Roberson et al.: Indirect validation of the age-reading method for Gadus macrocephalus 



157 



Bertalanffy equation (Ricker, 1975). However, because 

 we could estimate the age of fish at time of recapture, 

 we were able to manipulate the von Bertalanffy equation 

 to obtain the following equation: 



4-A = A„,n 



[(■ 



-KicL,-d-t„ 



-iV— > )], 



where L x = length at tagging; 



L 2 = length at recapture; 



L in f = maximum size; 



K = growth rate; 



a 2 = estimated age at recovery determined from 



our otolith ages; 



d = time at liberty; and 



r = age at length mm. 



Given von Bertalanffy parameters and age at recovery, 

 a (fish) length increment for time after tagging can be 

 predicted. Using published L ln{ and K estimates from 

 tagging data, L inf = 1043 mm, K = 0.222 (Kimura et 

 al., 1993), we estimated L 2 -L v One weakness in these 

 estimates is that the growth parameters estimated by 

 Kimura et al. (1993) were based on only positive growth 

 increments (there were some instances where recaptured 

 fish were smaller than they were at tagging, demonstrat- 

 ing negative growth increments). 



A value for t was estimated iteratively in the von 

 Bertalanffy equation by using the subroutine Solver 

 (Frontline Systems Inc., Incline Village, NE) from the 

 Excel software package with the following parameter 

 values: K = 0.222, t = 1 year old, L lnf = 1043 mm (Kimu- 

 ra et al., 1993), /, = length at age one = 180 mm (from 

 the 1977 year class [Foucher et al., 1984]). Because 

 these von Bertalanffy parameters are not based on 

 age determination, they provide an indirect method for 

 validating aging criteria. In addition, ages determined 

 by readers were scaled smaller (by 0.75) and larger (by 

 1.25) in order to simulate the results of younger and 

 older aging criteria. Plots of observed and predicted 

 growth increments should agree if the aging criteria 

 for a 2 reflect the true age of fish. 



E 



c 

 .2 



2.5 3 



Ln Otolith area (mm 2 ) 



Figure 2 



Relationship between Ln fish length and Ln otolith area 

 based on tagged and recaptured Pacific cod (r 2 = 0.735, 

 y=4.6+0.66X, n = 96). 



Results 



Predicting fish length from tagged fish and 

 back-calculations 



The parameter v used in all back-calculations in our 

 study was estimated by using otolith area and again by 

 using the major axis of the otolith (Fig. 1). Based on the 

 slopes from the regression of Ln fish length on Ln otolith 

 size (Table 2, [Fig. 2]), the coefficients should be v=1.01 

 for otolith length and v=0.66 for otolith areas. 



Back-calculations were performed by using the otolith 

 area and were repeated by using the major axis. Scatter 

 plots of estimated and observed fish lengths were used 

 to visually inspect how well back-calculation determines 

 fish length (Fig. 3). Assuming that the residuals of the 

 back-calculated length at tagging have independent 

 chi-square distributions, an F-test indicates that back- 

 calculations derived from otolith areas are significantly 

 more accurate than back-calculations derived from the 

 major axis (P<0.05). However, because we used the two 



