xxx. io RELATIVE GROWTH-RATES 737 



teeth and reduction of the lateral digits to short stumps, still three- 

 jointed and carrying hoofs, but vestigial in the sense of never touching 

 the ground. The presumption is that this type of structure was found 

 advantageous for life on large grassy plains produced by arid Miocene 

 conditions, the high-crowned teeth being needed to grind the tough 

 siliceous grasses. 



Apparently the type was very successful and in the Pliocene it 

 produced various populations. *Hipparion, with the two lateral toes 

 remaining as vestiges, spread through Eurasia in the Pliocene. *Nan- 

 nippus was a small form that remained in America. *Pliohippns was 

 another American descendant from *Merychippus, and here the lateral 

 digits were lost altogether in the Pliocene, the metapodials remaining 

 as long thin vestiges. When the land connexion with South America 

 became open this type of horse migrated there and produced a special 

 development, *Hippidion of the Pleistocene, with rather short legs, 

 perhaps correlated with a mountain habit. 



Meanwhile in the late Pliocene or early Pleistocene the *Pliohippus 

 stock of North America finally reduced the lateral metapodials to short 

 splint bones and produced the Equus-type, which spread thence over 

 all the available land-masses, becoming then extinct in North and South 

 America until reintroduced by man. 



10. Allometry in the evolution of horses 



Although Eqvus is certainly a very different creature from *Hyraco- 

 therium, we are fortunate in that many of the differences are due to 

 measurable changes in proportions. A beginning has been made with 

 attempts to estimate the rate of evolutionary change, as a preliminary 

 to study of the factors that influence it. Some of the changes in pro- 

 portion seen during horse evolution are a consequence of the increase 

 in size. If an organ grows relatively faster or slower than the body 

 as a whole it is obvious that its proportions will differ in animals of 

 differing adult size. The size of an organ, y, in relation to that of 

 the body, x, is often expressed as y — bx k y where the constant k 

 describes the relative growth rate. If k > 1 the organ becomes larger 

 in larger animals and is said to be positively allometric (J. S. Huxley). 

 The demonstration that growth actually follows this law in particular 

 cases is not easy, and the underlying assumptions have been questioned. 

 It is probably true, however, that organs do sometimes differ in rela- 

 tive growth-rates, and the method provides a means of investigation 

 of the proportions of an organ not only at one stage but throughout 

 the growth period, and indeed also between adults throughout an 



