378 



POPtJLATIONS 



greater. If rate of capture is very high indeed 

 and greatly reduces the number of spawners 

 it is conceivable that the rate of recruitment 

 may be adversely affected. But the number of 

 eggs produced by each spawner is so great, and 

 the proportion that can find room to grow is 

 so small, that we need not for the time being 

 consider this possibility too seriously. So far 

 as we know at present, there is no obvious cor- 

 relation between the number of eggs spawned 

 and the number surviving to reach the catch- 

 able stock, in any of the important species" 

 (p. 83). 



This argument is admittedly oversimplified 

 since it rests upon the large assumption 

 "that environmental conditions remain con- 

 stant, that there is, for instance, the same 

 average annual production of fish food." 



The crucial question as to the optimal 

 yield now arises: What level of population 

 stabilization safely permits the greatest 

 weight of catch, or, as Russell cogently 

 puts it, how may a stock be subjected to 

 "rational exploitation?" A general, first ap- 

 proximation is deducible from Russell's for- 

 mulation. If M is not great in proportion 

 to C, the maximum value of C obtains 

 when A + G, which is equal to C -f- M, is 

 maximal. Assuming that the average value 

 of A is not considerably influenced by 

 moderate changes in the intensity of fish- 

 ing activity, and assuming further that the 

 stock is subjected to active commercial fish- 

 ing, A -f- G will vary roughly in proportion 

 with G. Since G is the yearly upgrowth of 

 the population with the exclusion of the 

 fishes that are captured or otherwise elim- 

 inated, it is when G is maximal that the 

 greatest steady yield obtains. 



Suppose, says Russell, that two popula- 

 dons are fished at different rates: one at 

 30 per cent reduction year by year in terms 

 of number of catchable stock, the other at 

 60 per cent reduction. At the 30 per cent 

 rate the mean age and weight of the fishes 

 both in the catch and in the population 

 will be greater than at the 60 per cent rate. 

 Therefore, these differential exploitations 

 result in a changed age distribution be- 

 cause of differential rates of mortality. Un- 

 der the 30 per cent procedure there will be 

 proportionately more and heavier and older 

 fishes. As the intensity of fishing increases 

 there eventually comes a time when the 

 total weight of the catch decreases. "It fol- 

 lows also that a very intense fishery may 

 actually yield no more than a very mod- 



erate fishery, both being well under the 

 possible maximum" (p. 85). 



A hypothetical, yet reasonably realistic, 

 illustration of the relation of fishing inten- 

 sity to yield has been published by Graham 

 (1938). This is presented pictorially in 

 Figure 132, which contrasts events in a 

 population exploited at a rate of 90 per 

 cent capture per year with one at 30 per 

 cent capture per year. The natural mortal- 

 ity is assumed to be 5 per cent per year 

 for each population. Yield, in terms of 

 weight of catch, is shown, and the effect 

 of the differential exploitation on both 

 stock and catch is made clear. It is evident 

 that under the 90 per cent rate the catch 

 consists primarily of small, fight-weight 

 fishes. With one-third this amount of fishing 

 the catch consists of few small fishes and 

 more large fishes in their third and fourth 

 years of age. The total weight of the catch 

 is exactly the same in both cases, but under 

 the 30 per cent procedure a large stock, 

 some six times as great, of fourth-year 

 forms remains. "So that in a case hke this 

 you can catch as much in weight by fish- 

 ing at a moderate rate as you can by fish- 

 ing three times harder" (Russell, p. 86). 

 The general ecological and conservation 

 principle that emerges is this: With in- 

 tense exploitation the catch consists of a 

 preponderance of small forms of low 

 weight, while with more moderate exploita- 

 tion fewer forms are caught, but these are 

 of larger size. Thus, what is gained as 

 numbers through intensive effort may be 

 offset by a reduction in actual weight. 



Perhaps this is the chief point that can 

 be made about the optimal yield problem: 

 For many populations (at least for popula- 

 tions such as those that concern the marine 

 fisheries biologist) there exists an exploita- 

 tion rate, neither too high nor too low, 

 that, when in operation, results in the 

 maximum steady yield. When this yield is 

 realized, the product of the number of 

 fishes multiplied by their average weight is 

 maximal. 



It is obvious that our treatment of the 

 optimal yield problem, which is an adum- 

 bration of Russell's treatment, is presented 

 in an oversimpfified way. The role of cer- 

 tain factors such as natural mortality, 

 growth rate, density effects, food supply, 

 and so forth, has not been adequately eval- 

 uated. In part this oversimplification is a 

 deliberate attempt to present clearly the 



