218 



FISHERY BULLETIN OF THE FISH AND WILDLIFE SERVICE 



been expected on theoretical grounds. These 

 rather sHght discrepancies which affected only 

 three length intervals are not believed to invali- 

 date the conclusion that the body-scale ratio is 

 constant beyond the average body length of 4.6 

 inches. The scales from the fish with average 

 lengths of less than 4.6 inches were relatively 

 much smaller than the scales from the larger fish. 

 It is to be noted particularly that the relative size 

 of the scale increased rapidly as the average length 

 of the fish increased from 2.3 to 4.1 inches. The 

 increase in relative size follows approximately a 

 straight line but its slope is greater than that of 

 the line fitted to the data for the larger fish. 



The rapid increase in the relative size of the 

 scale during early life was expected from the 

 known facts of scale growth. The scales originate 

 as tiny isolated platelets when the yellow perch 

 has a total length of approximately 1 inch. The 

 scale, then, must grow more rapidly than the 

 body in order to attain the degree of imbrication 

 characteristic of larger fish. 



It is evident from table 3 and figure 3 that a 

 sharp break in the series of LjSc values and in the 

 continuity of the curve occurred between the 

 average lengths of 4.1 and 4.6 inches. A detailed 

 examination of the LjSc ratios for each millimeter 

 length indicated that the break occurred at a 

 length of 4.3 inches. The average ratio of the 

 4.2-inch individuals was comparatively high (1 .34), 

 but it fell suddenly to 1.13 in the 4.3-inch fish and 

 continued at that level in the lai-ger specimens. 

 It appears, then, that the LjSc ratio actually 

 assmnes constancy at a fish length of 4.3 inches 

 rather than at 4.6 and no corrections for dispro- 

 portionate growth of body and scale are necessaiy 

 for calcidated values greater than 4.2 inches. 

 Since the two discontinuous portions of the curve 

 of figure 3 were based on averages (in order to 

 obtain a smoother curve) and (for purposes of 

 correcting computed lengths below 4.3 inches) were 

 connected at points of average lengths (4.1 and 

 4.6), any calculated values that fall between these 

 two averages will be subject to correction. Any 

 correction of length between 4.2 and 4.6 inches 

 theoretically is unwarranted. However, as may 

 be seen from table 4, the corrections for lengths 

 between these hnaits are small and for all practical 

 purposes may be ignored. 



If the length of the scale were purely a function 

 of the length of the fish, the body-scale curve for 



the smaller individuals would be expected to join 

 smoothly the straight line that describes the body- 

 scale relation for the larger ones. The pronounced 

 discontinuity in the curve suggests that other fac- 

 tors must be involved. Changes in the relative 

 size of the head with increase in fish length may 

 have been a factor. The relative size of the head 

 was found to decrease progressively with mcrease 

 in fish length tlu'ough the 71 to 80 mm. interval or 

 up to the average length of 74.6 mm. (3.6 inches 

 total length) . Thereafter, variations in the relative 

 size of the head were small and without any detect- 

 able trend through the 171 to 180 mm. interval (8.0 

 inches average total length). Although the pro- 

 gressive decrease in the relative length of the head 

 may have contributed to the decrease in the values 

 of LjSc up to a fish length of 3.8 inches, it is 

 apparent that these changes did not produce the 

 observed sudden shift in the body-scale relation 

 between 4.3 and 4.7 inches. 



The possible effect of variations in the number 

 of scales in linear series on the body-scale ratio also 

 was investigated. It was foimd that fish with 

 standard lengths of 81 to 90 mm. (4.1 inches aver- 

 age total length) averaged 54.9 (51 to 58) scales 

 in the latei'al line, and that fish with lengths of 91 

 to 100 mm. (4.6 inches average total length), aver- 

 aged 55.1 (51 to 62). The small difference (0.2) 

 in the averages could have had little effect on the 

 changes in the body-scale ratio. If it is assumed 

 that this difference could affect the body-scale 

 ratio, then one would expect the larger fish to have 

 relatively smaller scales, a conclusion contrary to 

 the observed facts. It appears that the number 

 of scales in linear series was not a factor in the 

 sudden change in the body-scale ratio of the Lake 

 Erie yellow perch. 



Length of fish is the ouIa' factor iii these data 

 that can be demonstrated to have had an appreci- 

 able effect on the body-scale ratio. The failure of 

 the two portions of the curve to join smoothly can- 

 not be explained satisfactorily as j-et. 



CALCULATION OF GROWTH 



In the preceding discussion it was indicated that 

 because of the discontinuity of the LjSc curve 

 (change m average LjSc ratios) all direct-propor- 

 tion computations of length less than 4.6 inches 

 must undergo correction, and because of the con- 

 stancy in the average ratios no corrections were 

 needed for lengths of 4.6 inclies or more. The 



