I go 



GROWTH 



PRINCIPLES AND THEORY 



empirical characteristic of the species. It determines, however, the pertinent 

 growth type as will be shown in the following. 



(g) Metabolic types and growth types 



As there are different metabolic types with respect to the relation of metabolic 

 rate and body size, there are also several growth types distinguished by the 

 growth curves of the species concerned. It appears that definite connections 

 between metabolic and growth types can be established. 



If for m in the basic equation (5.18) (denoting the dependence of anabolism of 

 building material on body size) the value is inserted which is experimentally 

 found for the size dependence of resting metabolism, the growth laws for the 

 organism in question follow. 



In this way three metabolic and growth types can be distinguished. 



First type. In the first type (Fig. 8) respiratory rate is proportional to the 2/3 

 power of body weight, corresponding to the surface rule. In this case, the basic 

 growth equation becomes: 



dwjdt = T] ur'^ — y.w (5-24) 



Solution of this equation gives for growth in weight: 



(5-25) 



with Wq = weight at the time ^ = o. For growth in linear dimensions, propor- 

 tional growth presupposed, we obtain : 



dljdt = E~kl (5.26) 



'=f-S-'»)-" f^-^'* 



with /q = initial length and the new constants k = y.j'^ and E = 'nPlSI for linear 



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r^ 



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2400 



2000 



1600 



1200 



c 

 800 •- 



400 I 



0.5 2.5 4.5 5.5 8.5 10.5 12.5 

 Time in years 



length growth, weight growth. 



Growth equations: / = 46.84 — (46.84 — 6.8) <?-0.278f 



^ = [13-93 — (13-93 — 2-08) ^-0.235r]3 

 After BertalanflTy, 1934. 



Fig. g. Growth of Abrarnis brama. 



