Hightower" Rockfish harvesting policies in Washington-Oregon-California trawl fisheries 



647 



max 5;iog(C[t]) 



t 



ogh objective function). 



For most of the WOC trawl fisheries, the goal of the 

 Pacific Fishery Management Council is to maximize 

 long-term average yield by maintaining F at a specified 

 level. Thus the maxh objective function corresponds to 

 the current approach to management. Relative to maxh 

 policies, logh policies tend to provide less variable 

 catches so they may be more appropriate in fisheries 

 where price is sensitive to volume, the fishery provides 

 a substantial fraction of a fisherman's annual income, 

 or stability of volume is critical for marketing reasons 

 (Deriso 1985). Mendelssohn (1982) and Ruppert et al. 

 (1985) used maxh and logh policies to represent ex- 

 tremes along a risk continuum, in that maxh policies 

 are risk-neutral (marginal utility does not change with 

 increasing catch) and logh policies are risk-averse 

 (marginal utility decreases with increasing catch). 



I also evaluated a third more conservative objective 

 function for maximizing an exponential function of total 

 catch: 



max ^(1 



t 



exp(-C[t]/d)) (negx objective function) 



wliere 6 was a scaling factor (Raiffa 19(58). At small 

 values of 6 (relative to C[t] ), the marginal utility of ad- 

 ditional units of catch decreases rapidly. If 6 is large, 

 utility increases linearly with increasing catch. In order 

 to obtain highly risk-averse policies, I used 6 = 5 for C[t] 

 values of about 5 (2-species case) to 30 (5-species case). 

 Using this d value, negx policies were even more con- 

 servative than logh policies (Fig. 1). Of course, other 

 objective functions (and harvesting policies) could be 

 chosen that would provide greater reductions in the 

 variance of catch. For example, Murawski and Idoine 

 (1989) compared a series of constant-catch harvesting 

 policies for Georges Bank haddock Melanogramnius 

 aeglefinus. For a sufficiently low target catch (45% of 

 the average catch under a constant F = F„ i policy), 

 year-to-year variability in catch was zero. The logh and 

 negx objective functions used in this study were in- 

 tended to provide a compromise between maximizing 

 catch and minimizing variability of catch. 



Figure 1 



Alternative measures of the utility of the total rockfish catch in year 

 t (C[t] ). as determined by objective functions maxh:Utility(C[t] ) = C[t]. 

 logh:Utility(C[t]) = logjC[t]), and negx:Utility(C[t]) = l-exp(-C[t]/ 

 5). Utilities for each objective function were scaled to a maximum 

 value of 1. 



declines were noted for the unexploited splitnose and 

 shortbelly rockfish stocks. Because of its long life-span 

 and slow growth-rate, the splitnose rockfish stock con- 

 tinued to decline throughout the planning horizon. 

 Based on a series of optimization runs, I found that the 

 constant F for splitnose rockfish that maximized mean 

 harvest decreased as the horizon length increased for 

 policies up to 200 years in length. Planning horizons 

 greater than 100 years were impractical, however, due 

 to computing costs. Therefore, in order to obtain 

 results that were not dependent on the length of the 

 planning horizon, I obtained policies for the five-species 

 model using a 75-year transient phase within a 100-year 

 horizon (Law and Kelton 1982). Using this approach, 

 the objective function was based only on harvests 

 in years 75-100. Steady-state biomass levels were 

 reached within 100 years for all species except possibly 

 splitnose rockfish; thus, declines in stock size at the 

 start of the planning horizon were due only to high 

 initial biomass levels (Fig. 3). 



Planning horizon 



The uijtimization studies were done using a 100-year 

 planning horizon in order to obtain steady-state har- 

 vesting policies. In the two- and three-species cases, 

 the bocaccio, chilipepper, and widow rockfish stocks 

 declined to varying degrees at the start of the plan- 

 ning horizon luit reached steady-state levels by about 

 year 50 (Fig. 2). In the five-species case, sharp initial 



Errors in biomass estimates 



Most of the harvesting ] policies evaluated in this study 

 required biomass estimates for one or more species in 

 order to calculate the policy Fs used to determine the 

 annual quotas. To evaluate the practicality of these 

 policies, I introduced a random error term so that the 

 harvesting policy and resultant catch quota in year t 

 were based on simulated estimates B'Jt]. .B'Jt] of 



