FISHERY BULLETIN: VOL. 74, NO. 3 



auction blocks of the fresh fish markets in Hono- 

 lulu, the staff of the Honolulu Laboratory, Na- 

 tional Marine Fisheries Service, NOAA, collected 

 weight and sex data from large pelagic species 

 caught by the Hawaiian longline fleet. Details of 

 the longline fishery are given by June (1950) and 

 Otsu (1954). All fish were weighed to the nearest 

 whole pound. Due to the nearly complete utiliza- 

 tion of marlin by the dealers, only a small incision 

 could be made in the abdominal wall in order to 

 examine the gonads. At best, a small section of 

 gonad could be cut off and examined; no micro- 

 scopic determinations were made. Thus, it is possi- 

 ble that some misidentification of the sex of these 

 fish occurred, especially preceding sexual maturity 

 for both species and following spawning for blue 

 marlin. 



METHOD OF ANALYSIS 



Briefly, the analyses consisted of 1) transform- 

 ing the data into usable form by (a) calculating 

 length-weight relationships using functional re- 

 gressions (Ricker 1973), (b) converting weights to 

 lengths, and (c) grouping the lengths by sex, 

 quarter, year, and length interval; 2) separating 

 age-groups from the frequency distributions and 

 estimating their mean lengths; 3) setting up the 

 progressions of mean lengths and corresponding 

 age structures; and 4) fitting von BertalanfTy 

 growth models to the progressions of mean 

 lengths. Following these steps, tests were per- 

 formed to determine whether the yearly samples 

 were homogeneous and could be pooled. These 

 tests consisted of a series of nonparametric 

 Friedman two-way analyses of variance (Hol- 

 lander and Wolfe 1973:139) performed on the 

 number of age-groups, the mean lengths of age- 

 groups, and the percent representation of age- 

 groups separated for each year sampled, as well as 

 on the growth parameters of the different cohorts. 

 Also, a sign test (Siegel 1956:68) was used to test 

 for trends in mean length between sexes; and a 

 series of one sample runs tests (Siegel 1956:52) was 

 used to test for trends in mean length among 

 cohorts. If heterogeneity was not found, the 

 transformed yearly data were pooled, that is, the 

 year designation was ignored, and steps 2-4 above 

 were repeated on the pooled data. 



An initial inspection of the blue marlin length- 

 frequency distributions revealed some unusually 

 large specimens identified as males weighing up to 

 328 kg, whereas it had been contended that male 



blue marlin in the Atlantic (Erdman 1968) and in 

 the Pacific (Strasburg 1970) do not exceed about 

 136 kg. An examination of data collected under 

 ideal sampling conditions at Hawaiian Interna- 

 tional Billfish Tournaments revealed only 5 out of 

 385 individuals in 12 yr that exceeded 136 kg. Four 

 of these were under 143 kg while one fish weighed 

 171 kg. On the basis of these data, we accepted 

 Erdman's and Strasburg's contention as essen- 

 tially correct, assumed that all males over 143 kg 

 were misidentified due to the difficult sampling 

 conditions at the auction sites, and reclassified all 

 males over 143 kg as females (56 were reclassified 

 out of 2,710 specimens originally classified as 

 males). 



Transformation of Data 



Observed weights were converted from pounds 

 to kilograms and then to fork lengths in cen- 

 timeters (tip of bill to middle point on the posterior 

 margin of the middle caudal rays, FL). Length- 

 weight relationships used for the latter conver- 

 sions were calculated as functional regressions 

 from Skillman and Yong (1974) following the 

 recommendations of Ricker (1973). Briefly, the 

 differences between functional and the commonly 

 used predictive (linear) regressions, which are of 

 importance to this application, are as follows. 

 First, the predictive regression applies where it is 

 hypothesized that one variable is linearly related 

 to or dependent on a second variable, the in- 

 dependent variable. Whereas, the functional re- 

 gression applies where it is hypothesized that two 

 variables are interdependent, and the effect of one 

 cannot be disentangled from the effect of the 

 other. Second, the predictive regression tends to 

 systematically underestimate the magnitude of 

 the regression coefl^cient as the sample range 

 truncates the real range of the variates; the 

 functional regression does not do so. For striped 

 marlin, the data were insufficient to calculate 

 functional length-weight relationships for each 

 sex; therefore, a single relationship [FL = 73.4429 

 W 28o8) ^^.gg applied to each sex separately. For 

 blue marlin, separate functional length-weight 

 relationships were calculated (-^-^female = 

 65.4502 W 0-3030^ ^nd FLmale = 56.8780 W "-^^is). 

 As expected, the coefficients of allometry calculat- 

 ed using functional regressions increased over 

 those calculated in Skillman and Yong (1974) using 

 predictive regressions, and the difference between 

 sexes decreased by 36%. 



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