THE EVOLUTION OF LIVING BEINGS. 69 



will therefore have become homozygotic after a given 

 number of self fertilizations? 



Jennings, American Naturalist 1912 pp. 487 seq. 

 calculates this as follows: 



„Suppose that we begin with an organism in which 

 all separable characters are heterozygotically repre- 

 sented, 



i) „Consider first a single pair of such alternative cha- 

 „racters, which we may call i^ The gametes pro- 

 „duced will be A, a, A and a, and when these com- 

 „bine in all possible ways, they give zygotes AA + 

 „Aa + aA + aa; that is two homozygotes and two 

 „heterozygotes. Thus, the selffertilization of such 

 „an organism gives ^j^ the progeny homozygotic 

 „(with respect to this characteristic) V2 hetero- 

 „zygotic" 



„If we let X = the proportion of homozygotes, y 

 = the proportion of heterozygotes (with respect to 

 one character) then after the first selffertilization 

 X = Va of all 

 y = V2 of all 

 „Now, after the next self f ertiUzation, of course the 

 ,,homozygotes x remain pure, so that half of all 

 „the progeny are still homozygotes on this account. 

 „The heterozygotes J* of course again break up, in the 

 „way already set forth, one half into x, the other 

 „half remaining^/. Since^/ included half of all,this will 

 „give Va of 1/2 (= V4 of all) as x, V2 of Va (= V4 of 

 „all) as y. 



„So the total proportion for the homozygotes x 

 ..becomes after the second fertilization: 



