No. 562] THE PROBLEM OF INBREEDING 609 



(a) Continued self-fertilization. 



(b) Some form of gametic assortative mating which 

 increases the natural probability of like gametes uniting 

 to form zygotes. 



Really, of course, (a) is only one special form of (b). 

 Not only is self-fertilization the closest sort of inbreeding 

 possible when conceived in the sense of the idea of in- 

 breeding denned and developed in this paper, but also it 

 is necessarily the most extreme form of homogamy pos- 

 sible. No other kind of inbreeding is necessarily homo- 

 gamic. It of course may be, and in actual practise very 

 often is homogamic, but to make it so selection of some 

 sort is necessary. 



The above proofs deal with but one character pair, A, a. 

 By induction the proof could be extended to any number 

 of such pairs. There is a point which needs to be kept in 

 mind here, however. This is that the whole reasoning 

 applies only to such genetic differences as are left in the 

 strain after the operation of inbreeding. As will be 

 shown presently the number of original genetic differ- 

 ences in a stock is reduced by inbreeding in a manner 

 which is precisely measured by the coefficients here 

 proposed. 19 But there is no tendency for continued in- 

 breeding to increase, the proportion of homozygotes, 

 with respect to those characters in regard to which 

 there are genetic differences left after any partic- 

 ular inbreeding operation. Further it should be under- 

 stood that the elimination of genetic differences from a 

 strain is not through homozygosis, but by the dropping 

 out entirely from the network of descent of individuals 

 which potentially may bear such differences. 



The above discussion makes it evident that there is a 

 fundamental distinction between inbreeding in general 

 and the special case of self-fertilization. Before leaving 

 this phase of the matter it seems desirable to discuss in 

 a little more detail certain terminological usages of 

 workers in the field of plant breeding together with their 



"See p. 612 infra. 



