222 PROBLEMS OF RELATIVE GROWTH 



ened by the demonstration of the existence of growth-gradients. 

 As pointed out in Chapter IV, the method of Cartesian trans- 

 formation of related forms employed by D'Arcy Thompson 

 shows that the great majority of the striking changes in shape 

 and relative size of parts necessary for the evolution of a sunfish 

 (Orthagoriscus) from a Diodon-like ancestor not only need 

 not but cannot have been separately evolved ; they can only 

 be interpreted as due primarily to a single main change in 

 the form of the growth-gradient along the animal's axis. And 

 the factual evidence we possess, as well as a priori reasoning, 

 indicates that a mutation can act on a growth-gradient as a 

 whole, thus simultaneously altering the proportions of a large 

 number of parts. 



An even more fully worked-out example is that of the con- 

 formation of domestic breeds of sheep analysed by Hammond 

 (I.e.). As we have already seen in Chapter III, Hammond 

 has been able to show that the changes in proportions which 

 take place in foetal and post-natal life in improved breeds of 

 ' domestic ' sheep represent merely an accentuation of quali- 

 tatively similar changes which occur in unimproved breeds 

 and in wild species (Fig. 96). In other words, there is a 

 greater intensity of the relevant growth-changes, which means 

 primarily a steepening of the growth-gradients concerned. 

 Here again, the characters actually affected by selection are 

 quite few, namely the growth-gradients ; whereas the number 

 of what are usually called ' characters ' which are altered 

 during the process is very large. 



In general, we may say that the existence of growth-gradients 

 gives opportunity for mutation and selection to affect a 

 number of parts in a correlated way, thus greatly simplifying 

 the picture of the genetic and selective processes at work. 



The cases previously considered concern organs with specific 

 heterogony mechanisms. D'Arcy Thompson (1. c.) has drawn 

 attention at some length to the functional changes necessitated 

 by increase in absolute size. These are for the most part 

 well known, such as the need for increased relative weight of 

 skeleton in large land animals, the need for increase of absorp- 

 tive surface of the gut with increase of bulk to be nourished 

 (on which topic a recent essay of R. Hesse (1927) may be 

 consulted for further details), and so forth. In any case, 

 they do not so much concern us here, since we are chiefly 

 dealing with the automatic and primarily non-adaptive effects 

 of inherent growth-mechanisms. 



