VII 



RELATIVE GROWTH 



233 



3g 5g lOg 



50g lOOg 



500g 1kg 



5 kg 10 kg 



50kg 100kg 500 kg 1000kg kg 

 Body weight 



Fig. 35. Pulse rate and body size in mammals. It may be assumed that the rate of blood 

 transported per minute is proportional to basal metabolic rate, as the oxygen consumed 

 must be transported by the blood. This volume is equal to stroke volume (.S") x pulse 

 rate (F). In a first approximation, S may be taken as proportional to body weight (w). 

 Basal metabolic rate of mammals follows interspecifically the 34 power rule (p. 218). 



r" 3/4 



^,3/4 and F = ^^^~ 



Hence: 



S-F 



C" -1/4 



The figure shows that the allometry constant of pulse rate, a a — 0.28. Notwithstanding 

 the gross oversimplification which neglects anatomical, physiological, ecological, etc., 

 differences, absolute body size is the dominating factor determining pulse rate, in the 

 enormous range from the dwarf bat (4 g) to the elephant (2000 kg). Modified after 



Bertalanffy, 1942a, 1951a. 



physiological changes. The general validity of the principle of allometry for 

 physiological phenomena renders it unlikely that phenomena not yet investigated 

 should follow a basically different pattern because otherwise they would be 

 incompatible with the physiological phenomena observed and their dependance 

 on body size (Adolph, 1949). Important physiological rules, such as the surface 

 rule of metabolism (p. 181), are special cases of the principle of allometry. 



(/) Physiological and growth gradients 



Another developmental principle emphasized by Huxley (1932) is that of 

 growth gradients. The allometric equation only expresses total growth of the 

 organ concerned. However, organs seldom grow uniformly in all dimensions but 

 there are one or more growth centres around which growth rates vary in the 

 form of gradients. If parts of an organ growing allometrically as a whole are 

 examined, the allometry constants of the parts usually show a gradient. For 

 example, in the growth of an extremity, the distal parts show the highest negative 

 allometry. If growth gradients are plotted against the axis of the organ or organism, 

 growth profiles are obtained which indicate the pattern of growth upon which 

 morphogenetic changes are based. 



The principle of the growth gradients is closely related to the polarity of the animal 

 body and its ''physiological gradients''. According to Child (1941) axial gradients of a 

 quantitative nature represent the basis of the various manifestations of polarity. Such 

 gradients appear as susceptibility gradients (different susceptibility of regions of the body 

 toward noxious agents) ; as metabolic gradients (differences in respiration and cognate 

 processes) ; and as morphogenetic gradients (differences in specific potency of forming 

 organs such as the graded head-regeneration potency of different regions of the body in 

 planarians). According to Child, these physiological gradients are, in principle, uniform 



Literature p. 233 



