502 



FISHERY BULLETIN OF THE FISH AND WILDLIFE SERVICE 



which can be found easily by moving the jaw. The 

 body width was usually measured when the fisli 

 was balanced on its belly but occasionally when 

 the fish was on its side. 



Having in mind the difficulty in sexing Xiphias 

 gladius reported by LaMonte and Marcy (1941), 

 we expected that the marlins also might be 

 troublesome. We have, however, encountered 

 large numbers of marlins in which the eggs or milt 

 were unmistakable, and on examination of the 

 mature gonads of these fish we found difl^erences 

 that make it possible to determine the sex with 

 assurance. The most obvious difference is the 

 presence of a firm, connective-tissue sheath around 

 the ovary that is lacking in the testis. The in- 

 active testes superficially resemble the fatty tissue 

 of mammals. They are usually approximately 

 cylindrical, but when bent can be seen to be dis- 

 tinctly lobed and without a sheath. On the other 

 hand, the inactive ovaries are also roughly 

 cjdindrical but have a definite sheath and no evi- 

 dence of lobes. When an ovary is cut, the interior 

 is usually orange in color and appears distinctly 

 granular to the naked eye due to ova in early 

 stages of development. We have noticed no ex- 

 ternal sexual differences, except that in marlina 

 and ampla all specimens of more than 322 pounds 

 have been females. 



DETERMINATION OF ALLOMETRIC GROWTH 



In view of the known allometric growth ^ in 

 some parts of marlins it is desirable to examine 

 each diagnostic measurement to determine if 

 allometry exists. If so, it will be feasible to com- 

 pare samples only at specified body sizes, which 

 usually is done from regression equations. If the 

 growth is isometric we can use ratios. In addi- 

 tion, it will be shown that the size of certain parts 

 is completely unrelated to the size of fish (within 

 the range of fish sizes studied) and that it is pos- 

 sible to compare samples by use of the simple 

 length frequency and mean size. 



' We follow wlmt we believe to be the intent of Huxley and Teissier (1936), 

 who proposed that allometry be used in place of other terms to denote growth 

 of a part at a rate difTerent from that of the whole. This they defined to he 

 the case where the relative growth could be expressed by a formula of the type 

 y = bi'- with ap^l, in which y is the part, i the .standard or whole, and a and h 

 are constants. When a = l, growth would be considered to be isometric. 



We have used a growth equation of the type !i=a+hx, and have considered 

 growth to be allometric when aj^n, and the ratio of part to whole changes 

 with size of the whole. When a=0, the ratio is constant and the growth is 

 considered to be isometric. This is consistent with the proposal of Huxley 

 and Teissier because, if a^^O and the line is extrapolated from the data to the 

 zero point, a curve results, and if the formula j/=6r» is applied, then a^\. 



A determination of allometric growth suffi- 

 ciently accurate for our purposes can be had from 

 a plot of each character on graph paper. When 

 the points are in place, it is a simple matter to 

 fit by eye a trend line (curved if need be) and then 

 draw two other lines from the origin representing 

 constant ratios near the upper and lower bound- 

 aries of the distribution. It is convenient if the 

 boundary lines are drawn to represent even per- 

 centages of the abscissal character. Now, if 

 growth is isometric the trend line will be straight, 

 pass through the origin, and approximately bisect 

 the angle of the outer lines. If growth is not 

 isometric, the trend line will curve or cross one or 

 both of the outer lines and it is possible to judge 

 approximately how much the ratio changes over 

 the range of the data. In the marlin data, we 

 found it easy to judge when the trend line changed 

 over the range of the data more than about one- 

 third of the difference between the boundary 

 lines. When the change was greater we used 

 straight-line regression analysis. Wlien the trend 

 line was curved we omitted part of the data and 

 used only that from the straight portion. 



Such approximations are adequate for our pur- 

 poses for two reasons: (1) We are concerned here 

 principally with differences among species and 

 not the minutiae of racial or subspecific differences, 

 and (2) some of the marlin measurements show 

 curvilinear relationships which our samples arc 

 not adequate to describe precisely and which 

 cannot be dealt with easily through the loga- 

 rithmic growth equation. 



An example of the method is the plotting of the 

 length of the pectoral fin against the fork length, 

 using the data from the POFI collections (fig. 4). 

 Use of this character is appropriate because 

 MoiTow (1952a) found a slight, although not 

 statistically significant, negative allometry in this 

 character. We notice in our plot which includes 

 small specimens of audax and ampla that the 

 growth is probably curvilinear in both of these 

 species. But if we omit the specimens of less 

 than 200 cm. fork length, the evidence of allo- 

 metric growth is very small indeed. There is a 

 suggestion that the length of the pectoral in 

 audax increases or shows a slight positive allom- 

 etry (contrary to Morrow's finding), whereas in 

 ampla and marlina the allometry appears to be 

 trivial. However, if we omit the small speci- 

 mens, the trend in any one species changes only 



