GENETIC CHANGE AND EVOLUTIONARY CHANGE 417 



does such distortion of a system of coordinates mean in terms of biological 

 processes? The diagram would be interpreted to indicate that a center of 

 very active growth in the vertical dimension developed in the tail region, 

 and that the growth rate declined progressively from tail to head. Presum- 

 ably these changed growth rates arose as the result of mutation occurring in 

 the evolutionary line leading to the strange sunfish. Consequently, as the 

 descendants increased in size the posterior regions of the body increased in 

 height more rapidly than did the anterior regions, with the result observed. 



The reader is referred to D'Arcy Thompson's stimulating classic. On 

 Growth and Form ( 1942), for other and more complicated applications of 

 the method, including that to changes in skull shape encountered in the 

 evolution of the horse. The method offers admirable description of ob- 

 served trends, but the physiologic and genetic forces at work in production 

 of the trends remain largely undetermined. This condition should not be 

 permitted to continue. D'Arcy Thompson's studies offer real challenge to 

 anyone interested in evolution of animals as wholes. That this technique 

 of analysis is not being entirely neglected is indicated by its application to 

 changes in skull shape in evolutionary lines of prehistoric mammals (e.g., 

 Colbert, 1935; Patterson, 1949). 



In conclusion, we would not convey the impression that allometry offers 

 the key to all evolutionary change. But it illustrates how evolution can oc- 

 cur by means of mutation of genes controlling growth rates during em- 

 bryonic development. For example, suppose that in the evolution of a 

 rhinoceroslike animal a large nasal horn would be useful. How can we 

 visualize the action of natural selection in providing such a horn? Natural 

 selection might favor the possessors of a mutation that increased the rate 

 at which the horn grew as the embryonic head increased in size. Such a 

 genetic change, once inaugurated, might ultimately have far-reaching ef- 

 fects if the evolution of the species involved great increase in body (head) 

 size. 



Furthermore, allometry aids in explaining the development of neutral or 

 nonadaptive characteristics, those which have little or no significance in 

 the lives of their possessors. Natural selection itself can only account for 

 characteristics which are useful. But a horn, or a spine on the thorax of a 

 beetle, may become disproportionately long as the body itself becomes 

 larger, even though the lengthening is of no value to its possessor. We need 

 only suppose that the genes controlling growth of the horn or spine deter- 

 mine a disproportionately high rate of growth. So long as the lengthening 

 remains neither beneficial nor harmful natural selection will not operate 

 either for or against the rate-gene. As noted previously, other indifferent or 



