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INTRODUCTION TO EVOLUTION 



that of another is sufficiently precise so that a mathematical statement of 

 it may be made. The formula employed is: y = bx" (or log y = A: log 

 X + log b). In this formula, x is the size or dimension used as a basis for 

 comparison, frequently the general body size; y is the size or dimension 

 of the part of the body being compared; b is the "initial growth index," i.e., 

 a constant expressing the size of y when x is 1 ; A is a constant indicating the 



FIG. 18.1. Allometry (differential growth) exhibited by forelimbs of male beetles of 

 the species Euchirus longimanus. Specimen at extreme right is a female; other specimens 

 are males arranged in order of increasing size. (After Champy; from Huxley, Problems 

 of Relafive Growth, Methuen & Co., Ltd., 1932, p. 56.) 



ratio that y bears to x (e.g., the ratio of the size of the organ being com- 

 pared to the size of the body as a whole). 



In Fig. 18.2 we present a hypothetical but true-to-life example of the 

 manner in which differential growth works. Fig. 18.2A represents a small 

 rhinoceroslike animal with a tiny horn on its nose. As indicated, the horn is 

 2.5 cm. long, and the length of the head measured from the base of the ear 

 to the tip of the snout is 25 cm. Since we wish to study changes in length of 

 horn as the head increases in size, we designate length of head as x in the 

 above allometry formula, length of horn as y. Thus, at the outset x = 25, 

 y = 2.5. For the purposes of this example we arbitrarily decide that the 

 value of the constant k shall be 2. If k were 1, the horn would increase in 

 length at the same rate as that at which the head increased in length. A k 

 value of 2 provides that the horn shall increase in length more rapidly than 

 does the head. 



