of constant variance of the error term must be re- 

 jected for all cases. The results for blue marlin, trol- 

 ling data for females with 86 and 85 data points, and 

 for striped marlin presented in Figure 3 were rep- 

 resentative of all species plots. Comparing these 

 plots with those in Figure 2 showed that the non- 

 linear model did not fit the data as well as did the 

 log-linear model. Since both assumptions regarding 

 the properties of the error terms were rejected, it 

 must be concluded that the nonlinear model is not 

 appropriate for these sets of data. 



Coefficients of Allometry 



The coefficients of allometry that will be dis- 

 cussed in this section were obtained from the fitting 

 of the log-linear model. For those species and data 

 sets in Table 2 where the assumption of normality 

 of the residuals was rejected, the coefficients of al- 

 lometry were not tested. The hypotheses tested 

 were H^: a = 3.0 and H^: « / 3.0 (a two-sided 

 "t" test), and the results of these tests are pre- 

 sented in Table 4. For small blue marlin and sword- 

 fish, the null hypothesis that a = 3.0 was rejected 



on the basis of the data available. For black marlin, 

 large blue marlin (longline data), female blue mar- 

 lin, sailfish, and shortbill spearfish, the alternate 

 hypothesis that a / 3.0 was rejected on the basis of 

 the data available. 



DISCUSSION 



Weight-length relationships were fitted success- 

 fully for all six species of billfishes appearing in the 

 Honolulu Laboratory's collections (Figs. 4 and 5). 

 The log-linear relationships (Table 2) were found to 

 be more appropriate than the nonlinear relation- 

 ships (Table 3) for every species and data set. The 

 significance of all the relationships was not testable 

 since many of the error terms were not normally 

 distributed; however, the "R^" values indicated 

 that all of the relationships, except for the shortbill 

 spearfish, account for a high percentage of the var- 

 iance in the data. Hence, on the basis of fit and 

 amount of variance accounted for, these relation- 

 ships should be good predictors. 



However, the usefulness of the relationships as 

 predictors also varies according to the amount of 



SWORDFISH 



W^ 2,3296 X 10"' FU^"°* 





 100 



i 20 



1- 

 X 



o 



S 10 



^ 25 



BLACK MARLIN 



150 200 250 300 350 400 200 225 250 275 300 325 350 375 400 



SHORTBILL SPEARFISH 



W= 5 0083 X 10'^ FL 



8 cr. 38136 



oi — 

 130 



140 150 160 170 180 190 125 150 175 200 225 250 275 300 325 



LENGTH (CM) 

 SAILFISH 



W= 2.0739 X IO'fl^^'* 



V^ 



-J ^ L- 



175 200 225 250 275 300 



LENGTH (CM) 



Figure 4. — Weight-length relationships using the log-linear model for swordfish, shortbill 

 spearfish, sailfish, black marlin, and striped marlin. 



134 



