juvenile cod below the presumed density structure 

 was a problem because data from near bottom 

 were not available for many stations. Therefore, 

 the density of juvenile cod below the structure 

 was assumed to be the maximum calculated for 

 the density structure (i.e., that at 47 m in an 

 entire structure). The possible error in estimating 

 biomass of juvenile Arctic cod at the stations 

 under this assumption was not judged to be 

 serious because the sampling area was so shallow 

 that the bottom of the density structure was 

 usually close to the ocean bottom. 



Although the transformed data on cod 

 abundance vs. depth were useful for analyzing 

 the density structure at the stations, back 

 transformation of the estimates offered problems 

 of interpretation. At present there appears to be 

 no practical procedure for back transforming the 

 variance and estimates of a logarithmic-arith- 

 metic regression. Consequently, the density 

 structure was redescribed from the untrans- 

 formed data by fitting a parabolic regression with 

 least squares (Figure 4). The variables were 



1,300 - 



1,200 



. 1, 100 



200 



100 



Y = 6.72605 - 3.631466X + 0.33017x2 



A REPLICATE TOW 

 « MULTIDEPTH TOW 



20 30 



CORRECTED DEPTH (M) 



50 



Figure 4. — Number of juvenile Arctic cod per Isaacs-Kidd tow, 

 the depths corrected for apparent emergence or submergence 

 of the density structure (Tables 6 and 7). Weighted regression 

 (1/X^) fitted by least squares. 



FLSHERY BULLETIN: VOL. 72, NO. 4 



weighted by the inverse of the corrected depth 

 squared because the variance of number of cod 

 vs. depth appeared to be linearly related to the 

 square of the corrected depth. The result was 



Y = 6.72605 - 3.63466X + 0.33017X2 



and its integration 



./ 



y* = / y (X) dx 



V. 



= 4.51413 (L - [/) - 1.21968 (L^ - U^) 

 + 0.07386 (L3 - f/3) 



where Y = most likely estimate of number of cod 



in a tow at corrected depth. 

 X = corrected depth in meters, 

 y* = most likely estimate ofthe number of 



cod over the depth interval U-L in a 



trawl swath. 

 U = upper (shallower) level of depth 



interval, where 0^t/^L^47. 

 L = lower (deeper) level of depth 



interval. 



Accordingly, the density structure contained 

 approximately 5,186 juvenile cod over its depth 

 range (0-47 m) over the area of a trawl swath. 

 The most likely estimate of maximum density, at 

 47 m, was 379 cod/m of depth over the area of 

 a trawl swath (5,519 m^). 



Under these assumptions, composite estimates 

 ofthe number of juvenile Arctic cod in the water 

 column beneath a standard trawl swath was cal- 

 culated for all IKMT stations (Table 7). Totals 

 for each station were obtained by adding the 

 number of juvenile cod estimated for that section 

 of the water column occupied by the density 

 structure — 5,186 over 47 m of depth except when 

 the structure was truncated by the surface or 

 bottom — to the hypothetical number in the 

 column below the structure, or 379/m of depth. 

 For the replicate stations, where only one depth 

 was sampled, the hypothetical depth ofthe struc- 

 ture was obtained by comparing the average 

 catch (log transformed data) at the trawling depth 

 with the catch (log transformed data) that would 

 be expected at that depth if the apex of the 

 density structure coincided with the ocean sur- 

 face. If this comparison indicated that the apex 

 ofthe hypothetical structure was projected above 



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