No. 562] THE PROBLEM OF INBREEDING 613 



tion when all hereditary characters are taken into account. 

 This means, in last analysis, that each individual must 

 differ from every other by at least one unit factor, pos- 

 sibly more. Once mating of brother and sister will dimin- 

 ish the number of such differences by 50 per cent, from 

 what it would have been had no such mating occurred. 

 The number of homozygous individuals with respect to 

 the hereditary differences remaining, however, will not 

 increase. This is practically equivalent to saying that 

 while self-fertilization increases the proportion of indi- 

 viduals homozygous with reference to all characters, the 

 closest inbreeding other than self-fertilization, if con- 

 tinued, increases the proportion of characters with 

 respect to which all individuals are homozygous. Then 

 while both processes tend towards uniformity in the 

 progeny, it is a different kind of uniformity obtained in 

 a different way, in the one case from what it is in the 

 other. 



"While in the above discussion only brother X sister 

 mating is mentioned it is clear that the same reasoning 

 applies regarding the meaning of the coefficients of in- 

 breeding in all other types of mating. 



There are other theoretical relations of inbreeding 

 coefficients which are of interest, but to discuss them in 

 detail here would take us altogether too far afield in the 

 analytical side of determinantal inheritance theories. 



Concluding Remarks 

 In this paper has been presented a general method of 

 measuring the intensity or degree of the inbreeding prac- 

 tised in any particular case. The method proposed is 

 shown to be perfectly general. It is based on no assump- 

 tion whatever as to the nature of the hereditary process. 

 On the contrary, it is founded on the most completely 

 logical and comprehensive definition of the concept of 

 inbreeding that it seems possible to formulate. This is, 

 in simplest form, that the fundamental objective crite- 

 rion which distinguishes an inbred individual from one 

 not inbred is that the former has fewer different ancestors 



