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 -f 

 ,,Aa + aA -f- aa; that is two homozygotes and two 

 ,,heterozygotes. Thus, the selffertilization of such 

 ,,an organism gives 1 / 2 the progeny homozygotic 

 ,,(with respect to this characteristic) 1 / 2 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 = x /2 of all 

 y = i/ a of all 



,,Now, after the next selffertilization, of course the 

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

 ,,the progeny are still homozygotes on this account. 

 ,,The heterozygotes y of course again break up, in the 

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

 ,,half remaining y. Since y included half of all, this will 

 ,,give i/a of Va (= V 4 of all) as x, V 2 of V 2 (= X A of 

 ,,all) as y. 



,,So the total proportion for the homozygotes x 

 ,,becomes after the second fertilization: 



