FISHERY BULLETIN: VOL. 73, NO. 2 



70r 



60 



t 50 



I 

 t- 

 o 40 



z 



UJ 



> 

 o 

 o 

 m 



30 



20 



10 



40 60 80 100 120 140 



OTOLITH RADIUS ( mm) 



160 



180 



Figure 13.-A scattergram of mean body lengths per millimeter 

 of otolith radius (as taken from a 16 x photographic 

 enlargement) and superimposed curve of the function used to 

 back-calculate growth. 



some evidence in Table 7 that the radii of the first 

 one or two annual marks increase as the total age 

 increases, only otoliths from 7-yr-olds were used to 

 avoid any possible age-related effects. Older 

 specimens could not be used because they were not 

 available in sufficient numbers and younger 

 specimens had a growth history which was too 

 brief. Fifteen otoliths of each sex for each of the 5 

 yr were selected. The desired sample size (30 per 

 year class) was seldom obtained because many of 

 the otoliths had deteriorated in storage so that 

 opaque and hyaline zones could not be distin- 

 guished on the photographs. 



Back-calculated lengths are presented in Table 

 8, and a comparison of back-calculated growth 

 curves for the five year classes is made in Figure 

 15. It appears that year class variation was not 

 great among the 1957-60 year classes, but that the 

 members of the 1961 year class were on the 

 average noticeably smaller at age than members 

 of the other year classes. This latter observation 



Table 5.-Functions examined for the best fit of otolith 

 radius-body length data, corresponding residual sums of 

 squares, and mean squares. 



Function 



Residual sum 

 of squares 



Mean 

 square 



between estimated and observed values is 0.9860, 

 so an improved fit was not attempted. The Y in- 

 tercept is at 18.78957 cm indicating that the func- 

 tion does not adequately represent the otolith 

 radius-body length relationship in fish less than 1 

 yr of age. Therefore the back calculation of body 

 lengths beyond the range of the data fitted is ob- 

 viously not meaningful. 



The mean total otolith radii by age were used to 

 back calculate lengths at age which are presented 

 in Table 6 and compared in Figure 14 with ob- 

 served lengths at age from combined 1965-69 

 samples. The atypical 1961 year class was excluded 

 in this comparison. In spite of a certain amount of 

 variation in the back-calculated curve (probably 

 induced by the small sample size), the two curves 

 correspond very well. 



The lengths-at-age for five year classes 

 (1957-61) were compared by back calculating the 

 lengths of approximately equal numbers of males 

 and females from each year class. Because there is 



Table 6.-Mean otolith radii and back-calculated body lengths at 

 various ages for Pacific hake. 



Age 

 (years) 



1 



2 



3 



4 



5 



6 



7 



8 



9 



10 



11 



12 



13 



Mean otolith 

 radii (cm) 



Calculated body 

 lengths (cm) 



6.08 

 9.06 

 12.53 

 13.50 

 13.60 

 14.43 

 14.80 

 16.44 

 15.79 

 17.29 

 17.74 

 18.30 

 17.90 



16.57 

 26.19 

 41.13 

 45.44 

 45.88 

 49.45 

 51.00 

 57.30 

 54.92 

 60.11 

 61.44 

 62.92 

 61.88 



Figure 14.-A comparison of growth curves as constructed from 

 observed and backcalculated fork lengths at various ages. 



350 



