Reilly and Fiedler: Interannual variability of dolphin habitats 



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nique when species have bell-shaped response curves 

 or surfaces with respect to environmental gradients 

 (Ter Braak, 1986), which is consistent with general 

 ecological knowledge (e.g.Whittaker et al., 1973). The 

 models and algorithm used in the CANOCO imple- 

 mentation of canonical correspondence analysis are 

 documented in Ter Braak ( 1986). 



As part of the species-environment ordination, 

 CCA estimates a series of site scores (here, site=day) 

 that are linear combinations of the environmental 

 variables that maximize the species-environment 

 correlation. One set of site scores is estimated for 

 each canonical ordination axis. The interpretation 

 of environmental patterns represented by the axes 

 is made from the correlation coefficients and the 

 multiple regression or "canonical" coefficients of the 

 original environmental variables with the canonical 

 axes (Ter Braak, 1986). 



The results of canonical correspondence can be best 

 interpreted from an ordination "biplot," on which 

 species and sites can be represented by points and 

 environmental variables by arrows. The biplot dis- 

 plays the mean species scores or "optima" on two 

 canonical axes, usually the first two, which explain 

 the majority of the variance. The directions and rela- 

 tive lengths of the arrows for environmental vari- 

 ables represent their contributions to the ordination. 

 More important environmental variables are there- 

 fore represented by longer arrows. In making biplots 

 we used Hill's scaling (Ter Braak, 1986) in which site 

 scores were computed as weighted averages of spe- 

 cies scores (S=-l in our implementation of CANOCO). 



Community ordination was not our primary objec- 

 tive, but we used CCA for three reasons. It provides 

 a quantitative definition of habitat for each species/ 

 stock in reduced dimensionality. The method esti- 

 mates habitats using a nonlinear, unimodal model, 

 avoiding the unrealistic assumption of a linear rela- 

 tionship between animal abundance and environ- 

 mental gradients. CANOCO is also insensitive to a 

 high frequency of zero observations (Ter Braak, 

 1985), typically found in animal survey data. 



In assessing the contributions of environmental 

 variables we took the liberal approach of retaining 

 variables unless their contribution to the ordination 

 was almost entirely encompassed by other, more in- 

 fluential variables. That is, a variable of marginal 

 significance was not excluded if the apparent direc- 

 tion of its influence was different from the other en- 

 vironmental variables. Precision in estimating ca- 

 nonical coefficients was not compromised by retain- 

 ing these marginal variables because we had 956 

 cases and a maximum of only 13 environmental vari- 

 ables (considering years as five dummy variables). 

 We did not use stepwise procedures, which appear 



to offer an objective approach to variable selection, 

 but are notoriously problematic for other reasons (e.g. 

 Pimentel, 1979, p. 42-43). 



We examined the importance of interannual vari- 

 ability in two related ways. First, as noted above, we 

 included years as categorical explanatory variables, 

 in addition to the oceanographic variables. The im- 

 portance was then gauged by comparing ordination 

 results to those with just the oceanographic variables. 

 Second, we removed the variance associated with the 

 environmental variables (by defining them as 

 covariables), and then extracted axes associated with 

 variance among years, to test for interannual differ- 

 ences in the species data not associated directly with 

 interannual environmental variation. 



The significance of an ordination axis was deter- 

 mined by testing the null hypothesis that its eigen- 

 value was not different from zero. The procedure used 

 was a Monte Carlo randomization test (e.g. Hope, 

 1968) supplied with the program CANOCO. This 

 procedure randomly associated sets of environmen- 

 tal variables from one case with sets of species data 

 from another, then extracted canonical axes, and 

 estimated their eigenvalues. The procedure was run 

 1,000 times to produce a reference set of eigenvalues 

 representing random variability. The significance of 

 the eigenvalues from the original data was deter- 

 mined by comparison to these distributions. 



We extended the use of canonical correspondence 

 analysis in two ways for our study of interannual 

 variation in cetacean habitats. First, we mapped the 

 spatial distributions of the site scores from the first 

 two CCA axes, lightly smoothed and contoured. We 

 then plotted the localities of cetacean sightings over 

 these contours to allow visual appraisal of species- 

 environment patterns. We did this as an alternative 

 to plotting species and hundreds of sites together on 

 a biplot, which we found to be uninformative. Sec- 

 ond, we suggest two ways in which the results of the 

 canonical correspondence analysis can be used in the 

 monitoring of trends in cetacean abundance. 



Results 



Table 3 gives the weighted correlation matrix for the 

 six oceanographic variables, the four species axes and 

 four environmental axes from the CCA. The "spe- 

 cies-environment" correlations are the values for 

 equivalent axes, e.g. the correlation between the 

 dominant species axis (no. 1) and the first environ- 

 mental axis is 0.67. The correlation between the sec- 

 ond axes is 0.42, and so on. 



The ordination including the six oceanographic 

 variables explained 14.7% of the variance in the dol- 



