SECT. 4] FISHERY DYNAMICS THEIR ANALYSIS AND INTERPRETATION 469 



stock as a whole, and also that the operation of catching fish for tagging and of 

 attaching a tag to them should not adversely affect their subsequent survival. 

 For a further discussion of the estimation of mortality rates by these and other 

 techniques which can be used in similar circumstances, the reader is referred to 

 the original work of the authors (Beverton and Holt, 1956, 1957). 



Estimation of the parameters K and W& of the von Bertalanffy growth 

 equation seldom presents much difficulty if size and age data are available. It 

 could scarcely be expected that any simple mathematical function could give 

 a precise fit to the observed growth of fish under all conditions ; unequal 

 availability of food to fish of different sizes, for example, might produce distor- 

 tions in the growth curve which would not be followed closely by any except a 

 highly complex function. Nevertheless, the simple von Bertalanffy equation 

 has been found to give a satisfactory fit to the growth data of a wide range of 

 fish species, and serious exceptions are rare. 



It is obvious from (10) that the catch obtained from a year-class throughout 

 its fished life is proportional to its initial numbers when recruited ; and, indeed, 

 it can be shown that the average catch over a period is similarly proportional 

 to the average recruitment during that time. For most purposes it is not, 

 therefore, necessary to attempt to estimate the absolute number of recruits, 

 but instead it is sufficient to use the model to compute the "catch per recruit", 

 since this latter quantity is influenced by changes in the amount of fishing or 

 in the selectivity of the gear in the same proportion as would be the actual 

 average yield over a period. 



Having obtained estimates of the parameters in (10), the equation may be 

 used to compute either the equilibrium relation between catch and fishing 

 effort by varying the value of F, or the effect of changing the selectivity of the 

 gear by altering the value of the age t c at which fish enter the catch. Beverton 

 and Holt (1957) give a number of curves of equilibrium catch of this kind for 

 the plaice and haddock fisheries, and from a consideration of the effect of 

 changing both F and t c together have developed the concept of eumetric fishing , 

 in which the gear selectivity is so adjusted that it allows the greatest steady 

 catch to be obtained that is possible with the particular amount of fishing 

 effort which is being generated. 



In practice, it is seldom possible to obtain accurate estimates of all the 

 parameters, especially of the natural mortality coefficient M , although it may 

 well be feasible to establish a range of values within which the true value is 

 likely to lie. For example, Beverton and Holt (1959) have shown that within 

 certain groups of fish species, notably the clupeiods and the gadiformes, there 

 is a tendency towards a characteristic relation between natural mortality and 

 growth pattern, so that even if no direct estimate of M is available it may 

 nevertheless be possible to establish its likely range within certain limits simply 

 from a knowledge of the growth pattern. The analytical model may then be 

 used to test the effect of this range of uncertainty of the parameter in question 

 on the conclusion which is to be established from the properties of the model. 

 Sometimes it may happen that the answer to the question — for example, 



