36 



FISHERY BULLETIN OF THE FISH AND WILDLIFE SERVICE 



marked lake trout recaptured and, according to 

 the best available evidence, was also a charac- 

 teristic of the scales of most wild fish. 



It should be emphasized that, dependable as 

 lake trout scales may be as indicators of age, thej- 

 are not read easily. Considerable experience is 



required before a reader's interpretation of the 

 scale pattern becomes highlj' reliable. Even the 

 experienced reader can do accurate work only if 

 the scale preparations are clear and they are 

 studied carefully with the aid of the best optical 

 equipment. 



GROWTH OF MARKED LAKE TROUT 



The study of the growth of marked lake trout 

 is based principally on the 1,319 specimens for 

 which the age as read from the scales agreed with 

 the supposed age. This restriction excludes any 

 bona fide recaptures for which errors were made 

 in scale readings. The 1,319 fish may include a 

 few unmarked fish with abnormal fins that hap- 

 pened to be of the correct age at capture. There 

 is no reason to believe, however, that the number 

 in either of the groups is large; the restricted 

 sample, therefore, may safely be presumed to 

 consist almost entirely of marked fish and also 

 to include nearly all of the true recoveries. 



Measurements of the marked lake trout were 

 made in Ann Arbor before the fish were preserved 

 but after they had been shipped in ice from the 

 port where they were landed. Although most of 

 the fish were in good condition upon arrival, a few 

 were in advanced stages of decomposition so that 

 length and weight measurements could not be 

 determined accurately. Such fish have been ex- 

 cluded from tables and calculations for which 

 those measurements are requisite. In some tables 

 the total number of fish was further reduced by 

 dropping from consideration the older age groups 

 which were poorly represented. More lengths 

 than weights were obtained because some of the 

 lake trout were dressed (gills and viscera removed) 

 upon arrival in Aim Arbor. 



LENGTH-WEIGHT RELATION 



The commonly accepted formula expressing 

 the length-weight relation in fishes is: 



W=cL" 

 or log M'=log c+n log L 



where Ii'= weight 



L = total length 

 and c and « = constants 



As tlie measurements of length antl weight alike 

 are subject to error, a method developed by 

 Bartlett (1949) was used in fitting a line to the 

 logarithms of individual lengths and weights of 



1,197 lake trout ^' from northern Lake Micliigan. 

 The resulting estimate of the relation between 

 woiglit in ounces and total length in inches was: 



log ir= -2. 4698-1-3.1125 log L 



The value of 3.1125 for n (which measures the 

 relative rates of increase of weight and length) 

 shows that in these lake trout the weight increased 

 somewhat faster than the cube of the length. 

 In other words, the body form became more robust 

 as the fish grew longer. 



The departure of the lengtli-weight relation- 

 ship of the lake trout of northern Lake Micliigan 

 from the "cube law" probably was significant. 

 The 5-percent confidence interval of the true slope 

 /3 with ^ = 1.962 for 1,195 degrees of freedom, 

 when calculated by Bartlett's method was 

 3.13718±0.90129. At the same level of signifi- 

 cance, the least squares method gave 6xy = 

 3.08414 ±0.04332. 



Comparisons between empirical weights and 

 tlieoretical weights (as computed from the length- 

 weight equation) are to be found in table 17 and 

 figure 18; the straight line of figure 18 is a graph 

 of the equation. Because talile 17 contains actual 

 and computed values of both length and weight, 

 an explanation of the arrangement may be lielpful. 

 The first row of figures in the left section, for 

 example, states first that the single lake trout 

 7.2 inches long had a weight of 1.2 ounces at 

 capture (foiu-tli column). In the same row, it 

 is sliown furtlier that the expected weiglit for a 

 7.2-inch fish was computed to be 1.6 ovuices 

 (fifth column) and that the expected lengtli for 

 a 1.2-ounce lake trout would be 6.6 inches (third 

 column). 



Agreement between most empirical and calcu- 

 lated weights and lengths can be termed good. 

 Discrepancies usually are small (full agreement at 

 14 lengths). The larger disagreements occur at 



2' This numbor included all the lake trout weighed in the round, l.US 

 presumably marked and 79 for which the ages from scale readings and 

 deformed fins did not agree. 



