THE MEASUREMENT OF THE INTENSITY OF INBREEDING. I37 



able, if indeed it cannot be said to be highly probable, that no 

 two individuals among higher animals and plants are exactly 

 alike in zygotic constitution when all hereditary characters are 

 taken into account. This means, in last analysis, that each indi- 

 vidual must differ from every other by at least one unit factor, 

 possibly more. Once mating of brother and sister will diminish 

 the number of such differences by 50 percent from what it 

 would have been had no such mating occurred. The number of 

 homozygous individuals zvith respect to the hereditary differ- 

 ences remaining, however, will not increase. This is practically 

 equivalent to saying that while self-fertilization increases the 

 proportion of individuals homozygous with reference to all 

 characters, the closest inbreeding other than self-fertilization, 

 if continued, increases the jDroportion of characters with respect 

 to which all individuals are homozygous. Thus while both pro- 

 cesses 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 regard- 

 ing the meaning of the coefficients of inbreeding 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 is not 

 possible. 



Concluding Remarks. 



In this paper has been presented in abstract 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 assumption 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 most funda- 

 mental objective criterion which distinguishes an inbred indi- 

 vidual from one not inbred is that the former has fewer differ- 

 ent ancestors than the latter. It is believed that the proposed 

 coefficients of inbreeding may be made extremely useful in 

 studies of the problem of the eff'ect of inbreeding, whether in 



