Prager: A nonequilibrium surplus-production model 



387 



by the model. This is an excellent reason (but not 

 the only one) to avoid the equilibrium assumption. 



A final important point raised by Sissenwine ( 1978) 

 is that, because the world is stochastic, one is truly 

 more interested in maximum average yield (MAY) 

 than MSY. Several studies (Doubleday, 1976; May et 

 al., 1978; Sissenwine, 1978) have shown that in gen- 

 eral MAY < MSY; thus harvesting MSY indefinitely 

 would lead to stock collapse. This result does not 

 make production models less useful, but does em- 

 phasize the necessity to use their results in the con- 

 text of other knowledge about the stock and as part 

 of an evolving view of stock dynamics. Fishery as- 

 sessment and management are dynamic processes 

 that must adapt to changing conditions and new 

 knowledge. It is inconceivable that we will ever know 

 enough about any wild stock to establish a manage- 

 ment regime that could be effective into the indefi- 

 nite future. The failure of MSY to be such a regime 

 is no failure at all. 



Notes added in proof 



1 I have recently been made aware of several pro- 

 duction-model applications that were circulated in 

 the Collected Papers of the International Commis- 

 sion on Southeast Atlantic Fisheries (ICSEAF). Per- 

 tinent documents include those by Butterworth et 

 al., 1986; Andrew et al., 1989; and Punt, 1989. 



2 Anyone attempting to implement the methods 

 described here should be aware that Equation 6, 

 when solved for F, can be double-valued. 



Acknowledgments 



I thank A. Anganuzzi, J. Bence, R, Deriso, A. Fonten- 

 eau, K. Hiramatsu, W. Lenarz, A. MacCall, R. Methot, 

 C. Porch, J. Powers, A. Punt, W. Richards, G. Scott, 

 P. Tomlinson, J. Zweifel, and two anonymous refer- 

 ees for comments on the manuscript or assistance 

 with the techniques described. In addition, sugges- 

 tions from J. Hoenig and V. Restrepo were particu- 

 larly helpful in improving many parts of the work. 

 Portions of this work result from research sponsored 

 by NOAA Office of Sea Grant, U.S. Department of 

 Commerce, under federal Grant No. NA90AA-D- 

 SG045 to the Virginia Graduate Marine Science Con- 

 sortium and the Virginia Sea Grant College Program. 



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