LIFE HISTORY OF LAKE HERRING OF LAKE HURON 313 



largest. The H^IV ratios, of course, vary as the HJK. In the TJV ratios the 

 error due to age variation in head length is eliminated, while in the K/V fractions 

 the head measurement is included. It is to be noted that the K/ V ratios vary in 

 the same direction as the TJV, but not in the same relative amount. This indicates 

 that the head affects the K/V fractions, but only to an insignificant degree. The 

 age variation in head length can not account for any large or significant variation 

 that may occur in the body-scale (K/V) ratio with age after the third year. 



This conclusion may be substantiated by the application of the statistical formula 



for variability, c = -jrf, in which c is the coefficient of variability, c the standard devia- 

 tion, and M the mean. I applied the formula to the E/V and TJV ratios of years 

 III and IV only. The coefficient of variability was found to be 6.29 per cent± 

 0.8660 for the K/V ratios of year III, and 6.58 per cent ±0.9059 for the Tj/F ratios 

 of that year, 8.45 per cent ±0.4851 for the Z/F ratios of year IV, and 8.91 per cent 

 ±0.5116 for the Ti/F ratios of year IV. It is thus apparent that the Z/F ratios are 

 no more variable than the TJ V, and that head length, therefore, is an unimportant 

 variable in the former ratio. 



AGE VARIATIONS IN BODY SCALE (K/V) RATIOS BASED ON SELECTED (X) AND 

 UNSELECTED (NON-X) SCALES OF ADULT LAKE HERRING 



In a study of the correlation of body and scale length we may compare the 

 actual measurements of body and scale length directly or the body-scale ratios 

 {K/V) based upon these measurements. Both methods are employed for the lake 

 herring. 



To eUminate or minimize the errors due to the variability in the growth of 

 individual scales, I employed for tliis study corresponding scales (X scale)" where- 

 ever possible; but as the specified scale is not always available and much time is 

 consumed in locating it, it is not e.xpedient to employ it in life-history work. I there- 

 fore computed, for comparative purposes, the .E'/F ratio based on those scales (non-X) 

 actually used for the computations of fish length. As stated on page 274, these scales 

 were taken from the body area situated between the dorsal fin and the lateral line. 

 Three or four scales of each individual were mounted, but only one of these was 

 measured for the computations of fish length. The two series of ratios, K/V on. X 

 and E/V on non-X scales, are given in Table 10 for each year of Hfe of the herring 

 collected at Bay City, Mich. 



" For method employed to locate this special scale see p. 275. 



