VII 



RELATIVE GROWTH 



229 



The range of the allometric equation is illustrated by examples such as the interspecific 

 comparison of heart rate (Fig. 35) ; the oxygen consumption in Artemia salina, which follows 

 the surface rule over more than 5 orders of magnitude in weight (Bertalanffy and Kry- 

 wienczyk, 1953); or the relative growth of the human heart (Linzbach, 1955). The heart 

 maintains its allometry constant (a = 0.95) over a range of 5 orders, from i/ioo g in the 

 embryo weighing i g up to 300 g in the adult weighing 75 kg, while it increases from the 

 size of a pinhead to that of a fist, and undergoes all kinds of changes in shape, structure 

 and composition. 



6Kh 7Kh 8Kh 



4Kh 



5Kh 



ann 



2ann 



6 ann 



12 ann 



25 ann 



Fig. 31. Relative growth in man. Changes in proportion are expressed in head lengths 



(Kh). After Stratz, 1928. 



(b) Morphological applications of allometry 



In a newborn child the length of the head is approximately i /4 of the total 

 length of the body; in an adult, it is only 1/8. Conversely, the legs are compara- 

 tively much shorter in the baby than in the adult (Fig. 31). The proportions of 

 the adult human are established in the way that the head grows relatively slower 

 and the legs faster than the rest of the body. Thus relative growth, i.e. the ratio 

 of growth rates of the various parts of the body, leads to changes in proportion and 

 hence is a preeminent morphogenetic factor. 



The changes of form exhibited by a developing organism are, to a large extent, 

 changes in proportion determined by relative growth. In many cases relative 

 growth follows the equation of simple allometry, over the entire development or 

 at least over physiologically defined cycles of growth. The validity of the allometric 

 equation has been shown in many hundreds of cases from all animal classes. 

 Figs. 32 and 33 are illustrative examples. 



The theoretical implications of the principle of allometry require a brief discussion. 

 Classical morphology has spoken of a "budget law" (Goethe) or loi de balancement 

 (Geoffroy St. Hilaire) meaning that in an organism there is a characteristic and 

 constant "equilibrium" between the organs and, as we may add, the chemical 

 components. Thus overdevelopment of one part will be connected with lack in 

 another part; if the "equilibrium of the organs" is disturbed by removal of a part, 

 compensatory growth will set in, etc. This balance of organs, intuitively recognized 

 by the classical morphologists as modification of an ideal "type" or "bauplan" 



Literature p. 253 



