354 



FISHERY BULLETIN OF THE FISH AND WILDLIFE SERVICE 



incidental to fishing for skipjack (Katsuwonus 

 pelamis). Specimens of the small sizes were 

 mostly obtained, therefore, from landings at the 

 local tuna cannery, where most of the skipjack 

 catch is landed, particularly during the summer 

 season of good catches. These fish are landed 

 fresh soon after being caught, and are thus 

 comparable to the specimens from the flag-line 

 fishery. The original data on the 203 Hawaiian 

 yeUowfin tuna employed in this study are tabu- 

 lated in table 1. All length measurements are 

 in millimeters, taken as described by Marr and 

 Schaefer (1949). Weights were taken in pounds, 

 because at the auction market the fish were 

 weighed by commercial scales graduated in 

 poimds. Blanks in the table indicate that the 

 measm-ement or count was not taken on the 

 particular specimen. In addition, a few of the 

 tabulated values were omitted from the analj^ses, 

 because they were found to deviate more than 

 three standard deviations from the appropriate 

 regression line and seemed probably to be record- 

 ing errors. These values were as follows: 



Rejected 

 value 



1670-inrD. specimen, snout to insertion first dorsal. 423 



1780-mm. specimen, snout to insertion first dorsal 446 



1780-mm. specimen, snout to insertion second 



dorsal 835 



1464-mm. specimen, snout to insertion anal 767 



1629-mm. specimen, body depth 454 



1333-mm. specimen, longest dorsal finlet 34 



1259-mm. specimen, length first dorsal spine 97 



1397-mm. specimen, lengtli first dorsal spine 129 



969-mni. specimen, diameter of iris 26 



1605-mm. specimen, diameter of iris 52 



Many of the routine computations involved 

 in the analysis of the Hawaiian data, reanalysis 

 of American-west-coast data, and comparison of 

 the two, were performed by Dorothy Dung, 

 whose assistance is gratefully acknowledged. 



ON THE SELECTION OF REGRESSION 

 EQUATIONS 



It is characteristic of many animals — perhaps 

 of all — that the various parts of the body grow 

 at different rates, so that as the organism increases 

 in size the ratio of one dimension to another 

 changes. For yeUowfin tuna this has been 

 demonstrated by Godsil (1948), Schaefer (1948), 

 and Schaefer and Walford (1950). Since this is 

 the case, one cannot use the measm-ement ratios 



normally employed in systematic ichthyology for 

 comparing samples of tunas from different places, 

 except in the trivial case where the fish from the 

 two places are of exactly the same size, because 

 differences connected with size could be confused 

 with differences in form of fish of the same size. 



In order to avoid this difficulty, the authors of 

 the papers cited above have based their com- 

 parisons of samples on the comparison of the 

 regression of one dimension on that of another 

 (usually total length), taken as a measurement of 

 over-all size. This procedin-e is also employed in 

 the present paper. It may be noted that the 

 efficiency of sampling may be much improved over 

 simple random sampling in such chcumstances by 

 selecting the specimens according to total length 

 (the independent variate) to give an even repre- 

 sentation of all sizes available so far as is practical; 

 such a sampling scheme was employed in obtain- 

 ing the data for table 1. 



The comparison of body form among fish 

 popidations by comparison of regressions would 

 be a simple and straightforward process if the 

 relations between the body dimensions corres- 

 ponded exactly to the straight lines or simple 

 curves that must be employed in such analyses. 

 Unfortunately, they do not and this may lead to 

 some confusion in the analysis, particularlj'- in 

 situations where one is dealLug with smaU differ- 

 ences and large numbers of specimens. Over 

 restricted ranges of sizes at least, the dimensions 

 of some body parts relative to others seem to be 

 sufficiently well approximated by straight lines 

 (Schaefer 1948, Schaefer and Walford 1950). 

 Large samples of the same size range of the same 

 populations may reveal, however, that regression 

 curves of slight ciu-vilinearity give a better fit to 

 the data, as Godsil (1948) has found for certain 

 dimensions of the American-west-coast yeUowfin. 



In other cases, such as the fin lengths of yeUow- 

 fin tuna, the regressions are very strongly curvi- 

 linear but may, in some cases at least, be trans- 

 formed by the aUometry equation or other 

 transformation to a hnear or nearly linear relation, 

 as has been done in mj'' papers above cited. 

 Whatever the equation employed, however, it is 

 necessary to bear in mind two things. First, the 

 relation employed in the analj^sis (the mathe- 

 matical model of the true relation between 

 variables), be it Imear or otherwise, is only an 

 approximation to the true relation and as such 



