from the tip of the snout to the fork of the tail. 

 Where naris or eye-orbit fork length measures were 

 given, conversion to FL was performed with equa- 

 tions given by Royce (1957). All weight measure- 

 ments were taken to the nearest pound and were 

 converted to kilograms before analysis. 



Two of the data sets were derived from longline 

 catch records taken by research vessels of the Ho- 

 nolulu Laboratory while fishing in central Pacific 

 waters, mostly near the equator. The first of these 

 data sets (deck 1 ) was obtained from a morphometric 

 study of billfishes by Royce (1957) that was carried 

 out on a series oflongline cruises in 1950 to 1953. The 

 second data set (deck 2) was obtained from routine 

 information collected from longline-caught fishes for 

 the years 1950 to 1971. These two longline data sets 

 were combined in the subsequent analyses because 

 they represent the same type of data, though they 

 were collected for different reasons and, in general, 

 do not overlap in time. The last set of data (deck 3) 

 was collected by personnel of the Honolulu 

 Laboratory from fish caught by trolling between 

 1962 and 1971, inJune (once), July, or August during 

 the Hawaiian International Billfish Tournament 

 held in Kailua-Kona, Hawaii (Table 1). Since the 

 five species other than blue marlin were represented 

 in such small numbers in the sample, they were 

 pooled with the longline data. For blue marlin, the 

 trolling-derived data were analyzed separately from 

 the longline-derived data. The longline data repre- 

 sent a pooling over all seasons of oceanic-caught 

 fish while the trolling data represent only inshore 

 catches during the summer months 



All three data sets for most species contained 

 some determinations of sex and maturity, but only 

 the trolling data (deck 3) for blue marlin contained 

 enough information to allow an examination of the 

 sexes separately. All other species and pooled data 

 sets were examined without regard to the sex of the 

 individuals. 



Analysis 



The goal of this paper was to obtain length-weight 

 relationships for each species by using a statistical 

 model that fitted the data best. To accomplish this 

 goal, the steps listed below were followed: 



1 . The data were checked for different growth 

 stanzas by plotting the natural logarithms of 

 weight against the natural logarithms of 

 length. 



2. Length-weight relationships using log-linear 

 regression for weight on length were ob- 

 tained for all species. 



3. The normality of the error terms was tested 

 for those species that had enough data to 

 perform the tests. 



4. The log-linear relationships were tested for 

 their significance. 



5. Length-weight relationships using nonlinear 

 regression of weight on length were ob- 

 tained for blue and striped marlins. 



6. Statistical tests were performed to deter- 

 mine whether the log-linear or the nonlinear 

 model was more appropriate. 



7. The coefficients of allometry were tested to 

 see if they were different from 3.0. 



In subsequent paragraphs, brief discussions will 

 be given regarding adjustments made for the amount 

 of data available for each species, the statistical 

 models themselves, the criteria used to determine 

 best fit, and certain test statistics employed in the 

 analysis. 



As can be seen from Table 1, the amount of data 

 available for most of the species for any data deck 

 was very small. Even after pooling all of the data for 

 the black marlin, sailfish, shortbill speaifish, and 

 swordfish, there were too few data to evaluate the fit 

 of the statistical models. Hence, the most commonly 

 used statistical model, the log-linear, was fitted to 

 these species. Only the significance of the relation- 

 ships was tested. For striped marlin after pooling all 

 data, there were enough data to evaluate the fit of the 

 statistical models. In the analysis of blue marlin, the 

 data were not pooled because we believed that the 

 longline- and troll-derived data represented different 

 biological situations. The longline data were ob- 

 tained from a sampling program that neglected any 

 seasonally varying and sexually different length- 

 weight relationships, whereas the troll data were 

 obtained in the summer season for each sex. To aid 

 in the interpretation of the striped marlin data, the 

 blue marlin data were pooled for comparative pur- 

 poses only. There were enough data to evaluate the 

 fit of the models for all blue marlin data categories. 



As mentioned in the introduction of this paper, 

 fishery biologists, in general, have accepted the ap- 

 propriateness of the allometric growth equation as a 

 descriptor of the growth in weight to the growth in 

 length of fish. As expressed by Equation 1 , this 

 equation is mathematically a functional relationship 

 (Madansky. 1959) where weight is known exactly 



127 



