

 ware (SAS Institute Inc. 1991). tMI data (except when 

 calculating diversity) were log-transformed prior to 

 analysis. A two-way ANOVA was used to test for 

 differences in meiofauna and macrofauna abundance, 

 biomass and diversity among treatments and sampling 

 dates. Where treatment effects were significant, Tukey 

 multiple comparison procedures were used to find 

 pairwise, a posteriori differences among sample means 

 within a treatment. The Tukey test finds significant 

 differences among sample means, while maintaining 

 the experimentwise error rate {i.e., the probability that 

 one or more erroneous statements wiU be made in an 

 experiment) at 0.05 (Kirk 1982). This mediod, 

 therefore, ensured that study data were not 

 (incorrecdy) analyzed independentiy. 



Community structure of macrofauna species was 

 analy^ied by multivariate methods. TTie species data 

 were prepared for analysis by making a matrix where 

 each row represented an observation of the average 

 number of individuals in each station, or station-date 

 combination, and each column represented a unique 

 species. The data set was multivariate because there 

 were more than one species, which were the response 

 variables for the analysis. A common problem with 

 such matrices is that many of the variables {i.e., 

 columns) covary. The covariance can be either positive 

 (two or more species responding similarly to a stimuli) 

 or negative (two or more species responding in 

 opposite fashion to a stimuli). An example of a 

 positive covariance is when all species increase in 

 response to increased food. An example of a negative 

 covariance is where one species competes with or preys 

 upon another. Complex interactions among multiple 



response variables requires multivariate analysis to 

 illuminate the common patterns in the data set. 



Principal components analysis (PCA) is a multivariate 

 method that is also a variable reduction technique. 

 PCA is a useful tool because it transforms the species 

 data matrix into new variables that can be: 1) mutually 

 orthogonal {i.e., the new variables are uncorrelated to 

 one another) and 2) extracted in order of decreasing 

 variance {i.e., much of the iaformation of the original 

 set, like variance, of variables is concentrated in the 

 first few principal components (PCS)). The PCS can 

 also be used as predictors in regression analysis 

 because they are orthogonal and collinearity {i.e., a 

 linear relationship between variables) does not exist. 

 All multivariate analyses were performed with the 

 SAS FACTOR procedure (SAS Institute Inc. 1991), 

 using the PC method on the covariance matrix. When 

 performing PCA on the covariance matrix, the analysis 

 does not treat all the variables as if they have the same 

 variance. All count or measurement data was log 

 transformed prior to multivariate analysis. 



Results of the PCA are visualized in bivariate plots. 

 Generally, only the first two PC factors (PCI and PC2) 

 are used in the plots. The results are visualized in two 

 ways: as factor patterns and as loading scores. Each 

 data set is simply a matrix {i.e., rows of observations 

 versus columns of variables). The factor patterns are 

 the PC coefficients for each variable or column. These 

 vector patterns were used to interpret what PCI and 

 PC2 represent by plotting the column heading as the 

 symbol for each point. Next, the loading scores for 

 each observation were plotted using the site name as 

 the symbol for each point. The plot of the loading 

 scores allowed visualization of the relationships or 

 correlation among the sampling units, stations in the 

 present study. 



Chapter Five ♦ 5-5 



