SECT. 4] FISHERY DYNAMICS — THEIR ANALYSIS AND INTERPRETATION 48l 



of the fishing effort — the fishing power of the vessels and gear and their distribu- 

 tion relative to the fish population — should be thoroughly investigated so as 

 to be able to measure fishing effort in units which are as closely proportional as 

 possible to fishing mortality rate. 



Certain practical difficulties arising in the treatment and interpretation of 

 data are also present in both approaches, although their consequences may 

 differ. The most important of these, in general, concerns the effect of fluctua- 

 tions in recruitment which are uncorrelated with size of parent population. It 

 has been mentioned earlier that these are often so great that they completely 

 mask the underlying relation between stock and recruitment — whatever that 

 may be. In the Beverton-Holt approach this means that the only possible way 

 of treating recruitment in the theoretical model is to regard it as fluctuating 

 about a mean which is independent of population size ; this may not be the 

 truth, but in such a case no more information can be extracted from the data 

 available. The analytical model can still be used, nevertheless, for prediction on 

 a "catch per recruit" basis, and for many purposes this is a useful procedure 

 until such time as sufficient data have accumulated to enable the definitive 

 relation between stock and recruitment to be established. Fluctuations in 

 recruitment present similar difficulties in the Schaefer method; they cause a 

 scatter to appear in a plot of catch against population size and this may make 

 it difficult to fit any theoretical relation between them with any precision. 

 Again, the conclusions which can be drawn are correspondingly uncertain. It 

 follows, in fact, that if no relation between stock and recruitment can be 

 detected for incorporation in a Beverton-Holt model, then an analysis of catch 

 and effort data for the same fishery over the same period by the Schaefer 

 method would be equally inconclusive as far as this particular relationship is 

 concerned. 



It would obviously be valuable to be able to compare the results of applying 

 both the Beverton-Holt method and the Schaefer method to the same fishery, 

 but at the present time there are few, if any, in which the data required for 

 both methods are equally reliable. Such a comparison is now being made for 

 the yellowfin tuna of the Eastern Tropical Pacific, for which the growth and 

 natural mortality parameters have only recently been estimated, and will be 

 reported upon in the near future. A comparison can also be made theoretically, 

 however, and leads to certain important conclusions. It will be remembered 

 that in the Schaefer method the coefficient of natural increase is taken as being 

 a linear function of population biomass. This results in a paraboidal curve 

 relating equilibrium catch to population size, with the maximum catch occur- 

 ring at exactly half the maximum population size in the virgin state. Now a 

 relationship between catch and population, in which different values of the 

 latter are generated by changes in the amount of fishing, is also implied by the 

 Beverton-Holt type of model. A formal mathematical treatment of this 

 problem is not practicable, owing to the complex nature of the equations in- 

 volved, but graphical solutions may readily be obtained from which certain 

 general conclusions can be established. Thus it is found that the simple model 



