200 



GROWTH 



PRINCIPLES AND THEORY 



TABLE 11 



RATES OF C.ATABOLISM DETERMINED IN EXPERIMENT AND CALCULATED 



FROM GROWTH DATA 



^ Bertalanffy, 1934. 



2 Sprinson and Rittenberg, 1949b. 



^ Bertalanffy, 1938. 



(k) Deductive derivation of the system of growth equations 



Given one almost self-evident principle and a small number of empirical facts, 

 the family of growth equations can be derived by way of deductive mathematical 

 reasoning (Bertalanffy, ig4ib). 



Since the living organism is a metabolizing system maintaining itself by import 

 and export, building up and breaking down of component materials, it may be 

 expected that an organism grows when synthesis of building material exceeds 

 its degradation, in whatever way these processes are defined biochemically or 

 physiologically ^ The rate of synthesis and degradation is related to body mass 



^ The above statement applies to unicellular and animal organisms where, as a general 

 rule, the products of catabolism are exported and hence appear as a negative term in the 

 balance of metabolism and growth. It does not apply to higher plants where there is no 

 excretion comparable to that in animals, and living mass once formed persists. Conse- 

 quently, the model of growth discussed is applicable to unicellular organisms and multi- 

 cellular animals. It does not apply to plant growth which rather follows the principle that 

 increase is proportional to the living mass present, i.e. follows the logistic equation. The 

 good approximation of growth in plants by the logistic has been shown in numerous 

 examples. 



