414 INTRODUCTION TO EVOLUTION 



tionary history. Recall that k is slightly less than 1 in the allometry formula 

 describing the relationship between lateral digits and cannon bone in the 

 feet of three-toed horses. 



Finally, we should note that changes in the genes controlling growth 

 rates would constitute mutations having large eflfects. The effects might 

 even be so large that the mutations could rank as examples of the "systemic 

 mutations" postulated by Goldschmidt (1940) as necessary if drastic evolu- 

 tionary change is to occur. Yet in themselves these mutations might be ordi- 

 nary gene mutations requiring no special rubric of "systemic." In Fig. 18.2 

 we have presented a hypothetical example of horn evolution involving a 

 gene which determines that the horn shall grow in length faster than the 

 head increases in length. Suppose that in an immediate descendant of ani- 

 mal A that gene underwent a mutation, the effect being to lower the rate of 

 growth so that the horn increased in size more slowly than did the body as 

 a whole. That is, the mutation changed the allometric growth rate from 

 positive to negative. Then, through isolation, genetic drift, and other forces 

 discussed on earlier pages, two populations might become established, 

 one population possessing the unchanged gene, the other the mutated one. 

 If body size increased in both populations, we should find them coming to 

 differ greatly in the character of the nasal horn. The population with the 

 unchanged gene would develop long horns, as shown in Fig. 18.2. On the 

 other hand, the population with the mutated gene would develop relatively 

 short horns; indeed, as the animals became large the horns might have 

 become reduced to mere blunt, bony calluses (Fig. 18. 4A). What a dif- 

 ference in the end products of the two evolutionary Hnes! And all, 

 conceivably, the result of a single mutation occurring early in evolutionary 

 history. 



For sake of simplicity we have confined our discussion of allometry to 

 single dimensions, e.g., length of horn. But material objects have three di- 

 mensions, and growth in one dimension is not always proportional to 

 growth in the other two. In drawing Fig. 18.2 we have actually shown the 

 horn increasing in breadth as well as in length, although the point was not 

 mentioned previously. Suppose growth in length had been positively allo- 

 metric, as shown, but growth in breadth had been isometric, relative to 

 increase of head length. The result would have been a much slenderer 

 horn (Fig. 18.4B) than that shown in Fig. 18.2E. Or again, we have shown 

 the head itself increasing in height in approximate proportion to the in- 

 crease in length. This conception need not have been true. The growth rate 

 in height might have exceeded the growth rate in length. In that case E 

 would have had a much higher "forehead" than that shown. Conversely, 



