GENETIC CHANGE AND EVOLUTIONARY CHANGE 



409 



old). From that point on k = 1 ; in other words, growth is isometric, face 

 and cranium increasing in length at the same rate. 



Line B (Fig. 18.3) represents allometry in the phylogenetic line leading 

 to the modern horse. Here the growth ratio, k, seems to be slightly greater 

 than it is in the ontogeny of the modern horse (about 1.8). But each point 



45 

 41 

 37 



33 



29 



26 



23 

 re 



55 20 



o 

 E 18 



-E 



i 16 



o 



-. 14 



:S 12 



c 



re 

 Li. 9 



8 





y 



Pliohippus 

 ° Hypohippus 



Merychippus 



Mesohippus intermedius 



Mesohippus bairdi 



Hyracotherium 



_L 



5 7 8 9 10 12 14 16 18 20 23 26 29 



Cranium-length (cm) logarithmic scale 



FIG. 18.3. Allometry of facial length in horses. Line A: al- 

 lometry in the ontogeny of the modern horse. Line 6: allome- 

 try in the ancestral line leading to the modern horse. Plus signs 

 indicate modern horses (Equus); open circles indicate prehis- 

 toric horses. (Redrawn from Reeve and Murray, "Evolution in 

 the horse's skull," Nature, Vol. 150, 1942, p. 402.) 



on the graph is based on a single specimen; the difference from 1.5 might 

 not be found to be significant if a larger number of specimens were meas- 

 ured. Reeve and Murray ( 1942) pointed out that simple allometry of face 

 growth to cranium growth seemed to prevail until about the time of 

 Merychippus, when a change in skull proportions occurred "by an increase 



