Ralston et al.: An approach to estimating rockfish biomass from larval production 



135 



bias-correction term (cf^,,e/2) was applied prior to expo- 

 nentiation (Miller, 1984). However, because ct^^^^ was small 

 (0.00882), the correction had little effect on predictions of 

 weight at TL. Moreover, predicted values of weight at 

 length did not differ materially from those given in Phil- 

 Hps ( 1964) and Lenarz ( 1980). 



A total of 586 female shortbelly rockfish were aged from 

 trawl samples. The weights (g) of these fish were individu- 

 ally estimated from measurements of TL (mm) by using 

 the regression results described above. The derived weight- 

 at-age (yr) data were then fitted to the von Bertalanffy 

 growth equation by using a nonlinear regression routine 

 (SAS, 1987). The specific form of the fitted model was 



W^= W„^ll-e-^*i^-'o.*>]/*, 



tt)Q = the .v-intercept of the growth curve (yr); and 

 j3 = the allometric growth parameter estimated 

 from the regression of weight on length 

 (Ricker, 1975). 



The /3 parameter is often set equal to 3.0, implying isomet- 

 ric growth, although /3 was fixed at 2.980 in this applica- 

 tion (see above). Likewise, 535 adult male fish were aged, 

 their weights estimated from measurements of TL, and 

 the data fitted to the weight-based von Bertalanffy growth 

 model. Regression results for both sexes are presented in 

 Figure 3 and Table 2. 



A simple exponential mortality model is used to describe 

 the observed pattern of shortbelly rockfish abundance 

 with age. The model is of the form 



where Wq = female weight (g) 



W__Q = the asymptotic mean weight of females at a 

 hypothetically infinite age (g); 

 Kq - the instantaneous growth coefficient specific 

 to females (/yr); 

 T = age (yr); 



N.,. 



loe 



~MT 



where N-j. = the number of individuals alive at age T(yr); 

 Pq = the extrapolated number at age 7^=0; and 

 M = the instantaneous rate of natural mortality 



(/yr). 



