320 NATURAL SCIENCE [November 



of specific distinctness which the principle of Eeproductive Divergence 

 is propounded to explain, we will accept, for the sake of argument, 

 that parents of the same size breed true. Then of the 120 Ss of the 

 first generation 24 will copulate with small females and 24 each 

 with the other four sets ; hence there will be produced only 2 9 Ss. 

 These 2 9 will have to copulate with nine sets, and so on. The same 

 applies to LI. Or to put it generally, if A is the number of indi- 

 viduals of each original set, a the number of original sets, x the sur- 

 plus fertility, n the number of generations, then under the proposi- 

 tions adduced by Mr Vernon, 



n _ f ]Q0 + x \ H A 



bs " V 100 ;■ 



a ((a-l) 2 +l).((a-l)3 + l)...^(a-lf+l N ) 



In our case the numbers of S in the succeeding generations will, 

 therefore, be— T. = 120 ; II. = 29 ; III. = 4 ; IV. = 0, 3. 



That is to say, after the fourth generation, the largest and 

 smallest specimens will be weeded out, and this result will not 

 materially be altered, even if we assume that the largest and 

 smallest individuals are mutually absolutely sterile. (Compare also 

 Galton's regression towards the mean.) 



Although Eeproductive Divergence does not achieve what Mr 

 Vernon claims for it, it is not altogether to be rejected under other 

 premises than those accepted by Mr Vernon. There are certain 

 species, for instance among Lepidoptera, which vary in the same 

 locality in such a way, that there are two well-marked varieties 

 which breed freely with one another, but produce comparatively few 

 intergraduate specimens, the offspring belonging mostly to the one 

 or to the other variety. 1 Here Reproductive Divergence may 

 eventually have free play, and then necessarily will evolve incipient 

 dimorphism into complete dimorphism, and in so far Eeproductive 

 Divergence might be called a factor in evolution. 



Karl Jordan. 



Zoological Museum, Tring. 



1 Standfuss, " Handbueh f. Schnietterlingssammler," 1895. — See also Giard, Natural 

 Science I. p. 388 (1892) ; Romanes, ibid. p. 398. 



