SHOKTER ARTICLES AND DISCUSSION 



Has any one worked out formulas for determining the rate at 

 which organisms become homozygotic through continued self- 

 fertilization ? The problem is of interest in various connections, 

 but principally perhaps with relation to the "pure line" work. 

 Johannsen worked, for example, with self-fertilizing beans that 

 are held to be homozygotic in all respects. I have often heard 

 the questions raised: How probable is it that such plants really 

 are homozygotic? Is it indeed possible that they have reached 

 a purely homozygotic condition? 



I have not come across a working out of this matter, and 

 finding it necessary to deal with the problem in connection with 

 studies of inheritance in Paramecium, it will perhaps be useful 

 if I put on record the results. 1 



The principles which underlie the matter are the following: 

 (1) In self-fertilized organisms, all characteristics that become 

 once homozygotic, remain homozygotic forever after, since there 

 is no method in self-fertilization of introducing a gamete that 

 is diverse in this respect: (2) characteristics heterozygotically 

 represented become homozygotic in a certain proportion of the 

 offspring. The problem becomes essentially this: in what pro- 

 portion do the heterozygotic characters become homozygotic, and 

 how. great a proportion of all the organisms will therefore have 

 become thus homozygotic after a given number of self-fertiliza- 



Suppose that we begin with an organism in which all separable 

 characters are heterozygotically represented. 



Consider first a single pair of such alternative characters, 

 produced will be A, a, 

 this note I receive also the 



masterly pa p er f East and Haves ("Heterozygc 

 Plant Breeding," Bulletin 243, Bureau of Plant Tndiwrry. .Tun 

 in which this matter is dealt with and a general formula giv 

 Probable number of homozygotes and any particular class of he 

 ln any generation r is found by expanding the binomial [1 + I 



Possibly the present note may still be useful. 



487 



