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. 



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

 racters, which we may call j £• 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 self fertilization 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 /a of all 

 y = i/ 2 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 j>. Since j> included half of all,this will 

 „give V« of »/■ (= X A of all) as x, »/■ of Va (== l U of 

 „all) as y. 



„So the total proportion for the homozygotes x 

 „becomes after the second fertilization: 



