142 GROWTH PRINCIPLES AND THEORY 2 



The maximum size in a species or taxonomic group is determined by the plan 

 of organization and environmental conditions. Well-known examples are the 

 insects, the heavy chitin skeleton of which prohibits surpassing a relatively small 

 size limit, or the whales which, because of the density of the aquatic medium, 

 can reach a far greater size and body weight than terrestrial animals. 



An excellent survey of minimum and maximum sizes in the various taxonomic 

 groups as caused by organization and environment was given by Rensch (1954). 

 Rensch discusses in detail that allometric growth (p. 246), with change of body 

 size, leads to complex changes of proportion of organs and physiological functions 

 which become intolerable beyond a critical order of magnitude, thus setting a 

 lower and upper limit of body size. 



In this connection only one point will be mentioned which is closely related 

 to theoretical concepts to be presented later. In many physiological activities 

 absolute body size is the predominant factor governing the rate of processes, in spite 

 of otherwise enormous anatomical, physiological, and ecological differences. 



This applies, for example, to total metabolism or pulse and respiratory fi'e- 

 quency. The latter maintain the same relation to body size over seven orders 

 of magnitude, from a dwarf bat weighing 4 g to an elephant of 2,000 kg (Fig. 35, 

 p. 233). The predominant role of body size is particularly well illustrated by the 

 fact that arctic as well as tropical animals fit into the "mouse-elephant curve" 

 of basal metabolic rate (proportionality to W^l*, cf. p. 218), so that metabolic 

 rate is essentially determined by its relation to body weight and is not adaptive 

 (Scholander et al., 1950). This corresponds to the fact that, as shown by measuring 

 of models (Krumbiegel, 1933), absolute size plays a much more inportant role 

 in the surface-volume ratio (and hence the heat economy of warm-blooded 

 animals) than the shape of the body. 



In the allometric equation (p. 224) the constant a (slope of the allometric regression 

 line) indicates the size-dependence of the process under consideration. The constant b 

 (the validity of allometric relationship presupposed) expresses taxonomical, physiological, 

 ecological, etc. peculiarities of the group of species investigated. Benedict's (1938) objection 

 that logarithmic plots may obscure species-specific differences is therefore unfounded 

 because such plots rather lead to recognizing deviations from the general trend and so 

 indicate such peculiarities if present. 



In many respects surfaces of the body appear to be a limiting factor of body size. 

 This is particularly clear in the relations between intestinal surface and body size 

 (Hesse, 1927; Bertalanffy, 1940a, 1951a; Harms, 1955). For example, among 

 coelenterates species with a smooth cylindrical gut are small, while tubularians 

 and anthozoa, with the development of a larger intestinal surface by invagina- 

 tions, reach considerable sizes. In intraspecific comparison, the relation between 

 intestinal surface and growth was demonstrated in planarians. The same principle 

 even applies to mammals : Dogs of larger races have a greater development of 

 intestinal surface than smaller ones. It appears that in lower metazoa such as 

 coelenterates and flatworms resorbing surfaces act as growth-limiting factor, while 

 in higher animals correlations between respiration and growth can be established 

 (p. 180). 



