Douglas et al : Geographic variation in cranial morphology of Stenella longirostns 



57 



tude blocks, with each geographic block given a 

 numerical code (see Fig. 1). We had specimens from 

 35 blocks, although 10 were represented by only a 

 single specimen; the other 25 blocks were used as the 

 basis for most analyses of geographic variation. While 

 several of the remaining 25 blocks are represented by 

 relatively small samples, tests for geographic pattern- 

 ing (described below) suggest that, in general, sample 

 values are representative of what would be expected 

 for these blocks based on their geographic positions. 

 The 5° block size was selected, in part, because it was 

 judged that available sample sizes would not permit 

 detailed analysis of smaller geographic units. Further- 

 more, migratory movements and related factors were 

 less likely to significantly influence results when these 

 relatively large sampling areas were used. 



Douglas et al. (1986) showed that 5. longirostris in 

 the eastern tropical Pacific was sexually dimorphic for 

 13 of 36 characters. Because some specimens used in 

 that analysis were removed and new specimens added 

 (see above), we reanalyzed the data with a two-way 

 analysis of variance (ANO VA) for block and sex based 

 on specimens in 10 blocks that had at least four of each 

 sex (Fig. 1). We then produced a series of correction 

 terms to adjust measurements of the larger sex down- 

 ward and the smaller sex upward, thus producing sex- 

 adjusted or "zwitter" measurements (for details on this 

 adjustment, see Schnell et al. 1985a). These corrections 

 enabled us to combine specimens for both sexes in an 

 overall analysis of geographic variation. 



Correlation, ordination and clustering 



After conversion to zwitters, characters were then 

 standardized so that means for blocks were zeros and 

 standard deviations ones. Product-moment correlations 

 were computed among characters, and the general 

 associations among characters were summarized by 

 clustering characters using the unweighted pair-group 

 method with arithmetic averages (UPGMA). 



This type of hierarchical cluster analysis also was 

 performed to summarize average distance coefficients 

 (Sneath and Sokal 1973) calculated for all pairs of 

 blocks based on standardized data. Cophenetic correla- 

 tion coefficients were computed to indicate the degree 

 to which distances in the resulting dendrogram accu- 

 rately represented original interblock morphologic 

 distances. 



In addition, we analyzed standardized data using a 

 nonhierarchical /T-group method called function-point 

 cluster analysis (Katz and Rohlf 1973; described in 

 Rohlf et al. 1979). Blocks are assigned to a series 

 of subgroups at a specified level. The value for the 

 w-parameter used by the function-point clustering 

 method was varied. A hierarchical (but not necessar- 



ily non-overlapping) system of clusters can be obtained 

 by conducting the analysis at more than one cluster- 

 ing level. Results are presented in the form of a modi- 

 fied skyline diagram (Wirth et al. 1966) where, for a 

 given w-value, blocks joined in a common line are in 

 the same cluster. 



Based on standardized data, we constructed scatter 

 diagrams of blocks projected onto the first two prin- 

 cipal components (Sneath and Sokal 1973) extracted 

 from a matrix of correlations among the 30 characters. 

 Canonical variates analysis also was applied to deter- 

 mine the subset of variables that show the greatest 

 degree of geographic variation— in this case, those that 

 provide the greatest interblock separation relative to 

 the degree of intrablock variation (Program P7M of 

 BMDP; Dixon 1990). Plots of the first two canonical 

 variables show the maximum separation of blocks in 

 two-dimensional space. The original variables, which 

 in combination exhibited maximum interblock variabil- 

 ity, were then subjected to additional analyses. 



Mantel test for geographic patterning 



Using a test devised by Mantel (1967) and described 

 by Sokal (1979), we analyzed interlocality variation in 

 each character to determine whether values are geo- 

 graphically patterned, or vary spatially at random. This 

 procedure enabled us to determine whether differences 

 in character values between all pairs of samples are 

 statistically associated in a linear manner with corre- 

 sponding geographic distances. The observed asso- 

 ciation between sets of character differences and 

 geographic distances was tested relative to its permu- 

 tational variance, and the resulting statistic was com- 

 pared against a Student's i -distribution with infinite 

 degrees of freedom. Computations were performed 

 using GEOVAR, a library of computer programs for 

 geographic variation analysis written by David M. 

 Mallis and furnished by Robert R. Sokal (State Univer- 

 sity of New York at Stony Brook). 



Character differences were compared first with ac- 

 tual geographic distances (in nautical miles) between 

 centers of blocks and then wath reciprocals of distances. 

 In evaluations of reciprocals, where distances are 

 scaled in a nonlinear manner, longer distances are con- 

 sidered effectively to be equal, and the portion of the 

 scale involving smaller distances is expanded. Thus, use 

 of reciprocals of distances increases the power of anal- 

 yses to reveal geographic patterns that are "local" in 

 nature (i.e., involving closely placed blocks), whereas 

 tests involving nautical-mile distances evaluate 

 "regional" trends. Positive associations of character 

 differences and nautical-mile distances are indicated 

 by positive i -values, while negative ^-values denote such 

 associations when reciprocals of distances are used. 



