DECISION THEORY APPLIED TO THE SIMULATED DATA 

 ACQUISITION AND MANAGEMENT OF A SALMON FISHERY^ 



Gary E. Lord^ 



ABSTRACT 



A salmon fishery management model utilizing statistical decision theory has been constructed. The 

 model provides for the successive acquisition of data that can be used to formulate and maintain an 

 optimum management strategy. The Bayes risk is defined as the e.xpected economic loss resulting from 

 a set of fishery management decisions and the criterion of optimality is taken to be the strategy that 

 minimizes the Bayes risk. Specific functional forms are assumed where necessary in order to obtain a 

 closed form expression for the Bayes risk. The Bayes risk, in units of numbers of fish, can then be 

 computed for any particular sequence of fishery management decisions. 



This paper represents a continuation of an earlier 

 effort (Lord 1973) in which statistical decision 

 theory was applied to the data acquisition and 

 management of a salmon fishery. The crucial 

 feature was not that the species considered was 

 salmon but that the assumed fishery was both 

 dynamic and subject to errors in the population 

 estimation. The population is assumed to be sub- 

 ject to continuing assessment, however, so that as 

 the season progresses it is possible to make re- 

 peatedly more refined estimates of the true state 

 of nature. The management strategy may thus be 

 modified successively to reflect the additional data 

 as they become available. 



The development was quite abstract and pre- 

 sented only the basic theory in a relatively general 

 way. The present paper represents an inter- 

 mediate situation in which the theory is applied to 

 a specific model constructed to represent such a 

 fishery. The principal features of this model are: 1) 

 a Ricker spawner-return relationship, 2) simulated 

 sampling for population estimation purposes, and 

 3) an economic loss function based on maximum 

 substained yield (MSY). 



A limitation of the present model is that it is 

 constructed in such a manner that a closed analytic 

 form is obtained without recourse to Monte Carlo 

 or other approximate methods of analysis. In other 

 words, the Bayes risk may be computed exactly 

 upon the specification of well defined sets of 



'Contribution No. 456, College of Fisheries, University of 

 Washington, Seattle, WA 98195. 



^Fisheries Research Institute, College of Fisheries, University 

 of Washington; Present address: Applied Physics Laboratory, 

 University of Washington, Seattle, WA 98195. 



parameters. The imposition of such analytical 

 requirements constrains the choice of functions to 

 those that are mathematically tractable. An- 

 ticipating the final results. Equations (18) and (20), 

 I feel that about the maximum degree of gen- 

 erality has been retained consistent with analyt- 

 ical tractability. It is likely that models possess- 

 ing a greater degree of fidelity to the actual fishery 

 situations will require the use of Monte Carlo 

 methods as Mathews (1966) used in his simulation 

 of the cannery portion of the Bristol Bay fishery. 



ANALYSIS 



The notation used in Lord (1973), with only 

 minor changes, will be retained here. In this 

 section I will discuss the Bayes risk for a particular 

 fisheries model based on the Ricker spawner- 

 return relation. The criterion of optimality will be 

 taken as MSY. Economic losses will accrue as the 

 actual management strategies depart from the 

 optimum. Generally these losses will be reflected 

 in either a decreased present catch or in dimin- 

 ished future returns due to prior overfishing. 



A loss function proportional to the difference 

 between the optimum catch and the actual catch, 

 on an MSY basis, will be assumed. This is a simple 

 and intuitively reasonable concept but, nonethe- 

 less, a unique formulation of the loss function from 

 this criterion is no simple task. The difficulty arises 

 from the use of a spawner-return relation which 

 reflects the biological fact that the present state of 

 the system is necessarily the result of past actions 

 and, similarly, that future conditions will depend 

 on present actions. In the case of sockeye salmon, 



Manuscript accepted March 1976. 

 FISHERY BULLETIN: VOL. 74, NO. 4, 1976. 



837 



