LAKE HERRING OF GREEN BAY, LAKE MICHIGAN 



113 



I 

 I- 

 o 

 z 

 u 



Figure 7. — The effect of size at the start of a growing 

 season on the amoui of growth during that season. 



0.4. Similarly, the growth after time T of fish B 

 should be that of a r .rmal fish that hatched at Ob. 

 The compensatory effects of differences in the 

 growth of these two typical fish (hatched at the 

 same time) during the period T—T-\-\ is identical 

 with the compensation between the two typical 

 fish hatched at 0^ and Ob in figure 6. 



General growth in length 



Distorting influences of the negative correlation 

 between individual length of life anti rate of growth 

 make it impossible to establisli a general curve 

 that might repres nt the growth history of a 

 typical, or "avei, ^e," fish. Only growth of 

 particular age groups can be shown. Curves in 

 figure 8, based on data of all pound-net collections 

 (table 17), are believed to be the most reliable 

 means of representing the geneial growth of Green 

 Bay lake herring taken in the commercial fishery. 

 Age groups I, II, and VI are omitted from the data 



3 



ACE 



Figure 8. — Calculated growth in length of age groups III. 

 IV. and V of Green Bay lake herring as determined for 

 all fish of these age groups taken in pound nets. 1948-62. 



because of the bias introduced by their almost com- 

 plete absence from samples during some seasons, 

 and because they are represented by small num- 

 bers of fish. 



LENGTH-WEIGHT RELATION 

 GENERAL RELATIONSHIP 



The variation of the volume of an object of con- 

 stant shape with the cube of any linear dimension 

 is a well known principle of mathematics. It can 

 also be said that the weight of an object must 

 vary with the cube of any linear dimension if the 

 shape and specific gravity are both constant. If, 

 however, the shape or specific gravity changes the 

 relationship does not hold, but other relatively 

 simple relationships ordinarily can be used to in- 

 terpret the cha^-^es. The usefulness  f the "cube 

 law" in the study of the weight of animals was 

 recognized by Herbert Spencer in 1871 according 

 to a discussion of its application in this field by 

 Thompson (1942). Hile (1936) reviewed the use 

 of this principle in studies of the relation between 

 the length and weight of fish. 



The condition coefficient "C" determined by the 

 formula ('=WIU (C = the coefficient, U'=weight, 

 and Z,=length) is widely employed by fishery 

 workers as an index of changes in the form of fish 



