group, as indicated by the 95% confidence circles for 

 population centroids (Fig. 3). Although there is notice- 

 able overlap of individuals, particularly of fish from 

 Mexico and Ecuador, the fish of the eastern Pacific 

 (Mexico and Ecuador) are fairly distinct from those of 

 the central (Hawaii) and western Pacific (Australia and 

 Japan). The samples from Japan and Hawaii appear to 

 be more similar than those from Australia and Japan. 

 The canonical variate analyses suggest that size- 

 adjusted morphometric characters are useful for the 

 delineation of yellowfin tuna groups. I then used step- 

 wise discriminant function analysis to identify the most 

 useful characters and to estimate the classification 

 function. The stepwise analysis revealed that 11 of the 

 12 adjusted morphometric characters contributed 

 significantly to the multivariate discrimination of the 

 five groups of fish (Table 4). The approximate F 

 statistic computed from Mahalanobis D 2 indicates a 

 significant difference among the five groups (i^o.os = 

 40.77, df 44, 1585.8, P<0.01). The correct classification 

 rates estimated from the holdout procedure for the 

 11-variable discriminant function ranged from 61.5 to 

 95.3%, with an overall rate of 77.6%, which is 72.0% 

 (x) better than would have occurred by chance (95% 

 confidence intervals: 67.0%<k<77.0%). 



Pectoral fin length (PFL) is the single most useful 

 character for distinguishing yellowfin tuna from the 

 five groups (Fig. 4). Yellowfin tuna from Mexico and 

 Ecuador can be distinguished from one another and 

 from those from Australia, Japan, and Hawaii by this 

 character alone (Newman-Keuls multiple range test). 

 In addition to shorter PFL of fish from the eastern 

 Pacific, the second dorsal fin length and anal fin length 

 are shorter, relative to those of fish from Australia, 

 Japan, and Hawaii. Head length, however, is shorter 

 for fish from the western Pacific. 



Because I was interested in improving the ability to 

 delineate fish from Mexico and Ecuador, morphometric 

 characters of these fish were readjusted and subjected 

 to a second stepwise discriminant analysis. The com- 

 mon within-group slopes were used to adjust the mor- 

 phometric characters to those expected for the overall 

 mean total length for these two groups, employing the 



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JJ /" N H JE M E EE E M 



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-6-5-4-3-2-10123456 

 CANONICAL VARIABLE 1 



Figure 3 



Plot of individuals, group centroids, and 95% confidence circles 

 for population centroids on canonical variables 1 and 2 for the 

 five groups of yellowfin tuna, based on 12 adjusted mor- 

 phometric characters. Symbols for individual fish: M = Mexico, 

 E = Ecuador, A = Australia, J = Japan, H = Hawaii. Overlap 

 of individuals from different groups is indicated by asterisks. 

 Symbols for group centroids: 1 = Mexico, 2 = Ecuador, 3 = 

 Australia, 4 = Japan, 5 = Hawaii. 



previous formula. The regression of the discriminant 

 function score against total length was not significant 

 (P = 0.37), indicating that size effects had been removed 

 by the adjustment procedure. The frequency distribu- 

 tion of the canonical variable (Fig. 5) shows fairly good 

 separation into the two groups, with only a small 

 amount of overlap. Results of the stepwise discriminant 

 analysis are presented in Table 5. The correct classifica- 

 tion rate for the fish from Mexico and Ecuador was 

 81.3% and 88.5%, respectively, with an overall rate of 

 84.6%, which is 69.3% (x) better than would have oc- 

 curred by chance (95% confidence interval: 58.3% 

 <x<80.3%). Fish from the two groups were signifi- 

 cantly different (F . 05 = 40.00, df 6,162, P<0.01). 



