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



141 



38- 



OJ 

 ■D 



37- 



O 



124 



00000 d<ic 

 Oi 

 OOo 



Longitude 



Figure 11 



Map showing the spatial distribution of very young (0-2 d) shortbelly rock- 

 fish larvae sampled during February 1991. The size of the circles is propor- 

 tional to log_,( catch ^■l). 



Historical data from CalCOFI station 63.55 (Fig. 1) 

 showed that in the vicinity of Pioneer Canyon the sea- 

 sonal availability of prefiexion shortbelly rockfish larvae 

 peaks during January-March (see "observed" in Fig. 13). 

 These data were fitted to a normal curve (see "predicted" 

 in Fig. 13) and indicated that the distribution of prefiex- 

 ion larvae is centered on 7 February (calendar date /} = 

 37.88) and the spawning season typically lasts -70 d 

 (cr=17.39). Assuming that prefiexion larvae represent a 

 pool offish 1-15 d old (Laidig et al., 19911 that experience 

 a daily instantaneous mortality rate of Z = 0.11/d (Table 2), 

 the distribution of age-0 larval production is centered earli- 

 er in the spawning season, i.e. 2 February (calendar date ij„ 

 =32.62) and the spawning season is slightly less protracted 

 (cr,|= 16.86). The estimated long-term mean distribution of 

 age-0 larval shortbelly rockfish production at CalCOFI sta- 

 tion 63.55 (Fig. 1) is depicted in Figure 13 as a solid line. 



The midpoint of the 1991 bongo-net survey (DSJ-9102) 

 was 11 February (calendar date 42). If larval production 

 were normally distributed and centered at //q = 32.62, 



with cj,. 



16.86, we calculated that the area under the 



curve from 41.5 to 42.5 is 0.02026. This represents the 

 estimated fraction of the total annual larval production 

 that occurred per day at the midpoint of the cruise and is 

 the area under the curve between the two vertical lines 



shown in Figure 13. Thus, we expanded by 49.35 spawning 

 d/yr ( 1/0.02026) the estimated daily biomass ( 1366 t/d) to 

 67,392 t/yr, which is the estimated total stock biomass of 

 shortbelly rockfish in the study area. The standard error 

 of this estimate, based upon delta-method computations, 

 is 12,900 t/yr, yielding a coefficient of variation of 19Q. 



Sensitivity of the biomass estimate 



Presented in Table 2 is a simple sensitivity analysis of all 

 parameters estimated in the larval production spawning 

 stock biomass assessment of shortbelly rockfish. For each 

 of the 23 parameters, the coefficient of variation (expressed 

 as a percentage) is given. In addition, the effects of indi- 

 vidual parameter perturbations on the final estimate of 

 spawning stock biomass are shown. In each case, a param- 

 eter ( 0) was altered by plus or minus one standard error 

 of the estimate (s,,) and the resulting overall effect on the 

 assessment was expressed as the percentage change of the 

 perturbed biomass estimate in relation to the unperturbed 

 value, i.e. 



A = 100 



Br, 



