252 



FISHERY BULLETIN OF THE FISH AND "WILDLIFE SERVICE 



extremely high or low temperatures and severe 

 storms may lead to catastrophic destruction of 

 eggs and small fish, the strength of a year class is 

 believed to depend normally on the sum of the 

 effects of many factors. It seems entirely reason- 



able to suppose that the controlling factors have 

 to do with the coincidental occurrence of early 

 feeding by the newly hatched fish and the appear- 

 ance of suitable food organisms in adequate 

 amounts. 



LENGTH-WEIGHT RELATION 



The mathematical relation between length and 

 weight of the yellow porch of Lake Erie in 1927-37 

 was determined by fitting the equation W=cL" 

 to the average empirical length and weight of each 

 5-mm. standard-length frequency interval over 

 the range 106 to 250 mm. (5.0 to 11.4 inches total 

 length) . Length intervals both longer and shorter 

 than this range contained less than 28 fish each 

 and were not employed in the fitting of the equa- 

 tion because of possibly unreliable averages. The 

 data represent all yellow perch with standard 

 lengths of 106 to 250 mm. that were measm-ed and 

 weighed without regard for locality, sex, season 

 and year of capture, or gear employed. Data on 

 the length and weight of Lake Erie yeUow perch 

 in 1943—48 are not included because analysis of 

 these later data showed them to be similar in every 

 respect to those obtained during the earlier years. 

 The equation derived from the 1927-37 data ap- 

 phed equally well to the 1943-48 material. 



The equation that best describes the length- 

 weight relation of the Lake Erie yellow perch is: 



W=1.766X10-'D'"', 



in which PF= weight in grams, and L= standard 

 length in millimeters. Since n=3.015, it may be 

 said that the weight of the yellow perch in Lake 

 Erie increased approximately as the cube of the 

 length (n=3.0). 



Table 29 shows the actual and calculated weights 

 for each 5-mm. interval of standard length of the 

 yellow perch of Lake Erie from 1927 to 1937. 

 Weights were computed both from the cube rela- 

 tionship and from the more general equation (W= 

 ci"). It was found that weights calculated by the 

 general equation agreed closely with those com- 

 puted by the equation IF=1.91X10"'Z^ (The 

 weighted grand average K for all Lake Erie yellow 

 perch was 1.91.) Weights calculated by the two 

 equations were in complete agreement for all but 6 

 of the 31 frequency intervals for fish with standard 

 lengths of less than 236 mm., and in no interval 

 differed by more than 1 gi-am. The weights com- 



puted by the two equations agreed at no lengths 

 greater than 235 mm. The weights of these larger 

 yellow perch calculated from the cubic relationship 

 were always less than those computed from the 

 more general equation but at no length was the 

 difference between the two calculated weights 

 greater than 4 grams. It is true also that the 

 differences between the two corresponding calcu- 

 lated weights tended to increase progressively as 



Table 29. — Actual and calculated weights of Lake Erie 

 yellow perch by 5-millimeter length intervals 



[Data based on all flsh weighed during the investigation) 



' In 5-mm. intervals. 



