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construct a calibration model for that environmental variable (ter 

 Braak 1987). 



Principal components analysis is a linear ordination method in 

 which species demonstrate a linear response over the ordination axes 

 and species coefficients, called eigenvectors, are calculated as slopes 

 of those lines. In weighted averaging methods, which include 

 detrended correspondence analysis (DCA), species are assumed to 

 respond in a modal fashion over the ordination range, and 

 coefficients are equal to the center or optimum of their distribution 

 curve along the range of ordination values (ter Braak 1987). CANOCO 

 is an extension of DCA that also assumes a modal species distribution 

 over ordination axes (ter Braak 1987). 



Reciprocal averaging (RA), or factor correspondence analysis, is 

 an extension of principal components. Hill and Gauch (1980) 

 compared RA and DCA and concluded that DCA was a better method. 

 A main fault they cite with RA is that the second ordination axis 

 demonstrates an 'arch effect' that is a mathematical artifact relating 

 to no real structure in the data. Charles (1985), for instance, 

 observed this arch effect in his study of diatom communities of 

 Adirondack lakes and found it made ecological interpretations 

 difficult. A second fault of RA is that it does not preserve ecological 

 distances between species along the ordination axes (Hill and Gauch 

 1980). Anderson et al. (1990) have presented, on the other hand, an 

 argument that RA is a preferred method over DCA because DCA 

 destroys spatial relationships between successive samples that is 

 necessary to demonstrate a time trajectory of community response in 



