250 



REV. J. T. GtJLICK ON DIVERGEN^T EVOLUTION 



Segregation, having no power to ensure the propagation of the 

 varieties thus characterized, though they are fully adapted to 

 the environment. This is most easily brought to light by con- 

 sidering the effect of a high degree of this quality when Posi- 

 tive Segregation is entirely wanting, or when it is sufficient to 

 give simply a chance of Segregate Breeding by bringing each 

 individual near to its natural mate. Por example, let us suppose, 

 1st, that a male and a female each of several allied but mutually 

 sterile species are brought together on one small island, all other 

 tendences to Positive Segregation being removed, while mutual 

 sterility still remains ; 2nd, that a male and female when 

 once mated remain together for the breeding-season ; and 3rd, 

 that all find mates. 'Now, if we have 7 species, each represented 

 by one individual of each sex, what is the probability that all the 

 species will be propagated ? And what the probability for the 

 propagation of none, or of but one, or of but two, or of but three 

 of the species ? The answers, as I have computed them, are as 

 follows : — The probability that none will be propagated is 3- ff^ ; 

 that 1 species will be is ; that 2 species f'^/jj ; that 3 species 

 ; that 4 species ^-Jf^ ; that 5 species g-J|-jj ; that 7 species 

 ■^-Qj^' These numerators are found in the 7th line of a table of 

 figures which I call the Permutational Triangle. If we have 10 

 species, the probability that in any one trial no species will 

 match truly and be propagated is fff oT 5 ^^^^^ 1 species will 

 match truly and propagate is ^ ; that 10 will is ^ « ^is iro- 



This means that if 3,628,800 trials are made, one of them will 

 probably be a case in which each male pairs with the female of 

 the same species, while 1,334,961 will be cases in which none are 

 so matched, and 1,334,960 will be cases in which one pair is so 

 matched. It therefore appears that more than -^^ of the proba- 

 bilities are against the continuance of more than one of the ten 

 species. 



There will perhaps be some hesitation in receiving these 

 figures before I have given the method by which the results have 

 been reached ; but the necessary length of this paper, even when 

 restricted to the briefest discussion of general principles, induces 

 me to reserve my computations for another occasion. It is 

 not, however, necessary to have a complete solution of this 

 problem, in order to reach the conclusion that the origin of 

 separate races and species depends not only upon their adap- 

 tation to the environment and their mutual sterility when 



