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Fishery Bulletin 88(4), 1990 



in yield was reported for Atlantic menhaden Brevoor- 

 tia tyrannus (Ruppert et al. 1985), compared with 

 only 1-2% for Pacific whiting Merluccius productun 

 (Swartzman et al. 1983) and widow rockfish (Hightower 

 and Lenarz 1989). Because, in this study, there was no 

 apparent advantage in using variable F policies to max- 

 imize harvest, the remaining results and discussion 

 focus on a comparison of the traditional constant F 

 policy for maximizing harvest versus variable F policies 

 (5) and (6) for the logh and negx objective functions. 

 Compared with a constant F policy, variable F 

 policies (5) and (6) provided a substantial reduction in 

 the variance of total yield with only a negligible loss 

 in yield. (The reductions in variance would be slightly 

 less if constant F and variable F policies for the same 

 objective function were compared.) The reduction in 

 variance did not appear to be particularly sensitive to 

 the number of species included, their life-history char- 

 acteristics, or the degree of correlation among species 

 for recruitment perturbations (Hightower 1990). How- 



ever, the level of density-dependence in the stock- 

 recruitment relationship may affect the relative per- 

 formance of different harvesting policies. In limited 

 additional runs, I found that the difference between 

 constant F and variable P^ policies generally decreased 

 as the degree of density-dependence increased (i.e., as 

 stock-recruitment parameter A decreased). When re- 

 cruitment declined markedly with reductions in spawn- 

 ing stock, both types of harvesting policies were 

 necessarily quite conservative. 



The advantage of the variable F policies can be illus- 

 trated by examining a Pareto Frontier (Walters 1975), 

 which shows the relationship between mean catch and 

 its variance. I developed frontiers for the two-, three-, 

 and five-species cases by simulating the fishery at 20, 

 40, 60, 80, and 100% of the constant F levels that max- 

 imized harvest (Fig. 4). When results for the variable 

 F policies were compared to the constant F frontiers, 

 it was clear that the reduction in variance was much 

 greater than could be accounted for by the lower yield 



