14. 



by analyzing the degree of species similarity between samples. 

 This type of community analysis is usually referred to as 

 Q-mode analysis (Poole, 1974) . For this type of analysis the 

 sample compositions are normalized to a standard unit length, 

 so that the sum of squares of the species abundances within 

 each sample is one. As a result each sample contributes 

 equally to the analysis. It should be noted that this normaliz- 

 ation of the data does not change the proportional contribution 

 of the species to the sample composition. 



The cosine-theta statistic was used as a measure of 

 sample similarity. This measure can be visualized as the 

 cosine of the angle between sample vectors, where the vectors 

 are a geometrical representation of the samples' species com- 

 position in a hyperspace having dimensions equal to the number 

 of species. The cosine-theta statistic is computed by post- 

 multiplying the row-normalized data matrix by its transpose. 

 This statistic ranges from zero when samples are very dis- 

 similar (forming a large angle) to unity when the samples are 

 identical (forming a small angle) . The cosine-theta matrix 

 was then analyzed for its eigenvalues (amounts of the sample 

 accounted for by successive axes) and eigenvectors (composite- 

 species axes defining faunal assemblages) . This method allows 

 for the fewest possible assemblages describing the maximum 

 amount of the data, by constructing new component species 

 axes so that each successive axis accounts for the greatest 

 fraction of the remaining total sample variance. 



