FECUXDITY OF THE PACIFIC SARDINE 



433 



data for shad. Using his formula }'=a + 6A'', 

 S„ = 40.2 and a = -462.7. Using Y=a + bX\ 

 Sy=39.'.i and a = 19.0. As a approaches zero the 

 formula Y=bX^ would also give an S„ approxi- 

 mating the above two. 



Theoretically the number of ova is dependent 

 upon the volume of the ovary, a three-dimensional 

 function, and tlierefore shoukl l)etter correlate with 

 the cube of tiie length, length itself being, of 

 course, only linear. In Simpson's (1951) paper on 

 the fecundity of the plaice, the straight line re- 

 gression of fecundity on length cubed is consider- 

 ably better than that of fecundity on length 

 squared or length. The significant differences 

 between the regressions in this case are brought 

 out by the greater relative range in sizes of fish 

 used in calculating the regression lines. Measured 

 as a percentage of the length of the shortest fish 

 used, the range of Simpson's plaice is 162 percent, 

 that for Lehman's shad is only 66 percent and for 

 the 116 sardines 48 percent (56 percent including 

 Clark's 8 fish). 



Table 1. — Comparison of some possible fecundity-length 

 relationships 



Table 2. — Standard error of estimate of Y for ten milli- 

 meter length intervals using formula: 1^=0 + 6.^ 



|y=N'o. of ova In thousands; Jf=lcngth In mm.) 



Table 3. — Calculated number of ova in most advanced mode 

 for sardines of different lengths 



Obtaining a sample of Pacific sardines suitable 

 for fecundity determinations with a size-range 

 comparable to that of plaice would be an impossi- 

 bility. The size range of the sample of spawning 

 sardines might be doubled by including large fish 

 (270 to 290 mm.) from the northern part of the 

 sardine's range and small spawning fish from the 

 southern part of the range. (I have examined 

 some 145-155-mm. sardines taken off the southern 

 tip of Baja, California, that had apparently devel- 

 oping gonads.) This procedure could introduce 

 a considerable error. Simpson found that there 

 were geographical differences in fecundity among 

 stocks of plaice, those from the Baltic containing 

 many more eggs than those of comparable sizes 

 from the North Sea. 



In figure 5 the data for eacli of the 5 samples 

 have been described b}' regression lines, using the 



