386 



FISHERY BULLETIN OF THE FISH AND WILDLIFE SERVICE 



1.9 mm. (absolute values employed) and 7.2 mm. 

 It is not possible at this time to state to what 

 extent the difference between the Hile and Jobes 

 curve and the one determined in the present study 

 represent a true change in the population or to 

 what extent they reflect random variation. Un- 

 published data on body-scale curves derived from 

 different samples of Great Lakes fish (from a 

 single lake) do indicate a considerable sample- 

 to-sample variability, but the possibility of a real 

 change is not to be discounted. At any rate, it 

 was obviously proper to apply the more recently 

 derived curve to the 1943-55 collections. 



Key scales above the lateral line 



The graph of body-scale data (fig. 12) indi- 

 cated a linear relation between the standard 

 length and the scale radius for fish longer than 



20 40 60 80 100 120 140 

 SCALE RADIUS (MILLIMETERS, x 43) 



160 



75 mm. The straight line fitted by least squares 

 to data for fish longer than 75 mm. had the 

 equation : 



L = 30.5 + 1.63 S 

 where 



L = standard length in mm., 

 and 



S = scale radius (X43) in mm. 

 For practical use the intercept was taken to be 

 30 mm. 



Calculated lengths greater than 75 mm. were 

 computed by the formula: 



L n = 30 + (Zt ~ 30) S n , 



where 



and 



L n = calculated length at the end 



of n years, 

 L t = standard length at capture, 

 S n = scale radius to the nth annulus, 



S t = total scale radius. 



Calculated lengths less than 75 mm. obtained by 

 this formula are overestimates. Corrections for 

 these overestimates (table 24) were determined 

 from the body-scale curve (fig. 12). They are 

 the vertical distance between the empirically 

 fitted body-scale curve for fishes below 75 mm. 

 and the extension of the straight line. 



Taple 24. — Correction to be subtracted from standard lengths 

 of Saginaw Bay yellow perch calculated by formula 



[Scales from above the lateral line] 



Figure 12. — Relation between body length and scale 

 length of Saginaw Ray yellow perch (key scales from 

 above the lateral line). 



Comparison of lengths calculated from different scales 

 of the same fish 



Inasmuch as the two body-scale curves were 

 determined from selected or key scales it should 

 be expected that nearly identical estimates of 

 growth of fish in the sample would be obtained 

 from the two sets of scales. The comparison of 

 the growth histories of the same fish as computed 

 from measurements of scales from above and 

 below the lateral line (table 25) supports this 

 expectation with the exception of calculated 

 lengths at the end of the second year of life. At 

 this age the scales above the lateral line con- 

 sistently gave the higher calculated lengths; the 



