226 



GROWTH 



PRINCIPLES AND THEORY 



of a part stands in a constant ratio to that of another part or the whole, is in no 

 way obvious. In view of the tremendous complexity of the processes involved in 

 growth, it would rather be expected that parts start and cease to grow in some 

 irregular manner, without our being able to represent this process by a simple or 

 even a continuous function. That, at least in many cases, the simple allometric 

 relation applies is an indication that it is based upon general and fundamental 

 principles. It could also be objected that, owing to logarithmic plotting and scale 

 which maximize differences in small numbers and minimize them in large 

 numbers, the allometric relation is spurious and that almost any data plotted in 

 this way, can be fitted by straight lines. However, this objection is contradicted 

 by the facts. There are cases where data cannot be fitted by straight lines in the 

 log-log plot and hence the allometric relation is not applicable (Fig. 29) ; but such 

 cases are encountered only rarely. Conversely, if such approximation obtains, 

 it cannot be considered an artefact of logarithmic plotting. 



2 5 10 



Body weight in g 



20 



Fig. 30. Relative growth of testes in the mouse. The jump to a higher constant b takes 

 place at a body weight of about 7 g, corresponding to the growth cycles apparent in 

 growth-in-time of the body as a whole (Table 14). This shows the connection between 

 growth-in-time, relative growth of the testes, and change in hormonal balance (sexual 

 maturation). Teissier's data from BertalanfTy, 1951a. 



Breaks and jumps are frequently found in allometric plots so that all data 

 cannot be fitted by a single regression line (Figs. 23, 30). Then detailed analysis 

 usually shows that these discontinuities are not accidental but connected with 

 definable changes in the underlying process. If, for example, such discontinuities 

 are found in a number of processes in rats at a weight of c<z. 100 g {i.e. at the start 

 of sexual maturation), this is easy to understand in consideration of the changes 

 of hormonal balance at this period. 



A more serious objection against the allometric equation is of a mathematical 

 nature. If allometric equations apply to parts of an organ {e.g. the segments of 



