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



137 



5 



' I ' ' ' I I ' 



10 15 



Age (yr) 



20 



'"I 

 25 



Figure 4 



Weighted linear regression of log^.-transformed shortbelly 

 rockfish abundance on age (statistical weights based on 

 expansions of aged subsamples to full trawl catches; all 

 samples collected by trawling during February-March 

 1991). 



There was no evidence that the sex ratio of the fish 

 sampled during the 1991 spawning season (n = 1121 from 

 February and March cruises combined) varied with age. 

 A two-way test for independence of age and sex yielded 

 X^=27.55, df=23, P=0.23. Moreover, there was no evidence 

 that the overall population sex ratio was other than 50:50 

 (A^^->=586. N.y=535: ;f-=2.32, df=l, P=0.14). From these re- 

 sults, we concluded that females and males both enter the 

 population at approximately the same rate and thereafter 

 they experience a similar natural mortality rate. 



The maturity stage data were used to establish a ma- 

 turity schedule for female shortbelly rockfish collected 

 during the 1991 winter spawning season. Fish were first 

 stratified by size class (5-mm-TL intervals), and for each 

 size group, the mean coded ovarian stage was computed. 

 The data were then fitted by nonlinear regression (SAS, 

 1987) to a logistic model of the form 



S=l+- 



v 



l + e 



-p'TL-TL't 



where 



S = the mean coded maturity stage; 

 TL = total length (mm); and 

 V, p, and TL' = fitted parameters. 



Results show (Fig. 6, Table 2) an abrupt change in ovarian 

 condition at a length of 135 mm. At the time of sampling 

 (February-March), virtually all fish above that size were 

 gestating or had already released their larvae, whereas 

 fish smaller than that cutoff size were almost exclusively 

 immature. All females were therefore assumed to be 

 reproductively mature if TL was greater than 135 mm. 

 The proportion of fish in each age class that exceeded 

 135 mm TL was used to define an empirical age-based 



100 



150 200 



Total length (mm) 



250 



Figure 6 



Fit of the logistic maturity function to coded ovarian devel- 

 opmental stage data. Circles are means, which are brack- 

 eted by ±1.0 standard deviation (all samples collected by 

 trawling during February-March. 1991 ). 



maturity ogive. Results indicated that 7.9^; of l-yr-old fish 

 spawned, whereas 99. 0"^/ of 2-yr-old females reproduced. 



When coupled with some type of recruitment model, the 

 four functional relationships given in Figures 3-6 can be 

 used to estimate population weight-specific fecundity and 

 a weight-based population sex ratio. These latter two vari- 

 ables are presented in Table 3 as part of a life table projec- 

 tion for shortbelly rockfish. In the table, age is increment- 

 ed discretely in one year steps to a maximum life span of 

 30 yr, which extends well beyond the maximum observed 

 age of 22 years (Pearson et al., 1991). All calculations were 



