i8o 



GROWTH 



PRINCIPLES AND THEORY 





-(l-m)xA 1/1-w 



) 



(5-19) 



with Wq = weight at time t = o. 



Equation (5.19) is isomorphic with equation (7.13) which will be discussed 

 later (p. 236ff.) : 



y = {i — re-^'')" (5-20) 



Hence the discussion given there applies. The curve has no inflexion (for 

 positive /)ifi/i — m = a ^ i, but is sigmoid for a> i, the point of inflexion 

 lying between o and i/e (0.37 of final size), and shown as function of a (> i) 

 by the curve for /j (a) in Fig. 39, p. 237. It can be seen that weight-growth curves 

 will always show an inflexion because ( i — m) < i , but curves of length growth 

 may or may not have an inflexion (see below). 



Anabolism of building materials, i.e. synthesis of high-molecular cell compounds 

 needs, on the one hand, building blocks such as amino acids, sugars, phosphates, 



TABLE 6 



METABOLIC TYPES AND GROWTH TYPES 



A. Anabolic processes depend on resorption (resorbing surfaces), (a) Micro-organisms: (i)Propor- 

 tional growth: linear and volume growth curves as B, I; spherical bacteria, yeast. (2) Growth 

 almost exclusively in length: linear and volume growth curves exponential; rod-like 

 bacteria, (b) Probably turbellarians. 



B. Anabolic processes depend on respiration. 



Metabolic type 



Growth type 



Growth equations 



Examples 



I. Respiration 

 surface- 

 proportional 



(a) Linear growth curve: 

 attaining without inflexion 

 a steady state. 



(b) Weight growth curve: 

 sigmoid, attaining, with 

 inflexion at ca. 1/3 of 

 final weight, a steady 

 state 



dw/dt = 7]w-li - v,w 



a) / = /*_(/*_/^)g-x//3 



•J 3 ^ — 



b) w = [V t«*-(V tw*- 



-\/ Wq)^-^'!^^ 



Lamellibranchs, 

 fish, mammals 



w, I: Weight, length at time t; w^, l^: initial weight, length; w* , /*: final weight, length; 

 Tj, x: constants of anabolism and catabolism. 



