CH. x] A. NUMERICAL 101 



TEST-CASE VIII. THE HALVING OF THE 

 SPECIES IN A FAMILY 



We have seen (p. 96) that, in general, there is one genus in 

 each family which on the average has at the present time nearly 

 a hundred species more than the second genus ; the difference is 

 only on the average thirty-two between the latter and the third 

 genus, and so on. Only when one comes down into the smaller 

 genera does coincidence in number happen at all seriously, and 

 it happens more and more the nearer one comes to the bottom 

 of the list, so that at last, if of any size, the family ends with a 

 streamer of monotypic genera, or genera of one species each. This 

 hollow curve, which is always formed, is what is to be expected 

 upon the theory of differentiation, and natural selection is 

 helpless to explain it. 



The hollow curve is due to the continual doubling of each genus 

 in turn by the throwing of a new genus so that, as time goes on, 

 the total number of genera undergoes an increase, which is con- 

 tinually more and more rapid, as the numbers grow. And as time 

 goes on, the genera already formed are supposed to increase their 

 number of species in the same way. We have supposed, as the 

 simplest solution of the problem for the meanwhile, that each 

 genus will on the average throw a new genus rather than a new 

 species once in every so many throws. In the counting that is 

 being used for this particular paragraph, ^ the total number of 

 families with more than one genus is 235. Taking the number of 

 species in each genus of a family, and arranging the genera in 

 descending order, the total number of species has been counted 

 for each family, and halved, and a dividing line drawn immediately 

 to the right of the genera required to make up the full half. This 

 of course means that the genera on the left may contain the 

 exact half (this is rare) or slightly or even considerably more ; but 

 the numbers on the right-hand side of the line never exceed, and 

 very rarely equal, those on the left. For example, three families 

 are given : 



Aristolochiaceae 300 



Basellaceae 14 



Elatinaceae 19 



60 10 8 1 

 3 111 



19 



All of these have the dividing line after the first genus, and this 

 proves to be the rule when the family is small, but not when it is 

 large. Out of the 235 families, no fewer than ninety-eight, or 

 41-7 per cent, have the dividing line after the first genus, as shown 



1 The numbers are continually being revised for my Dictionary, 



