102 TEST CASES [ch. x 



above. Fifty of them have two, three, or four genera, the actual 

 figures for the whole number being 22/2 (twenty-two of two 

 genera), 21/3, 7/4, 9/5, 8/6, 6/7, 2/8, 5/9, 2/10, 2/11, 1/12, 1/13, 

 2/15, 2/17, 1/19, 2/21, and one each of 24, 26, 28, 78 (Moraceae) 

 and ninety-nine genera (Solanaceae). Arranging these ninety- 

 eight families in order of size of the largest genus in each, one 

 finds that though the average size of the families in each group of 

 ten goes down with the average size of the largest genus, there 

 are nevertheless, in the first ten, four families with less than ten 

 genera each, but each headed by a very large genus {Begonia, 

 Oxalis, Piper, Impatiens). 



The next lot of families is composed of those where the dividing 

 line comes after the second genus, as in Primulaceae: 250, 120, 90, 

 and so on to ten ones, total 651. While the average size of the 

 ninety-eight families with dividing line after the first genus was 

 7-9 genera with 201 species, the average size of those with the line 

 after the second genus is 14-9 genera with 249 species. Going on 

 in the same way through the whole number, we get the following 

 table : Average 



Figures in italics break the regularity of the table of averages. 



The larger, on the average, that the family becomes, the more 

 is the dividing line pushed to the right, until in the Compositae, 

 the largest family of all, it only appears after the thirtieth genus. 



It is clear that there is some arithmetical reason behind all this, 

 and the simplest explanation is that it is due to the continual 

 increase of species in genera other than the original one, when 

 the latter divides off new genera (which again divide) at average 

 intervals. In any case, the facts do not agree with any hypothesis 

 of gradual adaptation working from below upwards. 



These numerical tests, to which others might be added, are 

 thus all in favour of differentiation rather than of natural 

 selection or of gradual adaptation. 



