1897] REPRODUCTIVE DIVERGENCE 319 
of intermediate size will, in succeeding generations, decrease in 
number, while the individuals of small and large size will increase. 
To show that inference (#) is correct, Mr Vernon argues as 
follows :—(1) Variety S varied originally from 64 to 67 inches, the 
mean being 65:5, and L from 70 to 73, the mean being 71°5 ; (2) 
let us then suppose that by the principle of Reproductive Divergence 
the average of S were reduced to 64, [the specimens varying now 
from 62°5 to 65:5 |, and that of L increased to 73, [ the individuals 
varying from 71°5 to 74:5]; (3) then “ it follows that these groups S 
and L would (approximately) contain individuals varying between 
62°5 to 65°5 inches, and 71°5 to 74°5 inches respectively.” But 
surely this inference (3) is merely a re-statement of assumption (2) ! 
And as to the conclusion (5) that the intermediate individuals, 
will disappear, it has apparently escaped Mr Vernon that the figures 
given under II. are nothing else but a re-statement of the proposition 
that 100 pairs of equal size give birth to 120 offspring (etc.) ; the 
result of the chance-breeding is quite different. We must divide 
the original 900 individuals into five sets, and then compare these 
five sets with the five sets of II., thus :-— 
f- £80;-180; 160, 730, 180= 900. 
TE $205 190.260; 190, 120 = 900; 
It is not for me to point out under which new conditions the range 
of variation would be widened and the species be split up into 
varieties. Under those propositions upon which Mr Vernon bases 
his mathematical demonstration, the mean of S will not decrease, and 
that of L will not increase, but the smallest and largest specimens 
will very soon disappear altogether, and the species become mono- 
morphic, as a mathematical consideration of the chance-breeding in 
succeeding generations will show. If we start with 300 S, 300 M, 
and 300 L, the number of small, medium-sized, and large individuals 
in the first generation of offspring will depend on the size of the 
offspring of each pair; the offspring of a pair may be the same in 
size as the parents, or may be smaller or larger. It is sufficient to 
consider two of the infinite possibilities. (1) The 300 S produce on 
an average equal numbers of small, medium-sized, and large offspring, 
and so do the 300 M and 300 L. The result will be that the 
numbers of different-sized individuals will not be altered in suc- 
ceeding generations, and the variation of the species will also remain 
the same. This is the usual result of chance-breeding, if no special 
factors come into play. (2) The 100 S which copulate with 100 s 
will produce 100 small specimens Ss, no medium-sized and large 
ones; the same applying as to M and L. This is what Mr Vernon 
assumes to take place. Though this assumption cannot be allowed to 
stand, as what is here assumed to be true is one of the characteristics 
