194 



GROWTH PRINCIPLES AND THEORY 



recruitment, growth, capture, and natural mortality within such populations. This 

 analytical treatment was prompted by practical considerations of the fishing indus- 

 try in view of problems of overfishing and conservation. Discussion of the complete 

 model accounting for the primary factors mentioned is beyond the scope of the pre- 

 sent paper, even though it is connected with the concepts of "open systems ", "steady 

 states", and "general system theory" (Bertalanffy, 1950b) as applied to populations. 

 It is, however, worth emphasizing that a theoretical model of fishery as an important 

 branch of applied biology includes the equations under discussion as one of the fun- 

 damental factors. It appears that these equations are also introducedinjapanese fish- 

 eries (Kubo and Yoshihara, 1957 ; personal communication of Dr. Yoichi Yoshida) . 



-2 fO 



t' 



2000 



1500- 



1000 



500 



10 



15 20 



Age (yrs) 



Age (yrs) 



Fig. 13. Growth in length [a) and in weight {h) of plaice. After Beverton and Holt, 1957. 

 Curves are fitted by the Bertalanffy equations (5.28 and 5.29), with q = 0.00892 according 

 to Fig. 12. This example shows the sensitivity of the equations for demonstrating compli- 

 cating factors. Fit of the observed data by the equations is satisfactory, except for the 

 youngest age groups. For explanation, see Fig. 14. 



A relation similar to that derived by Bertalanffy et al. from the surface depend- 

 ence of respiration was found by Yoneda and Yoshida (1955; Yoshida, 1956) in 

 food intake. The quantity of plankton consumed by the sardine is proportional 

 to the square of body length, and the same appears to be true for assimilating 

 organs, such as the gill-rakers and the gut. 



Yoshida (1956) interprets these results in terms of energy. If Mj = energy 

 intake, M2 = maintenance metabolism, M^ = working metabolism, M^ = repro- 

 ductive metabolism, and Afj = growth metabolism, and if these terms are partly 

 proportional to w^'^, partly to w, the balance: 



