COMPAEISON OF YELLOWFIN TUNA OF HAWAIIAN WATERS AND THE AMERICAN WEST COAST 359 



result is similar to that obtained from Central 

 American and African yelIo\\'fin tuna (Schacfer 

 1948, Schaefcr and Walford 1950) and illustrates 

 again the generalization that, owing to dif- 

 ferential growth rates, comparison of dimensions 

 expressed as ratios is invalid for yellowfin tuna. 



Also similar to previous Central American and 

 African results, is the finding that the growth of 

 the pectoral fin of Hawaiian yeUowfin tuna is 

 such that over the entire range of sizes available 

 in our sample, the relation between length of fin 

 and total length is well described by the equation 



2/=491.9 log x-1184, 



a linear regression giving a good fit to the length 

 of fin plotted against logarithm of total length. 

 The regression statistics are given in table 2. 



For Central American and African fish, the 

 lengths of second dorsal and anal fins plotted 

 against total length were found to be fitted by an 

 equation of the type y=az^, so that a linear 

 regression was obtained by plotting logarithms 

 of fin length against logarithms of total length. 

 The sizes of fish involved were from about 50 cm. 

 to 160 cm. in total length for the fish from both 

 regions. For Hawaiian yellowfin tuna, a linear 

 relation between logarithm of fin length and loga- 

 rithm of fish length provides a fairly good fit over 

 the range of sizes 60 cm. to 178 cm., but when 

 smaller sizes are included, the regression is ob- 

 viously curvilinear (fig. 2 and 3). Linear-regres- 

 sion equations were fitted, for comparative 

 pm-poses, only to the data for fish 60 cm. and over 

 in total length, the results being tabulated in table 

 2. To provide a reasonable fit to the data for 

 all sizes, however, the second-degree polynomials 

 illustrated in the figures were fitted, the equations 

 being, for logarithms of length of second dorsal 

 (?/i) on logarithm of total length (xi), 



2/, = 7.64965-5.59555j-, + 1.26613x,2 s=. 05238 



and for logarithm of length of anal (y,) on loga- 

 rithm of total length (Xi) 



2/i = 4.79192-3.82511z, + 0.99707xi2 



s=. 03607 



It is obvious that the relative rates of gi'owth 

 of the second dorsal and the anal fins accelerate 

 very rapidly with increase in size of fish, the large 

 fish having, relatively, enormously longer fins. 



The equation y = ax*' was found to provide a 

 good fit to our Hawaiian data over the entire 



998351 — 52 2 



range of sizes for length of longest dorsal spine (the 

 fu-st spine in each specimen) and length of longest 

 dorsal finlet relative to total length, the loga- 

 rithms of the dimensions plotted against logarithm 

 of total length being well fitted by linear regres- 

 sions, the constants for which are given in table 

 2. Tn previous studies of Costa Rican and 

 African fisli, linear regressions were found adequate 

 for those relations over the size range 50 cm. to 

 160 cm., and for only that range of sizes it would 

 be difficidt to perceive that the allometry equation 

 provides a better fit to the Hawaiian data. The 

 availability of a longer range of sizes from Ha- 

 waiian waters made it possible to observe the 

 slightly curvilinear natiu"e of the relation. How 

 little it differs from a straight line may be seen 

 from the closeness to lunty of the values of b 

 tabulated in table 2 for these regressions. 



The weight of Hawaiian yellowfin varies almost 

 exactly as the cube of the length, the relation 

 between length in millimeters (x) and weight in 

 pounds (y) being expressed by the equation 



log 2/=2.996x- 7.35477 



COMPARISON OF TUNA FROM HAWAII 

 AND FROM THE AMERICAN WEST COAST 



Fin lengths 



The most outstanding differences revealed by 

 this study between yello\vfin tuna from Hawaii 

 and those from waters off Costa Rica are the rela- 

 tive lengths of the pectoral, second dorsal, and 

 anal fins. There seem also to be small but depend- 

 able differences in length of longest dorsal spine 

 and length of longest dorsal fiidet. 



Figure I illustrates the relation between length 

 of pectoral fin and total length for Hawaiian and 

 Costa Rican fish. The points plotted in this figure, 

 and in the other figures in this paper, do not repre- 

 sent individual fish but are the mean values of the 

 two variables for each 10-cm. size category. This 

 method of plotting recommends itself because the 

 data for uidividual fish are too numerous to be 

 clearly depicted. It lias also tlie advantage of 

 making possible a visual comparison of mean values 

 of the dimension under consideration for fish of 

 each single 10-cm. size category from the two 

 populations. The inlierent disadvantage is, of 

 course, that each point does not represent the 

 same number of fish, so that their positions are of 

 varying degrees of reliability. The regression 



