570 



Fishery Bulletin 90(3). 1992 



accuracy resulting from the beta approximation is often 

 small. 



Another fact to keep in mind is that the model pre- 

 sented by Press (1989) is only one possibility. Despite 

 the pessimism conveyed by Holloway (1979), it is con- 



Estimated variance of q 



2 3 0-4 5 0,6 7 0,8 9 10 



Least-squares estimate of q 



Figure 8 



Loci of parameter values under which a beta approximation 

 to the truncated t distribution gives an R- value of 0.95. if ' 

 was calculated by comparing the two distributions at q values 



of 0.01, 0.02 0.99. For n =5, parameter combinations 



lying to the interior of the two curves correspond to i?- 

 values <0.95. For n = 10, R' values <0.95 correspond to 

 parameter combinations lying above the curve. 



ceivabie that other models could yield the beta distribu- 

 tion as an exact result. 



Comparison with previous studies 



Of the many previous applications of Bayesian decision 

 theory to fisheries, the studies by Ludwig and Walters 

 (1982), Clark et al. (1985), and Walters and Ludwig 

 (1987) are most closely related to the present work. The 

 various features of the four approaches are outlined 

 in Table 1. The three previous studies exhibit certain 

 common features which distinguish them from the 

 present study, namely: (1) use of a discrete time scale; 

 (2) inclusion of an explicit adaptive management strate- 

 gy; (3) inclusion of environmental stochasticity as well 

 as parameter uncertainty; (4) inclusion of a positive dis- 

 count rate in the objective function; (5) assumption of 

 a normal form for the pdf of the uncertain parameter; 

 and (6) inability to derive an exact analytic solution, 

 even in the myopic case (except for one special instance 

 considered by Clark et al.). The present study is also 

 the only one of the group which includes both a 

 biomass-based model and a risk-averse loss function. 

 Ludwig and Walters (1982) found that the deter- 

 ministic optimum escapement level can be less than half 

 the value of the Bayesian solution. Although the con- 

 tinuous form of the model used in the present study 

 makes it difficult to talk about escapement per se, 

 equilibrium stock size might serve as a suitable proxy 



