GULLAND and BOEREMA: SCIENTIFIC ADVICE ON CATCH LEVELS 



The simplified description above does not in 

 fact fit precisely the actual situation in the 

 sea. Two main divergences may be mentioned: 

 1) the fact that the net rate of natural increase 

 will depend on past events as well as on the 

 current abundance and 2) there are many 

 sources of variation, other than exploitation, 

 in the abundance of populations. The most 

 important of these for many fish species of 

 commercial importance is natural fluctuations, 

 especially in recruitment, caused by variations 

 in environmental conditioning. Other causes of 

 variation, e.g., changes in the availability or 

 distribution of fish, will have significant effects 

 on the success or otherwise of the fishery in a 

 particular season, but will not be discussed 

 here. The first of these is particularly significant 

 for whales, and the second for some fish popula- 

 tions, especially in temperate and subarctic 

 waters. 



LAG EFFECTS 



For whales, the net rate of natural increase in 

 the exploitable part of the population is usually 

 expressed in numbers and is the difference 

 between the number of animals dying from 

 natural (nonfishery) causes, which will be 

 some fairly constant proportion of the number 

 in the current stock, and the numbers of recruits 

 entering the exploitable stock, which will be 

 closely proportional to the numbers of mature 

 animals alive some years previously, at least 

 at small to moderate population sizes. As the 

 population approaches its equilibrium, un- 

 exploited level, the recruits will be less, or the 

 mortality more, or both, than expected from a 

 purely proportional relationship with popula- 

 tion abundance. If the abundance of the stock 

 is changing, the concept of a sustainable yield 

 becomes complicated. If, for example, the stock 

 has recently been reduced, then the recruits 

 during the year will have come from a parent 

 population that is greater than the current 

 mature stock. The number of recruits may 

 then be appreciably greater than the number 

 of natural deaths, so that quite a large catch 

 could be taken and still leave the population 

 at the end of the year the same size that it was 

 in the beginning. However, such a catch could 



not be sustained indefinitely, since the number 

 of recruits in later years will decrease. For 

 such a stock a number of different terms may 

 need to be defined. 



The replacement yield for a given year is the 

 catch which, if taken, will leave the abundance 

 of the exploitable part of the population at the 

 end of the year the same as at the beginning. 

 This is specific to a particular year and includes 

 no concept of continuity. Even if the replace- 

 ment yield is taken in one year, it is unlikely 

 that the replacement yield in the following year 

 will be the same, unless this population has 

 remained at around the same abundance for 

 some time (not less than the time span between 

 birth and recruitment). 



The simple definition of the sustainable yield 

 refers to an equilibrium situation and cannot 

 strictly be used in a situation of changing stock 

 size. When the population has been changing it 

 may be convenient to define the (equivalent) 

 sustainable yield as the sustainable yield from 

 a population of the same abundance (or with 

 the same abundance of the exploited phase), 

 which has remained at this level of abundance 

 for a long time. It is the value that would be 

 obtained from reading off the yield correspond- 

 ing to the abundance in a figure such as Figure 

 1. Hence if the catch taken is set equal to this 

 sustainable yield, the population abundance will 

 not, in general, remain unaltered. 



It is evident that if the stock (or its exploit- 

 able phase) has recently been decreasing, and, 

 as in the case of whales, the recruits are 

 roughly proportional to the abundance of an 

 earlier and larger parent stock, the replacement 

 yield is greater than the sustainable yield of 

 the present stock size. If, on the other hand, 

 the stock has recently been increasing, the 

 replacement yield is equal to the difference 

 between the recruitment from a smaller parent 

 stock and the natural mortality of the greater 

 present stock and may therefore be lower than 

 the sustainable yield of either the parent stock 

 size or the present stock size. 



In a situation in which the stock is above the 

 level of maximum sustainable yield, the main- 

 tainable yield, as defined above, which is equal 

 to the maximum sustainable yield, is not 

 affected by recent changes in stock size. If the 



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