648 



Fishery Bulletin 88(4). 1990 



Figure 2 



Mean rockfish biomass from lUO replicate 100-year simulation runs 

 for the three-species model, using the constant fishing mortality rates 

 that maximized harvest and assuming that the coefficient of varia- 

 tion for biomass estimates was 0. Results for the two-species model 

 with only bocaccio and chilipepper were similar and are not shown 

 here. 



Figure 3 



Mean rockfish biomass from 100 replicate 100-year simulation runs 

 for the five-species model, using the constant fishing mortality rates 

 that maximized harvest and assuming that the coefficient of varia- 

 tion for biomass estimates was 0. 



the actual biomass levels BJt]. .Bj,[t]. Following an 

 assumption made by Pope and Gray (1983) regarding 

 data used in stock assessments, I assumed that errors 

 in biomass estimates were lognormally distributed and 

 independent over time. The coefficient of variation 

 (CV) for biomass estimates was either 0, 25, or 50%, 

 liased on a review of the stf)ck-assessment literature 

 (Rivard 1981, Pope 1988, Pope and Gray 1983, Sen 

 1984, Weinberg et al. 1984, Methot 1986). 



Because the WOC trawl fisheries for rockfish are 

 regulated through catch quotas, F' (the policy F based 

 on estimates B'i[t]. .B'Jt]) was used to calculate the 

 annual quota Cj[t] as B',[t]F'j[tl(l - exp(-M| - F'|[t])/ 

 Z'j[t]. Bco I (the virgin biomass level used in the vari- 

 able F policies) and M, were assumed to be known 

 without eri'or. The actual F required to obtain CJt] 



from B|[tl (F|[t]) was either higher or lower than the 

 intended F (F',[t]), depending on the direction and 

 magnitude of errors in B'Jt]. .B'Jt]. 



Life-history information 



The relialiility of the jtarameter estimates (Table 1) 

 varies, depending on the length and magnitude of the 

 historical fishery for each species. A significant fishery 

 for widow rockfish developed in 1979, with average 

 1980-85 landings of 17200 t (Hightower and Lenarz 

 1986). Fisheries for bocaccio and chilipepper have ex- 

 isted for decades; average 1980-85 landings were 3200 

 t for bocaccio and 1 700 t for chilipepper (PFMC 1986). 

 Preliminary stock assessments based on catch-at-age 

 data have been completed for all three species. Land- 



