A-13 



Distributional patterns of faunal assemblages were 

 studied by analyzing the degree of species similarity between 

 samples. This type of community analysis is usually re.f erred 

 to as Q-mode analysis (Poole, 1974). For this type of analy- 

 sis 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 contri- 

 butes equally to the analysis. It should be noted that this 

 normalization 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 

 postmultiplying the now-normalized data matrix by its trans- 

 pose. This statistic ranges from zero when samples are very 

 dissimilar (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 variance accounted for by successive axes) and 

 eigenvectors (composite-species axes defining faunal 

 assemblages) . The method allows for the fewest possible 

 assemblages describing the maximum amount of the data, by 



