FISHERY BULLETIN; VOL. 72, NO. 4 



or gadoids. Both plaice and halibut grow by more 

 than an order of magnitude during their adult 

 lives. Gushing (1972) distinguished growth 

 overfishing from recruitment overfishing. In the 

 first the stock loses weight by too much fishing, as 

 Petersen suggested, but recruitment is not af- 

 fected. In the second, recruitment is affected; it is 

 noticeable in the pelagic stocks at a lower rate of 

 exploitation than in the demersal stocks because 

 the pelagic fishes have less capacity for stabiliza- 

 tion, being less fecund. 



Populations were well described by the logistic 

 curve, which expressed the theory of balance in 

 stating that any change in the carrying capacity of 

 the environment was compensated by a change in 

 the net rate of increase of the stock. From the 

 changes in biomass in time, average estimates of 

 the two parameters (net rate of increase and carry- 

 ing capacity) can be obtained. Such models are 

 called descriptive because the parameters are not 

 estimated independently but are derived from the 

 changes in biomass. In fish populations the con- 

 tributions of growth and recruitment are com- 

 pounded in the application of the logistic curve, 

 whereas it would be desirable to distinguish them. 

 Both Thompson and Bell (1934) and Graham 

 (1935) concluded from the application of the logis- 

 tic curve that age determination was no longer 

 necessary. Had this conclusion been applied quite 

 firmly the distinction between the effects of 

 growth and recruitment in fish populations would 

 have become impossible. 



Graham's (1935) major explicit achievement 

 was the application of the logistic curve to fish 

 populations. Another achievement, an implicit 

 one, was to encourage the application of the 

 methods of operational research arising from the 

 second world war to fish population dynamics by 

 Beverton and Holt (1957), which led to the solu- 

 tion of the problem of growth overfishing. The 

 logistic curve was developed more fully by 

 Schaefer (1954, 1957). He derived a catchability 

 coefficient from the relation of stock density to 

 fishing effort and used it to obtain catch, which he 

 then related to effort in the form of a parabola. 

 Over a long time period, enough annual observa- 

 tions give an estimate of maximum sustainable 

 yield. The advantage of this method is that the 

 result can be expressed simply and convincingly. 

 The disadvantages are 1) that at least a patient 

 decade of data collection is needed to establish the 

 position of the maximum, given a sufficient spread 

 of fishing effort and 2) that upward or downward 



trends in recruitment would be distinguished with 

 difficulty. 



THE ANALYTIC MODEL 



The first analytic model was Russell's (1931) in 

 which the changes in stock were separated into 

 components of growth, recruitment, and mortal- 

 ity. Beverton and Holt (1957) devised a series of 

 models, including the well-known yield per re- 

 cruit one and the less well-known self-regener- 

 ating yield curve, in which they incorporated their 

 stock and recruitment relationships. The catch, 

 or yield, was expressed as a function of fishing 

 mortality and of the age at first capture. The most 

 important point about the yield per recruit model 

 is that the maximum yield is obtained from infor- 

 mation on growth and fishing mortality, inde- 

 pendently of the catches. There is no need to wait 

 for a long time to establish the curve, and manage- 

 ment decisions can be taken quickly, other con- 

 siderations being equal. 



The yield per recruit model was the theoretical 

 solution to the problem of growth overfishing, and 

 the practical solution was to increase the age at 

 first capture with increased mesh size in the 

 trawls. For management it is a clear solution and 

 it is likely that the present agreement on man- 

 agement in the North Atlantic originated in its 

 simplicity. There were lengthy discussions on the 

 science and on the technology, but there are now 

 agreed minimum landed sizes and minimum mesh 

 sizes for a number of species throughout the North 

 Atlantic. It must be said, however, that conserva- 

 tion by mesh regulation is least conservation be- 

 cause it is adapted to the smaller and numerous 

 species like the haddock in the North Sea; larger 

 species (for example, cod or turbot) are not neces- 

 sarily conserved there as well as they might be. 



In the yield per recruit model it is assumed that 

 recruitment does not decline under the pressure of 

 fishing. The argument presented by Beverton and 

 Holt was that recruitment is so variable that the 

 downward trend at low stock would be very 

 difficult to detect. In management there was an 

 unforeseen consequence: that fishing could con- 

 tinue until recruitment was seen to fail. Then, 

 because of the same high variability of recruit- 

 ment, fishing would continue until it was too late. 

 However, with care, the yield per recruit model 

 can be used when the stock and recruitment rela- 

 tionship is unknown; for example, if fishing is 

 reduced, the yield per recruit will not decline and 



860 



