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 (a) is correct, Mr Vernon argues as 

 follows: — (1) Variety S varied originally from G4 to G7 inches, the 

 mean being 65*5, and L from 70 to 73, the mean being 7l'o ; (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 6 2 "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 7l'o to 74*5 inches respectively." But 

 surely this inference (3) is merely a re-statement of assumption (2) ! 



And as to the conclusion (b) 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 : — 



I. 180, 180, ISO, 180, 180 = 900. 

 II. 120, 190, 280, 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 



