GROWTH IN TIME OF THE TOTAL ORGANISM 



193 



(h) Application of the Bertalanjfy growth equations in fishery biology 



The Bertalanffy equations have been extensively used in fisheries biology, and 

 this material provides valuable evidence for both theoretical verification and 

 practical application (Beverton, 1954; Graham, 1956; Beverton and Holt, 1957). 

 Based upon the large material of the Fisheries Laboratories of the British 

 Ministry of Agriculture, Fisheries and Food as well as that of the Fisheries 

 Biology Branch of the FAO (Food and Agriculture Organization of the United 

 Nations), Beverton and Holt state: 



"The equation we shall use throughout ... is that due to Von Bertalanffy; not only 

 does this give a growth curve closely similar to that shown in Fig. 13 (as reproduced in 

 this paper. Von B.), but the underlying concepts are, in our opinion, much the most 

 satisfactory of those which have so far been put forward . . . From an examination of the 

 published growth data for a number of species offish, it would seem that the von Bertalanffy 

 growth equation has a wide application. In most cases the fit to the data is . . . good . . ., 

 while in the remainder the departures are not greater than might be expected from 

 sampling errors or biological factors" (in Graham, 1956, p. 381; Beverton and Holt, 

 i957» P- 288). 



Not only the wide applicability of the growth equations under consideration 

 is important; it is of crucial significance that, if deviations from the typical curves 



50r 



1000 

 Weight (g) 



Fig. 12. Relationship between weight and length in plaice. After Beverton and Holt, 1957. 

 Weight is expressed by the equation w = 0.00892/-^ showing that equation (5.5) is ap- 

 proximately true and hence the relation between weight growth and length growth 

 expressed in equations (5.28, 5.29) applies in fair approximation. Deviations from equation 

 (5.5) are expressed in differences in the x values as calculated from length and growth 

 data (Figs. 9, 10). It can be seen, however, that these differences are small; if the constant x 

 be considered a physiological magnitude, the difference of calculated values would hardly 



exceed experimental errors. 



are encountered, they can be explained by interfering factors, detailed analysis 

 of which leads to the disappearance of the seeming discrepancies. Cases such as 

 exemplified by Figs. 12, 13, 14 are of especial interest as verification of the theory 

 and equations. 



The Bertalanffy growth equations are used by the British researchers as part 

 of a dynamical model of exploited fish populations which takes into account 



Literature p. 253 



