2i8 PROBLEMS OF RELATIVE GROWTH 



Perhaps the most interesting evolutionary aspect of the study 

 of relative growth is when we find a series of related forms pos- 

 sessing a markedly heterogonic organ, which not only differ in 

 size, but also succeed each other in order of absolute size during 

 evolutionary time. A classical example is afforded by the 

 deer (Cervidae). It was long ago pointed out that in a broad 

 way the antlers of deer increased in complexity from their first 

 geological appearance up to the Pleistocene, much as do the 

 antlers of an individual deer during its single lifetime, and 

 this was adduced as an example of the laws of recapitulation. 

 So in a sense it is, but it appears to owe its existence to the 

 presence of a fundamental heterogony-mechanism for antler- 

 growth, accompanied by increase of body-size both during 

 ontogeny and phylogeny. Increase of absolute body-size 

 automatically brings about disproportionate increase of antler- 

 size, and increase of antler-size appears to be of necessity 

 accompanied by greater complexity of branching (or palmation). 

 And this applies equally to the individual and to the race. 



Theoretically, the most interesting case is that of the 

 Titanotheres, worked out by H. F. Osborn (1929, and earlier 

 papers there cited). These, like so many other mammals, 

 begin their evolutionary career as small organisms, and steadily 

 increase in size until they become extinct. They also begin 

 hornless, and end with a single bifurcated frontal horn. 



But — and this is the salient feature of this example — Osborn 

 has been able to distinguish at least four distinct lines of 

 descent in the group, characterized by differences in skull- 

 shape, dentition, leg-size, etc., and presumably mode of life ; 

 and in each of the groups we meet with the same phenomenon 

 of small and hornless forms steadily increasing in size and 

 eventually becoming horned. Thus we find the origin of 

 horns of the same type, growing from the same location, taking 

 place independently in four separate groups : and Osborn 

 insists that this must be interpreted as true orthogenesis — in 

 the strict sense of the term, as implying predetermined varia- 

 tion of the germ-plasm, not merely of directional evolution. 



However, as pointed out earlier (Huxley, 1924; and see 

 Sturtevant, 1924), our studies make it clear that this interpre- 

 tation is not necessary. Granted (a) that there existed in 

 the germ-plasm of the ancestor of the four lines of descent 

 the hereditary basis of growth-mechanism for a frontal horn, 

 and (b) that increase of size up to a certain limit was advan- 

 tageous for Titanotheres in general, as would seem inherently 



