Fischer et al.: Age, growth, mortality, and radiometric age validation of Lut/anus gnseus 



315 



However, a likelihood ratio test indicated growth models 

 for males and females were significantly different from 

 one another <x 2 =494.77; df=2,714; P<0.001) (Table 2). 

 The resultant sex-specific von Bertalanffy growth models 

 were 



Male L, = 655.411 -e 1 " 0231 "]] 



(F 2 407 =19,732.9; P<0.001; r 2 =0.73) 



Female L , = 657.311 - e l-o.2i</»] } 



(F 2307 =13,015.2; P<0.0001; r 2 = 0.72). 



Instantaneous total mortality (Z) was calculated with 

 catch curve analysis. Full recruitment to the gray snap- 

 per fishery began at age 4 and was completed by age 8 

 and there was no discernible peak in the catch curve 

 dome (Fig. 8). For the purposes of Z estimation, age 4 

 was used as the age of full recruitment to the fishery. 

 Z was estimated at 0.18 for all fish (age range: 5-28 

 years) and 0.17 for all fish when the age range was 

 truncated at 16 years. The age range was truncated 

 at 16 years because older age classes contained fewer 

 than 10 individuals. 



Estimates for natural mortality (M) for gray snap- 

 per varied substantially and were dependent upon the 

 method used. Hoenig's (1983) longevity-mortality rela- 

 tionship produced the lowest estimate of 0.15. Hoenig's 

 (1983) relationship modified for sample size yielded 

 an estimate of 0.30. The regression method of Ralston 

 (1987) produced an estimate of 0.40. Finally, Pauly's 

 (1980) method using a mean annual water temperature 

 of 25°C and parameter estimates L, and k derived from 

 the von Bertalanffy growth equations produced the 

 highest estimate of 0.51. 



Discussion 



Validation of the periodicity of opaque zone formation 

 is critical when using otoliths to determine the ages of 

 fish (Beamish and McFarlane, 1983). The lack of data 

 during the winter months prevented us from making a 

 definitive statement on the timing of opaque zone forma- 

 tion based on edge analysis alone. However, we present 

 evidence that suggests that opaque zone formation may 



