196 



GROWTH PRINCIPLES AND THEORY 



(z) Metabolic types and growth types (continued) 



Second type. A second metabolic and growth type is found in insects (cf. also 

 G. A. Edwards, 1953), Helicidae, etc., where (Table 8) metabolic rate does not 

 follow the surface rule but rather is proportional to weight itself (Fig. 1 5). Here the 

 allometric regression line of metabolic rate against body weight has a slope of 45°. 

 Inserting m ^ i into equation (5.18) we obtain: 



dw 



ri w — y. w = cw (5'37) 



dt 



or integrated : 



w =w,e^', I =l,e^"' (5.38) 



Hence, an entirely different growth curve is to be expected. In the first type, 

 there is an asymptotic approach to a steady state because surface-proportional 

 anabolism is caught up by volume-proportional catabolism and eventually a 

 balance is reached. In the second type, anabolism and catabolism, both being 

 weight-proportional, run at the same pace. Hence growth rate does not decrease 

 but always increases, growth is not limited but exponential, and no steady state 

 is reached. Growth rather is stopped by essentially different mechanisms. In 



20 3040 60 80100 200 300 



Weight in mg 

 (Tenebrio) 



Fig. 



20 40 60 80 



Time in hours 

 (Drosophila) 



15. Second metabolic and growth type: Insects, a Dependence of metabolic rate on 

 body size, b Growth curve. After Bertalanffy and Muller, 1943. 



