Length-weight, length-to-length, and weight- 

 to-weight relationships are necessary in popula- 

 tion analyses for converting one measurement to 

 another. In this paper I present the relationships 

 o*" the following: round weight-straight fork 

 length, round weight-dressed weight, and straight 

 fork length-curved fork length. 



During my review of bluefin tuna literature, I 

 found a lack of information on size relationships. 

 Mather and Schuck (1960) used a length-weight 

 curve based on 778 bluefin tuna from Cape Cod to 

 estimate length. They did not indicate, however, 

 when these fish were collected. They did not give a 

 regression formula for the length-weight relation- 

 ship, but they did present a straight length-curved 

 length relationship based on 185 measurements 

 fitted by inspection. Rodriguez-Roda (1964, 1971) 

 collected 793 bluefin tuna and then determined 

 the length-weight relationship. Of these, 467 

 bluefin tuna (prespawning) were entering the 

 Mediterranean during May and June and 326 

 bluefin tuna (postspawning) were leaving the 

 Mediterranean during July and August 1956, 

 1958, 1959, and 1961. Butler (1971) determined 

 the length-weight relationship by the standard 

 least squares regression method for 237 giant 

 bluefin tuna caught during July through Sep- 

 tember 1966 from Conception Bay, Newfound- 

 land. Mather et al. (1974) presented regression 

 equations for converting from weight to length for 

 bluefin tuna from Newfoundland, Libya, and the 

 Bahamas from data supplied by the Fisheries Re- 

 search Board of Canada, the International Council 

 for the Exploration of the Sea, and the Woods Hole 

 Oceanographic Institution. They also presented 

 an equation for converting dressed weight to 

 round weight. The method of determining the 

 equations, the sample sizes, and time period sam- 

 pled were not presented. Coan (1976) gave a 

 length, weight, and age conversion tablefor bluefin 

 tuna of both sexes. He converted length to weight 

 based on a length-weight regression given in 

 Sakagawa and Coan (1974), who had in turn, ob- 

 tained this regression from Frank J. Mather, 

 Woods Hole Oceanographic Institution. Unfortu- 

 nately, there was no mention of sample size, loca- 

 tion, or date. 



Methods 



Bluefin tuna length and weight measurements 

 were collected during 1974 through 1977 from var- 

 ious landing points and processing plants along 



996 



the east coast of the United States from Florida to 

 Maine and from the Bahamas. These fish had been 

 caught by purse seine, rod and reel, handline, and 

 harpoon. Straight fork length (centimeters) was 

 measured by caliper, and curved fork length (cen- 

 timeters) was measured along the body contour by 

 tape. Round weight (total weight of fish when 

 caught) and dressed weight (head, viscera, and tail 

 removed) were recorded in pounds and later con- 

 verted to kilograms. 



Ricker ( 1973) showed that the geometric mean 

 (GM) regression can be used for a majority of 

 biological situations as a reasonable and consis- 

 tent estimate of the functional slope because most 

 of the variability is natural. 



The functional (GM) regression was calculated 

 for the. logarithmic transformation of the length- 

 weight relationship for 3,578 bluefin tuna taken 

 from May through October. The GM regression 

 was also calculated for the relationship between 

 round weight and dressed weight for 685 bluefin 

 tuna taken from July through September, and for 

 the straight fork length to curved fork length rela- 

 tionship for 606 bluefin tuna taken from July 

 through October. 



The general equation for the GM regression as 

 given by Ricker is: Y = u + vX, with variables X 

 and J^, and u is they-axis intercept, where u =Y 

 - vX, V is the slope, and v = [1y^l1x^\^. where y 

 = y, - y and X = Z, - X. The limits on all i are 

 i = \, . . . , n. 



The standard error of the slope was computed for 

 each regression equation using the following equa- 

 tion from Ricker (1973): S, = [S^^'^I^'^W where 

 Si, is the standard error of the slope and 

 Svj ^ is the mean square or variance of the obser- 

 vations from the regression line in the vertical 

 direction. 



Results and Discussion 



Based on the classification system of Rivas and 

 Mather (in press), the fish sampled mainly con- 

 sisted of two size categories, giant bluefin tuna 

 ( >180 cm straight fork length and 130 kg round 

 weight) and small bluefin tuna ( < 130 cm straight 

 fork length or '45 kg round weight). Based on 

 previous growth studies by Mather and Schuck 

 (1960), the giant fish are probably age 9 and older 

 and the small bluefin tuna are most likely age 4 or 

 younger. Very few medium bluefin tuna ( 130-180 

 cm straight fork length and 45-130 kg round 

 weight) probably ages 5 through 8 were sampled. 



