20 MANAGEMENT OF HIGH SEAS FISHERIES 



well known methods of computing compound interest. Assuming 

 a constant natural mortality rate, a constant growth of 5 cm. per 

 year based on some imperfect data on North Sea Plaice, and a con- 

 stant recruitment, he was able to show that when the mortality rate 

 was less than the growth rate, the total catch from such an ideal 

 fishery would rise with the fishing rate until it reached a maximum 

 and then Avould fall at higher fishing rates. At a maximum rate of 

 fishing the catch would equal the weight of the fish recruited. 



As the rate of natural loss was increased to equal or exceed the 

 growth rate the maximum disappeared from the yield curve. 



This relationship was later developed independently by Thomp- 

 son and Bell (Thompson and Bell, 1934). They went farther than 

 Baranov, however, since they demonstrated that by application of the 

 theoretical relationships to the catch records of northeastern Pacific 

 halibut they could explain the variations that had occurred in both 

 total catch and catch per unit of effort on the basis of the changes 

 that had occurred in the amount of gear fished. Again, the recruit- 

 ment, natural mortality rate, and gro^vth rate were all held constant 

 in each model used. The theoretical models were fitted to the data 

 by choosing different values for the natural mortality. The growth 

 rate used was that determined for halibut by H. A. Dunlop, former 

 Director of the IPHC. These models dealt with the changes that 

 occur from year to year in the catch as a result of changing rates of 

 fishing rather than confining their attention to equilibrium condi- 

 tions. The major contribution of this work was to demonstrate that 

 the fishery was the dominant factor in controlling the abundance of 

 halibut. The situation was obscured by a paper published by Bur- 

 kenroad (1948), which concluded that the change in abundance of 

 northeastern Pacific halibut was due to a natural fluctuation in 

 abundance and was not due to regulation of the fishery. Burken- 

 road's conclusion resulted from an improper use of data published 

 by the Commission, as shown by Thompson (1950) and others. 

 Nevertheless, Burkenroad was quoted by McDougal and Burke 

 (1962), and by Fukuda (1962). It is now generally accepted by 

 fishery scientists that the recovery and stabilization of the halibut 

 fishery of the northeastern Pacific has resulted from the Interna- 

 tional Pacific Halibut Commission's regulations. 



Later works by Ricker (1940, 1958) and Schaefer (1954) have ex- 

 pressed the same relationship in different ways. Ricker expressed the 



