FISHERY BULLETIN: VOL. 78, NO. 1 



4 .8 1.2 1.6 2.0 2 4 2.8 3.2 3.6 4.0 4.1 4.8 



X 

 Figure 3.— Continued. 



varies for fixed values ofi?i , cr^, both the mean and 

 the variance vary significantly. Table 4 reinforces 

 this impression to a degree. If the mean per period 

 harvest does not vary significantly with changes 

 in the value of cr^, it might be expected that the 

 present estimate of a^ will suffice. This is borne 

 out by Table 4, where the bounds on the maximum 

 expected total loss is <0.01, which is <1% of the 

 optimal Bayes expected value. 



Some significant expected loss in value wheni?2 

 varies is seen, but the loss is less than might be 

 expected from Table 3. The values in Table 4 when 

 i?2 varies are all <4% of the true value. These 

 results suggest that if Equation (1.1) is the correct 

 form of the model, and the present parameter es- 



timates have relatively small variance, then little 

 is gained in expected value if the more complicated 

 policy is used. The same may not be true if the 

 population size is unobserved. 



All of these results suggest a model that is fairly 

 robust to our lack of understanding of nature. A 

 possible explanation for this can be made from the 

 discussion on the effect of grid size. As long as 

 there is some cutoff population size below which no 

 harvesting is allowed, and this cutoff assures that 

 the absorbing state cannot be reached with proba- 

 bility one, then our management can only damage 

 the stocks to a degree. 



All of the policies examined in this paper have 

 such a minimum cutoff. The rest of the policy will 

 determine the relative mean and variance of the 

 harvest, and techniques are presented to examine 

 these features in detail. Uncertainty about the 

 values of the parameters will affect the total re- 

 turn, but present estimates often can give a satis- 

 factory approximation. The truly risk adverse de- 

 cision maker can use present estimates of the 

 parameters that are weighted to be on the cautious 

 side. 



SUMMARY 



Uncertainty in fisheries management can be 

 faced head on. Techniques exist that allow us to 

 gain much insight on managing randomly varying 

 populations. Optimization procedures allow us to 

 reduce our attention to the few best policies, and to 

 analyze their properties, rather than to pick 

 policies ad hoc that meet no special criteria. 



Optimization under uncertainty can also lead to 

 a reconsideration of what is valued in managing a 



Table 3. — ^Trials with varied parameters. 



Rrver 



Value CJf fl2 



Value of (7 



Optimal policy 



Mean per 

 penod harvest 



Variance 



% time 

 no harvest 



Wood 



Wood 



Wood 



Wood 



Branch 



Branch 



Branch 



Branch 



Table 4. 



-Largest possible deviation in value of the approximate policy compared with the 



true Bayes policy. 



48 



