738 PERISSODACTYLS xxx. 10- 



evolutionary sequence. Thus Robb (Fig. 490) shows that the length 



of a horse's face increases between embryo and adult along a line 



similar to that found in the series *Hyracotherium to Equus, and that 



adult horses of different sizes vary similarly in face proportion. A 



nearly fitting line gives constants b = 0-25 and k = 1-23. Other 



methods of plotting, for instance face length against cranium length, 



give somewhat different results and it cannot be considered certain 



that no new genetic factors have 



A Huracotnerium- Equus u • 1 j • ^.u 



? „ „„ y been involved in the increase 



B Equus, 5mo-25u. / r r . , , . , 



r c pa a/ f •••' 01 face-length throughout the 



C ******** Equus, Snet/ancf- / n b . b 



7 Percheron / u whole evolutionary sequence. 



-^ Lj=Z5x Ji- Again, reduction of the lateral 



digits of the toes is perhaps not 

 based on any steady genetic 

 change except that related to 

 size. However, in this case 

 there was probably one rela- 

 tively sudden change in the 

 constant b (which may be said 

 to express the body size at 

 which the toe begins to form). 

 Thus in the three-toed horses 

 the length (y) of the side toes 

 is related to that of the cannon 

 x, log skull length bone of the central digit (x) by 



Fig. 490. Relative rates of growth in horses, the equation 

 The lines show regression of log skull length 0>g7 



on log face length; in A, the line of horse phylo- J ~~ * 5 



geny ; B, the ontogeny of Equus; c, various races j , one-toed horses from 



of Equus of different sizes; D, y = 025 .v 123 . in ™ ° ne XOetl Ilorbeb iroin 



(After Simpson from the data of Robb.) *PUoMppuS Onwards 



y = o-8 x°-". 



There has therefore been little change in the relative growth-rate, 

 which is negatively allometric in all horses, so that the lateral toes 

 are relatively smaller in the larger animals. 



1 1 . Rate of evolution of horses 



Study in the same way of other horse characters, for instance those 

 involved in hypsodonty, shows that special genetic changes may be 

 involved and that genetic change does not go on at a constant rate. 



Estimates of rate of evolution for the whole animal have also been 

 made by Matthew, Simpson, and others. Assuming that the genus is 





5) 



J I I L 



