CHARACTERIZATION OF THE OPTIMUM DATA ACQUISITION 



AND MANAGEMENT OF A SALMON FISHERY AS A 



STOCHASTIC DYNAMIC PROGRAM' 



Gary E. Lord^ 



ABSTRACT 



The optimum data acquisition and management of a typical Bristol Bay sockeye salmon 

 fishery have been expressed as a problem in statistical decision theory. Optimality has been 

 defined as that set of sequential decision rules that minimizes the Bayes risk over the dura- 

 tion of the run. Economic losses or costs are ascribed to acquisition of catch and escapement 

 data in such a manner that an optimal data acquisition scheme can be defined in addition 

 to defining the set of optimal management strategies. 



The management and inshore harvesting of 

 salmon stocks characteristically consist of sev- 

 eral interrelated phases. Stock assessment and 

 run profiling are of importance both to the man- 

 agement personnel and to segments of the in- 

 dustry in planning their respective operations. 

 Prior knowledge of the run size and time pro- 

 file is useful in the jireliminary planning of a 

 management strategy that will in some way per- 

 mit the escapement of the desired number of 

 spawners. Similarly, such information also 

 serves the industry in planning the level of its 

 anticipated activities (Mathews, 1967). The 

 theoretical investigation described here was mo- 

 tivated by specific consideration of the data gath- 

 ering and management schemes currently ap- 

 plied in the Bristol Bay sockeye salmon fisher- 

 ies. However, the formulation is relatively 

 abstract and of sufficient generality so that, 

 properly interpreted, it may apply to a variety 

 of fishery situations which are evolutionary or 

 time varying in nature. Indeed, it is this dy- 

 namic aspect of the i)roblem that is at once the 

 crucial feature of the analysis and also the 

 principal source of analytical and computation- 

 al difficulty. 



Rothschild and Balsiger (1971) treated the 

 optimum management of the Kvichak fishery 

 of Bristol Bay as a problem in linear program- 



• Contribution No. 385, College of Fisheries, University 

 of Washington, Seattle, Wash. 



2 Fisheries Research Institute, University of Washing- 

 ton, Seattle, WA 98195. 



ming in which the various entities comprising 

 the run could be optimally allocated, subject to 

 various constraints on escapement, sex ratios, 

 etc., over the duration of the run. Optimality 

 was chosen as that set of allocation rules which 

 maximized the economic return, expressed as a 

 linear objective function, subject to the satisfac- 

 tion of a set of linear inequality constraints. 

 This formulation and solution as a linear pro- 

 gram are particularly powerful since the solu- 

 tion, easily obtained by standard techniques, is 

 particularly rich in interpretive detail. 



The formulation and solution as a linear pro- 

 gram suffer from several disadvantages, as 

 Rothschild and Balsiger noted in their paper. 

 First, the solution is deterministic in that it 

 assumes precise knowledge of the run size and 

 its time profile. In actual practice, although 

 there is considerable investment in stock assess- 

 ment and run forecasting, the resulting esti- 

 mates are subject to considerable variation. Sec- 

 ond, not all of the constraints are "firm," i.e., 

 inviolable. This applies especially to the escape- 

 ment. Presumably a unique optimum escape- 

 ment for each actual realization of the run ex- 

 ists, but it is not necessarily imperative that this 

 escapement be attained. Instead it may be as- 

 sumed that an escapement below the optimum is 

 accompanied by some economic loss, suitably 

 discounted, for the diminished future returns. 

 Similarly, an excessive escapement will result 

 in a loss due to the decreased catch and, if in 

 the right-hand tail of a dome-shaped (Ricker 



Manuscript accepted April 1973. 



FISHERY BULLETIN: VOL. 71, NO. 4, 1973. 



1029 



