174 GENERAL DISCUSSION [ch. xiv 



sarily killed out, as was the rule under natural selection. In fact, 

 as the curves must be the result of uniform pressure, they could 

 not result from, or under, natural selection. 



The logarithmic curve undoubtedly shows some marked devia- 

 tions from the straight line at the further end (cf. p. 37), and 

 Longley (25) says "the hollow curve, we may therefore reasonably 

 assume, results from some sort of compounding of a series of 

 geometric series of different common ratio, but all lying between 

 the limits of J and 1 ". 



But if genera and species are formed like this, it must almost 

 certainly have been by single steps, and if the old ones were not 

 killed out, natural selection can have had little or no influence in 

 the matter. They cannot have been formed by structural adap- 

 tation. Gradual mutational change is no more satisfactory than 

 the gradual changes that were supposed to have been effected by 

 natural selection, for in the vast majority of cases where such 

 small changes have been seen, there has been no possibility of 

 imputing to them any functional value whatever. On the Dar- 

 winian theory, where the parent is killed out, it is very hard 

 indeed to see how there can have been any increase in numbers 

 (Test case i, p. 90). 



One great advantage of the large mutations for the formation 

 of species, and still more of genera and families, that are de- 

 manded by the theory of differentiation, is that at one step they 

 will cross the "sterility line", the rough and ready distinction 

 that separates a species from its nearest relative. The new form 

 will at once become isolated (chap, vii), and there will be little 

 likelihood of its being lost by crossing. As we have seen, isolation 

 may be of very great importance in the establishment of new 

 species, if not also in their evolution. 



When one considers the fact (pp. 132-4) that the more 

 primitive things are more widely distributed, that a genus (unless 

 monotypic) occupies a wider area than at any rate all but one of 

 its species, and again that there is no evidence to show that there 

 is any adaptational reason why a small variety should become a 

 larger one, or the latter a species, a species lead to a genus, and 

 so on, it would seem, as it seemed to (the late) Dr Guppy and to 

 the writer over thirty years ago, that we have been to a large 

 extent trying to make evolution work backwards. It was in- 

 finitely simpler to work forwards throughout evolution, beginning 

 always with the family, deriving the genus from that, the species 

 from the genus, and the variety from the species. In fact, with 



