452 



Fishery Bulletin 101(2) 



20 



16 

 5 12 



CO 



o 008 

 a. 



0.04 



000 



Length 



Length group 



Figure 1 



Graphs of Equations 1-3 (A=Eq. 1; B=Eq. 2; C=Eq. 3) showing two 

 different age groups with overlapping length distributions. Sections 

 A, B, and C are referred to in the description of the model in the 

 "Materials and methods" section of the paper. 



the standard deviation of length in February (cr, ), respec- 

 tively. A linear length increment between surveys was as- 

 sumed for individuals in a cohort, and the average length 

 in a given month was estimated by interpolating from the 

 linear growth curve (i.e. the length corresponding to the 

 mid-point of the month). Although the p^/s were estimated 

 from mean lengths specific to a given year, the standard 

 deviation of length at age was assumed constant and to in- 

 crease linearly with time (or age) for a cohort. A regression 

 analyzis of age and average standard deviation of length at 

 age gave the fitted line in Figure 2. The equation from this 

 regression was used to calculate ct^, for a given age (where 

 age is measured in months). Abundance indices (estimate 

 ofN^^) from the Norwegian bottom trawl survey in the Bar- 

 ents Sea were taken from ICES,^ and the relative number 



of individuals in each age group was assumed constant in 

 the rest of the year The size of the length group intervals 

 *^niin .s~ ^max s '^1 Eq.l) was 5 Cm, and the number of length 

 groups in the model was set to 30. 



All recorded individuals of Northeast Arctic cod that were 

 sampled randomly from commercial catches were pooled 

 over each month (these data are available from 1985 on- 

 wards). Monthly length distributions (5-cm length groups) 

 and corresponding (observed) age distributions were then 

 constructed. The predicted proportion of each age group in 

 a given month (based on the length distribution) was 



J,a.N. 



/N. 



^ ICES. 2001. Report of llie Arctic Eisherics Working Croup, 

 Bergen, Norway,24. April -3. May 2001 ICES CM 200 1/ACEM: 19, 

 380 p. ICES, PalEegade 2-4 DK-1261. Copenhagen K, Denmark. 



where Q^,^ = the theoretical age-longth key (from Eq. 3); 

 A^^, = the observed number of individuals in length 



group .s'; and 

 A^ = the number of sampled individuals. 



