142 



Fishery Bulletin 101(1) 



1.0 



0.0 



'a 

 u 



S -10 H 



C 



n 



B _2.0 



o 



-3.0 - 



-4.0 



2.0 -n 



- 1.5 - 



10 



05 



0,0 



I I ' ' ' I ' ' ' ' I ' ' ' ' I ' ' ' ' I 



Dfla 



10 15 



Age (d) 



II I "I II ' 



20 



25 



Figure 12 



Fit of ordinary least-squares regression of log^-transformed 

 coded lar\'al abundance (/ixlO "l on corrected larval age 

 (T+0.5) (upper panel). The lower panel shows the back- 

 transformation of the log^-linear model (with bias correc- 

 tion) superimposed on the original abundance data. 



where Aq = the relative sensitivity of the assessment to 

 parameter "0"; 



the resulting biomass after altering param- 

 eter "0" by ±8,^,; and 



the original unperturbed biomass estimate 

 (67,392 t^yr). 



B. 



Bn 



Perturbations equal to ±1 s,., were selected to reflect the 

 level of statistical uncertainty in the parameters them- 

 selves. Results showed that within this range of uncer- 

 tainty, certain parameters had essentially no effect on the 

 final estimate of spawning stock biomass (e.g. log^JHol- ^'' P' 

 f ), and others had a more substantial effect. In particular, 

 the assessment was most sensitive to estimates of the two 

 fecundity parameters (log,.|0| and 6) and to the intercept 

 term of the larval production and survival model (log^lNgl); 

 both of these findings are consistent with intuition. 



Also note that the estimate of adult natural mortality 

 rate (M) has only a minor influence on projected biomass. 

 Low sensitvity to this parameter is important because 

 M alone governs the adult age-structure, implying that 

 variation in age-structure has little effect on the overall 



stock assessment. This conclusion was portended by re- 

 sults presented in Figures 7 and 8, which illustrate the 

 relative insensitivity of weight-specific fecundity to age. 

 Fundamentally, this conclusion is due to the nearly lin- 

 ear relationship between individual female fecundity and 

 specimen weight (6=1.14, Table 2, Fig. 5); that is, a fixed 

 mass of mature females produces roughly the same larval 

 output, irrespective of its age composition. 



This property is quite useful because it suggests that 

 an accurate estimate of M is not required to make use- 

 ful projections of total biomass. As discussed previously, 

 obtaining a representative sample of adult rockfish is 

 difficult (Lenarz and Adams, 1980); yet such a sample is 

 usually needed to estimate mortality. Pearson et al. ( 1991 ) 

 also highlighted the problem of estimating the natural 

 mortality rate of shortbelly rockfish. Using empirical 

 longevity estimates {T,,,^^ q=22 yr, T,„ax. o'=20 yr) as inputs 

 to Hoenig's (1983) regression equation and sample size 

 model, they concluded that for shortbelly rockfish 0.20 < M 

 < 0.35/yr Even over this rather broad range of plausible 

 natural mortality values, our results indicate that bio- 

 mass estimates vary by only ~9'7e (Fig. 14). 



In contrast, mis-specification of the temporal progres- 

 sion of spawning could have a very large effect on the total 

 biomass estimate. Results presented in Figure 15 show the 

 sensitivity of the total biomass estimate to a range of values 

 for //q. Because this parameter depends directly on fj and 

 CT,, which were estimated with good precision (Table 2), the 

 expected effect on the total biomass estimate is relatively 

 minor Even so, if the mean of the spawning distribution ac- 

 tually occuiTed two weeks earlier (i.e. 18 January instead of 

 2 February), the biomass estimate would be grossly in error 



Discussion 



It is widely recognized that most age-structured stock 

 assessments depend critically on the availability of aux- 

 iliary information to adequately constrain solutions to 

 these complex models (Deriso et al., 1985; Hilborn and 

 Walters, 1992; NRC 1998; Quinn and Deriso, 19991. How- 

 ever, even with lengthy time series of landings, discards, 

 age compositions, length compositions, survey CPUE data, 

 and logbook effort statistics, it is by no means certain 

 that complex stock assessment models will precisely or 

 accurately estimate total stock biomass (NRC, 1998). 

 Faced with this dilemma, simple procedures like the one 

 presented here become far more attractive, particularly 

 because the coefficient of variation on the final biomass 

 estimate from this pilot study was relatively precise (i.e. 

 I9''t ). Moreover, the estimate of absolute biomass does not 

 depend on the development of a long time series of data 

 and it can be obtained rather quickly 



We note that in comparison with previous hydroacoustic 

 assessments, which ranged from 153,000-295,000 t,' our 

 estimate of the total biomass of shortbelly rockfish in the 

 vicinity of Pioneer and Ascension Canyons (67,400 I) is 

 substantially lower Because one of the primary goals of 

 our study was to obtain a more precise biomass estimate 

 than the hydroacoustic estimates, it is important to care- 



