CH. xiv] GENERAL DISCUSSION 183 



(p. 94) it is shown that while natural selection can make no 

 predictions, under differentiation it is clear that on the average 

 the size of the largest genus in the family must go with the size 

 of the family itself, which proves to be the case, whilst in case iii 

 (p. 95) the gap in size between first and second genera, second 

 and third, and so on, is predicted as, and proves to be, a rapidly 

 diminishing one. In case iv (p. 97) it is predicted, and proved, 

 that the proportions of very small genera, considereti as relics 

 under natural selection, must on the average be larger the larger 

 the family, while it would be expected to be the reverse under 

 selection. In case v (p. 99) it is shown that the hollow curve is 

 entirely in favour of differentiation, and in case vi (p. 100) that 

 "Size and Space", a corollary of Age and Area, is equally so. 

 Case, VII (p. 100) refers to a paper by Yule and Willis (76), 

 showing that "the manner in which evolution has unfolded itself 

 has been relatively little affected by the various vital and other 

 factors, these only causing deviations this way and that from the 

 dominant plan", a conclusion which obviously does not harmo- 

 nise with the action of natural selection. Case viii (p. 101) shows 

 that while on the average the parent genus in small families has 

 as many species as all the rest, more and more genera are required 

 to halve the family when it grows larger. This could be predicted, 

 and is against natural selection. The numerical tests are all clearly 

 in favour of differentiation. 



Morphological tests are described in chap. xi. In the important 

 case IX (p. 110), differences in generic rank are dealt with. 

 Natural selection can make no predictions, and simply regards 

 all genera as generic stages in evolution, and of rank as nearly 

 the same as the systematist can compass. Differentiation, how- 

 ever, says that the rank of a genus of a very small family will be 

 approximately equal, on the principle of divergent mutation, to 

 that of the sub-family of a large family. This proves to be the 

 case, giving very strong evidence indeed for evolution by diver- 

 gent mutation, and showing that the rank of a genus varies with 

 its position, and the size of it and of its family. In case x (p. 114) 

 the fact, hitherto almost totally ignored, is considered, that the 

 characters of plants are generally shown in their perfect condi- 

 tion, and especially so those of the higher groups. This could not 

 happen under selection, to which 95 per cent or less of perfection 

 would be as good as 100 per cent. This is a simple, but destructive 

 argument against gradual acquisition of characters. In case xi 

 (p. 115), the difficulty as to how natural selection got a grip upon 



