FISHERY BULLETIN: VOL. 69, NO. 1 



cations. This is because a particular manage- 

 ment scheme might be on-the-average quite prof- 

 itable in the long run but might frequently 

 completely bankrupt the system for the first 20 

 years of operation. 



The problem of sex ratio is quite important 

 because it appears that the objective function 

 would be quite sensitive to selectively decreasing 

 the number of males in the escapement and thus 

 increasing the catch perhaps substantially. As 

 indicated previously, Mathisen's study (1962) 

 gives us some guidance on this subject and it 

 would appear that, in some instances, the 3:1 

 ratio might be conservative. Furthermore, 

 it should be mentioned that a year-to-year modi- 

 fication of sex ratio might be a useful cushion 

 for approaching stability for some economic as- 

 pect of the fishery. Finally, the problem of 

 escapement eludes us because in the wealth of 

 literature on the subject there appears to be 

 very little that is useful in setting the egg-min- 

 imum constraint. It is generally agreed that the 

 stock-recruitment relation for salmon is the fa- 

 miliar Ricker-type curve. It is well known that 

 the variability in these relations is quite large 

 (in the case of the Naknek-Kvichak run, at- 

 tempting to draw similarities between stock and 

 recruitment places tremendous stresses on the 

 imagination anyhow) and as a consequence, if 

 the dome-shaped model holds, a minimum escape- 

 ment set sufficiently, but not unreasonably high, 

 could, on the average be reducing the return 

 rather than increasing the return. 



It might be difficult even after several years 

 of setting the minimum escapement value at too 

 high a level, to detect, owing to the variability 

 in the system, the effect of this policy. If this 

 is true, then again we are asking the wrong 

 questions by studying the stock and recruitment 

 model per se. We are faced with a system that 

 is so variable, either intrinsically or in terms of 

 measurement techniques, or both, that a large 

 number of data points is required before we can 

 evaluate the relation between the empirical data 

 and the theoiy and then use the theory to jjredict. 

 There is but one point a year and so we are 

 asking nature to "stand still" for a large number 

 of years. Given these observations and our past 

 experience, we wonder whether it might not be 



more appropriate for management purposes to 

 avoid looking at stock and recruitment per se, to 

 intensify study of the physiology and behavior 

 of very young stages of fish, and thus examine 

 fundamental problems of cause and eff'ect, vis- 

 a-vis the variables that influence the magnitude 

 of egg production and survival of these eggs 

 and larvae or other young stages through the 

 first several months of their life. And finally, 

 in the meantime, would it be more appropriate 

 to consider measuring stock and recruitment in 

 terms of transition probabilities which might 

 be estimated by computing the median stock 

 and the median recruitment? Stock sizes which 

 are below the median would be poor, those which 

 are above, good, and similarly with recruitment. 

 The empirical data could then be used to esti- 

 mate probabilities of good-good, good-poor, poor- 

 good, and pooi'-poor transitions. We need not in 

 this procedure be restricted to medians, but 

 could in fact use any fractile, and in fact we 

 need not be restrained by fractiles because we 

 might want to place the dividing line at some 

 "optimal value" and explore the consequences. 

 In conclusion, then, we have formulated a LP 

 model for salmon runs and have shown how it 

 might be related to the Naknek-Kvichak run. 

 We see in this relationship that, given informa- 

 tion on the structure of the run, we can both in- 

 crease the value of the fish on the dock and at 

 the same time reduce processing time. Whether 

 it is worth obtaining the information in terms 

 of the indicated data and the ability to select 

 fish from the run to approach this allocation 

 and whether decreased processing time is, in 

 fact, a saving, are questions that must be an- 

 swered by the processing industry in light of 

 the increased value of salmon on the dock. If 

 our estimate of increased value is approximately 

 correct, we can see that allocation can add an 

 interesting value to the catch, but far greater 

 additions could come from reducing the escape- 

 ment, if this is possible, and alleviating the open- 

 access related problems. Perhaps the most in- 

 teresting feature of the model is the richness 

 of interpretations that LP aflfords in the salmon 

 situation and the nature of questions and data 

 needs raised by the model. Finally, we emi)ha- 

 size that, as Hillier and Lieberman (1967) note. 



138 



