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Fishery Bulletin 88(4), 1990 



catches (particularly in the 100-149 fm depth interval) 

 would likely contain bocaccio and chilipepper as well 

 (Gunderson and Sample 1980). The greatest degree of 

 overlap would be for bocaccio and chilipepper. Bocac- 

 cio occur over a greater latitudinal range than chilipep- 

 per, but in the area off California where both species 

 are abundant, it could be difficult to maintain marked- 

 ly different catch levels for the two species. An im- 

 proved version of this model would incorporate prob- 

 abilities for different levels of bycatch, so that the 

 optimal policies would be constrained by the degree of 

 targeting that was feasible (Pope 1979). 



Another important assumption is that the species in- 

 cluded in the objective function are interchangeable in 

 the marketplace. That is a valid assumption for the 

 commerically important Sebastes species, including 

 widow rockfish, bocaccio, and chilipepper. However, 

 demand for splitnose rockfish has been low because of 

 its small size and low fillet yield (Lenarz 1986). A low 

 price would be expected for shortbelly rockfish because 

 they are small in size and must be processed rapidly 

 (Lenarz 1986). Lenarz (1986) suggested that better 

 marketing approaches will be needed before significant 

 quantities of either splitnose or shortbelly rockfish can 

 be harvested. For the model used in this study, dif- 

 ferences in price among species could be accommodated 

 easily and the objective function could be modified to 

 maximize some function of income. It would also be of 

 practical importance to determine whether all vessels 

 participating in these fisheries caught all the species 

 used in the objective function. Policies that result in 

 variable catches of the species used in the model would 

 be less appropriate if some fishermen did not catch or 

 were unable to market some of the species. 



The objective function could also be modified to in- 

 clude costs of fishing (see, for example, Pikitch 1987). 

 However, the current practice of the Pacific Fishery 

 Management Council is to manage for maximum sus- 

 tainable yield; costs of fishing are not considered. Stock 

 assessments are restricted to estimation of Acceptable 

 Biological Catch (ABC), and the Council considers some 

 socioeconomic factors when determining "Optimum 

 Yield" from the ABC. 



A limitation of this study was the assumption that 

 model parameters M, B^, and A were known. Those 

 parameters strongly affect equilibrium yields; conse- 

 quently, when they are not well estimated, the passive 

 policies used in this study might be outperformed by 

 an adaptive probing strategy (Walters 1986). Under 

 such a strategy', short-term fluctuations in fishing mor- 

 tality and yield would be accepted in order to better 

 estimate the productivity of the stock and improve 

 long-term management. 



Another potential limitation of the model used in this 

 study was the assumption that errors in estimating 



biomass were not autocorrelated. That assumption may 

 be valid when estimates are based on methods such as 

 a swept-area trawl survey, although the fishery man- 

 ager would be expected to balance any single estimate 

 of stock size against observations from prior years. 

 Autocorrelated errors would be likely in cases where 

 estimates were based on a time-series of catch data. 

 Such errors would be expected to have more serious 

 consequences than the independent errors assumed 

 here. An approach for introducing autocorrelated 

 errors might be to use CVs of the same magnitude as 

 assumed here but to use a 2- or 3-year moving-average 

 estimate of biomass to set quotas. Errors in estimating 

 biomass might also be correlated among species; for 

 example, swept-area trawl surveys may underestimate 

 the biomass of several species. 



A possible limitation of this model was the assump- 

 tion that the reliability of assessment data was equi- 

 valant for all species. If differences in the reliability 

 of estimates were substantial, it might be found that 

 a reliable single-species policy would be preferable to 

 a multispecies policy that incorporated unreliable in- 

 formation on additional species. 



Summary 



1 When constant F policies for different objective 

 functions were compared, the optimal F, total yield, 

 and variance for total yield decreased as the level of 

 risk aversion increased. 



2 Single-species and multispecies variable F policies 

 for maximizing harvest did not increase total yield 

 significantly compared with constant F policies. 



3 Single-species and multispecies variable F policies 

 for the logh and negx objective functions provided a 

 substantial reduction in the variance of total yield, com- 

 pared with a constant F policy for maximizing harvest. 



4 For the logh and negx objective functions, the 

 variance for total catch was lower for the multispecies 

 than for the single-species variable F policies, except 

 for some cases for a five-species model or when biomass 

 CVs were 50%. 



5 Constant F policies for maximizing harvest (the cur- 

 rent management approach) were essentially identical 

 for different levels of random, non-autocorrelated 

 errors in estimating biomass. Mean yield was slightly 

 lower at higher biomass CVs for both constant F and 

 variable F policies. 



Acknowledgments 



I thank W.H. Lenarz, who suggested this research 

 topic and, along with P.B. Adams and K. Uelier, pro- 



