Table 1.— Analysis of covariance of length-weight relation of 

 yellowfin tuna. 



Source 



Degrees of Sum of Mean 



freedom squares square F-value 



Categories 



Samples witfiin categories 



Residual 



Total 



24 1.321851 0.0550771 3.4115* 



128 2.066484 0.0161444 6.7748" 



3,485 8.304751 0.0023830 



3.637 11693086 



'Significant at ^°c level. 



Table 2. — Analysis of covariance of length-weight relation of 

 skipjack tuna. 



Source 



Degrees of Sum of Mean 



freedom squares square F-value 



Categories 20 2.560355 0.128018 5.0189- 



Sample within categories 84 2.142605 0.0255072 7.3030* 



Residuals 2,448 8.550099 0.0034927 



Total 2,552 13.253059 



"Significant at 1% level. 



1% level. The F-value for difference among 

 samples within a category is greater than that 

 among categories. Table 2 presents results for 

 skipjack tuna. Again the F-value is statistically 

 significant at the 1% level, and the F-value among 

 samples within categories is greater than that 

 among categories. The reasons for the differences 

 are not known. Although there was considerable 

 overlap of sizes of fish encountered among the 

 samples, size composition of the samples did differ 

 and may have contributed to the differences in 

 the length-weight relations because Equation (1) 

 may not perfectly describe the length-weight 

 relation for fish of all sizes. Figure 2 illustrates 

 the variability found in the length-weight 

 relations of yellowfin tuna. The variability among 

 the relations increases with size as Equation (1) 

 assumes. 



Statistics of length-weight relations from 

 combined samples for each species are presented 

 in Table 3. 



Discussion 



Length-weight relations for yellowfin tuna from 

 the Pacific (Chatwin, 1959), from the Atlantic 

 (Poinsard, 1969), and from the present study are 

 illustrated in Figure 3. There is reasonably close 

 agreement among the three curves at small sizes. 

 The Pacific yellowfin tuna appear to be heavier 

 at larger sizes than fish from the Atlantic, but 

 Chatwin did not include fish larger than 115 cm 

 in his work. Two relations are used in Poinsard's 

 work. A relation between fork length and predor- 



/ /,/ 



90. 6 112.5 



FORK LENGTH (cm.) 



Figure 2. 



-Estimated length-weight relations for all sample 

 categories of Atlantic yellowfin tuna. 



sal length and one between predorsal length and 

 weight. Poinsard tried several functions to ex- 

 plain the relations. In the case of fork length and 

 predorsal length he chose the following function: 



(2) 



LD^ = -16.58774 + 4.66294 JL 

 where LD^ = predorsal length 



He based his choice on the fact that Equation 

 (2) resulted in the highest value of r (correlation 

 coefficient) of the several functions he tried. The 

 value of r when Equation (2) was used was 

 0.99402, but when a power relation similar to 

 Equation (1) was used the value of r (0.99386) is 

 only slightly less. Figure 3 is based on the square 

 root relation between fork length and predorsal 

 length as recommended by Poinsard. It is very 

 difficult, however, to interpret differences be- 

 tween r values when different dependent vari- 

 ables are used: predorsal length in one case, log 

 (predorsal length) in the other. Equation (2) seems 

 a poor choice because it implies that LD^ < 

 when L < 12.65. The estimated weights using 

 Poinsard's logarithmic relation are illustrated in 

 Figure 4 — the two curves are very similar for 

 all lengths. This similarity indicates that the 

 results of Poinsard and of this study are accurate 

 estimates of the average length- weight relation- 

 ship of eastern tropical Atlantic yellowfin tuna. 



849 



