FISHERY BULLETIN: VOL. 71, NO. 2 



The maintainable yield would in this case 

 have been 3,134 whales, leading to a stock size 

 of about 78,360 whales in the later 1970's 

 (Figure 2b). 



These examples demonstrate some general 

 features. Firstly, they show that catch regula- 

 tions based on replacement yield, equivalent 

 sustainable yield or maintainable yield will all 

 lead to an equilibrium situation in which the 

 stock size and permitted catch reach a stable 

 level. In the case in which the stock has recently 

 been changing, regulation based on replacement 

 yield will maintain the stock at the level at 

 which it was at the start of this regulation, but 

 catches regulated at the level of sustainable 

 yield or of maintainable yield will lead to a 

 different stock level. If the stock had recently 

 been declining, the long-range stock level and 

 yield would then be rather higher than that 

 based on taking the replacement yield, and if 

 the stocks had recently been decreasing, the 

 long-range equilibrium would be reached at a 

 somewhat lower stock size. Although there 

 are some differences in catch level between 

 regulations based on sustainable yield and on 

 maintainable yield in the first years after intro- 

 duction, the long-term effects of these two 

 criteria for regulation are very similar. 



It would thus seem that replacement yield, 

 which maintains the stock at the same level, 

 but requires changing quotas in the first years, 

 and maintainable yield, which is the highest 

 catch that can be maintained indefinitely from 

 the stock size available, but will lead to a change 

 in stock size in the first years, will provide the 

 best guide for whaling management decisions 

 in situations in which stock sizes have recently 

 been changing. 



Any scientific advice on these matters should 

 be clearly defined. Part of recent confusion 

 about frequently changing estimates of permis- 

 sible yield by the Scientific Committee of the 

 IWC has been due to insufficient definition of 

 the terminology as outlined above. 



Finally, it may be noted, from the arguments 

 given above, that the rate of increase of popula- 

 tion depleted well below its level of MSY, but 

 completely protected thereafter, is less than 

 the net recruitment rate in an equilibrium 

 situation. For example, for recruitment rate 



8% , recruitment age 5 years, and natural mor- 

 tality rate 4% , the net recruitment rate in 

 equilibrium situation is 4% , but the rate of in- 

 crease in recovering, unfished, population in 

 any year would be about 3% of the stock size in 

 that year, or about 3.5% of the size of the parent 

 stock (the stock size 5 years earlier). 



NATURAL FLUCTUATIONS 



For fish, on the other hand, the lag effects on 

 the average are less disruptive to the simple 

 model than natural fluctuations, among which 

 changes in year-class strength are the most 

 striking. Where differences in year classes are 

 very large, it is likely that when a strong year 

 class enters the fishery the stock will increase 

 whatever catch is taken (within practicable 

 limits); when a succession of strong year classes 

 is replaced by a run of poor ones, the stock may 

 decrease even if fishing is cut back virtually to 

 nothing. In this situation it is difficult to talk 

 about a sustainable or maintainable yield. 



However, it is precisely in the situation of a 

 declining stock, when strong year classes are 

 being replaced by weak ones, that concern about 

 the management of the stock is likely to be 

 greatest, and when scientists are often asked for 

 advice (e.g., regarding herring in subarea 5 

 of ICNAF). Sometimes the advice is requested 

 in general terms, allowing the scientists to 

 describe the situation in detail, but leaving the 

 decision as to the control measures (such as the 

 level of catch quotas) to administrators. At 

 other times the administrators cannot decide 

 easily among themselves on the amount of catch 

 that should be taken and ask the scientists for 

 an explicit figure of the "correct" or "desirable" 

 catch. This requires some objective basis for 

 determining this, analogous to the sustainable 

 or replacement yield for whales. 



The simplest case is that in which the 

 abundance of recruits (strength of the year 

 class) is independent of the abundance of the 

 parent stock. All that management can do is 

 make the best use of whatever recruitment 

 happened to occur, that is, to maintain fishing 

 at whatever level is considered the optimum 

 position on the yield-per-recruit curve. In the 

 simplest situation the curve of yield per recruit 



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