432 



FISHERY BULLETIN OF THE FISH AND WILDLIFE SERVICE 



{Sy = 8.76 thousands of ova) is more than 5 

 times as large as the variation attributable to 

 sampling and counting techniques. 



There has been some difiPerences of opinion 

 among various authors as to whether length, 

 length squared, or length cubed should give the 

 best straight line correlation witli fecundity. 

 Lehman (1953) correlated the fecundity of 22 

 shad (Alosa sajndissim.a) with their lengths. His 

 equation (least squares) for the line of average 

 relationship is r=— 462.691+40.090X in which 

 F=the number of ova in thousands, and ^Y=the 

 length in inches. 



Clark (1934:21), referring to eight fecundity ob- 

 servations on the Pacific sardine, states: 



By the method of least squares from the formula 

 N=FL^, where A^ indicates the number of eggs; L, the 

 length; F, a constant; and x, the exponent expressing the 

 relationship between the number of eggs and the length 

 of the fish; x was found to have a value of 1.9868. This 

 suggests that the numbers of ova produced by individual 

 sardines increase as the square of the length. But because 

 the calculations were based on very scanty data, these 

 conclusions can be tentative only. 



Simpson (1951j expressed fecundity observa- 

 tions for 256 plaice {Pleuronectes platessa) by the 

 formula F=KU, where F=the number of ova; 

 K, a constant; and U, the cube of the length of 

 the fish. 



The line of best fit (least squares) for the 116 

 sardine fecundity observations is plotted in figure 

 4 for each of four different relationships. 



Table 1 gives the I'-intercepts (a), slopes (b), 

 standard errors of estimate of Y (Sy) and coeffi- 

 cients of correlation (r) of the four lines for the 

 116 fish and for each of the five samples which 

 together constitute the 116 fish. The standard 

 errors of estimate of Y for 10-millimeter length 

 intervals are presented in table 2. Table 3 gives 

 the number of ova in the most advanced group 

 calculated by each of the four different formulas 

 at each of 9 different 10-millimeter length inter- 

 vals. It is apparent from these comparisons that 

 convenience, rather than theoretical considera- 

 tions should be the deciding factor in selecting one 

 of the regression formulas to describe these data. 

 The same is true for Lehman's (1953) fecundity 



^v- 



60 



D 

 O 



O 

 UJ 



o 



Y=a+bX 



Y=a*bx2 



Y=a+bX^ 



- _ Y=bX^ 



-L 



_L 



_L 



_L 



180 190 200 210 220 230 



STANDARD LENGTH IN MILLIMETERS 

 Figure 4. — Comparison of fecundity-length regression lines. 



240 



, 



