No. 562] THE PROBLEM OF INBREEDING 583 



volved in the breeding of Alpha. In the second pedigree 

 it is assumed that there were only two different indi- 

 viduals in the fourth ancestral generation. In other 

 words, all the individuals in generation 3 of this pedigree 

 II are brothers and sisters, though different animals (i. e., 

 produced, by hypothesis, at successive matings of o x and 

 p x ). A condition in considerable degree approaching this 

 is very frequently found in livestock pedigrees. On the 

 other hand in pedigree I all of the individuals of the 

 fourth generation are different and are assumed to be 

 absolutely unrelated, with the single exception of indi- 

 vidual o, which appears twice in this generation. The 

 point I think is clear : according to the Lehndorff measure 

 both of these pedigrees show the same degree of inbreed- 

 ing (free generations =2), whereas actually there is a 

 wide difference between the two. 



In developing a general measure of the intensity of in- 

 breeding we may well start from the conception set forth 

 in the preceding section, namely that the inbred individual 

 possesses fewer different ancestors than the maximum 

 possible number. Besides this factor account must be 

 taken of the generation or generations in which the re- 

 duced number of different ancestors is found, and the 

 extent to which these generations are removed (in the 

 sense of Lehndorff discussed above) from the individual 

 «>r generation under consideration. In other words the 

 two factors which must be included in a general measure 

 of the intensity of inbreeding are (a) the amount of 

 ancestral reduction in successively earlier generations, 

 and (b) the rate of this reduction over any specified num- 

 ber of generation-. 



Both of these demands are met, 1 think, by taking as a 

 measure of the intensity of inbreeding in any generation 

 the proportionate degree to which the actually existent 

 number of different ancestral individuals fails to reach 

 the maximum possible number, and by specifying the 

 location in the series of the generation under discussion. 



This statement, is amplified and made more precise in 

 the following propositions. 



