114 



FISHERY BULLETIN OF THE FISH AND WILDLIFE SERVICE 



that result from such phenomena as maturation 

 and release of sex products or variations in the 

 amount of fat or flesh. If the cube relationship 

 is maintained throughout life then C is an un- 

 biased expression of condition and it is possible to 

 compare the coefficients of fish of different length. 

 Thompson (1942) pointed out, however, that, 

 "* * * inasmuch as the animal is continually apt 

 to change its body proportions during life, k [his 

 sj^mbol for condition coefficient] also is continually 

 subject to change." In this situation C becomes 

 a function of length and the C values of fish of 

 different length are not directly comparable as 

 measures of departure from the "normal" for the 

 stock. Hile (1936, p. 23S) stated that— 



Although the cube law does appear to apply to the length- 

 weight relationship in some species * * *, these instances 

 appear to be the exceptions, for the * * * inadequacy of 

 the cube law in describing the length-weight relationship 

 in fishes have been repeated by numerous investigators and 

 on many forms of fishes. 



The situation is further complicated by the fact 

 that not only does the length-weight relation de- 

 viate from the cube law, but it is not the same for 

 different populations of the same species and it 

 varies from year to year within the same popula- 

 tions (Hile 1936). 



The relation between length and weight in most 

 populations of fish is represented satisfactorily by 

 the formula W=cL", where Tr=weight, Z=length, 

 and c and n are constants. However, since the 

 relation between length and weight in a popula- 

 tion varies with respect to sex, season, method of 

 capture, and year of capture, as will be shown 

 later, no single equation can describe the situation 

 at all times and any general relationship that 

 might be established is of necessity artificial. 

 Nevertheless, a general length-weight equation 

 based on all available data, regardless of sex, 

 maturity, collecting gear, or season of capture, can 

 be useful as an estimate of the average situation. 



An estimate of the length-weight relation of 

 Green Bay lake herring based on all data is 



log H'-:— 2.4386-^3.0729 log L, 

 where W equals weight in ounces, and L equals 

 total length in inches. Data upon which this 

 estimate was based are shown in table 27. The 

 weights computed from the mean length of fish 

 in each length group are the basis of the curve in 

 figure 9; the empirical data are shown by dots. 

 Comparisons of calculated and actual weights 



e 8 10 12 



TOTAL LENGTH (INCHES) 



Figure 9. — Length-weight relation of the lake herring of 

 Green Bay. The dots show the empirical data; the curve 

 is the graph of the equation given in the text. 



prove that this formula does not describe the 

 empirical data precisely. Calculated weights are 

 generally less than actual weights for fish under 

 9 inches, greater for fish between 9 and 12 inches, 

 and less for fish longer than 12 inches. A close 

 fit was hardly to be expected in view of the 

 known heterogeneity of the material. Few fish 

 under 9 inches and over 12 inches were taken, and 

 these were not equally represented in all seasons 

 (table 7). This variation in representation to- 

 gether with seasonal differences in weights of fish 

 of the same length are responsible for the irregu- 

 larities. 



SEASONAL CHANGES IN WEIGHT 



The study of seasonal changes in weight of Green 

 Bay lake herring (table 28) is restricted to fish 

 captured in the same calendar year (1949), in the 

 same area (extreme southern Green Bay), and in 

 the same gear (pound nets). In the 12 h^igth 

 intervals represented by 3 or more fish on all three 

 collection dates the October fish were heaviest in 

 11 and the May fish were lightest in 11. Febru- 

 ary specimens were, of course, cliaracteristically 

 intermediate (10 of 12 comparisons). Over the 

 length range at which all dates were represented, 

 the October specimens averaged 4.8 percent 



