THE MEASUREMENT OF THE IXTEXSITV OF rXBREEDINX. 1 25 



generation or generations. This appears to be the most general 

 form in which the concept of inbreeding may be expressed. In 

 whatever way the mating of relatives is accomplished, or what- 

 ever the degree of relationship of the individuals mated 

 together, the case in last analysis comes back to the above state- 

 ment, namely that there are actually in the pedigree of the 

 inbred individual fewer different ancestors in some particular 

 generation or generations than the maximum possible number. 



The Measuremext of the Degree of Ixbreedixg. 



This brings us to a consideration of a practical and general 

 measure of the degree of inbreeding exhibited in a particular 

 pedigree. This problem has been attacked by a number of 

 other investigators, but so far as I have been able to learn, all 

 previous measures have been modifications in one form or an- 

 other of the scheme of Lehndorff. All systems based on the 

 number of "free generations" alone, as in Lehndorff's, do not 

 furnish a precise or reliable measure of the real intensity of 

 inbreeding. The essential reason for this failure, stated baldly, 

 is that they do not take account of the composition of the gen- 

 eration to which the "common ancestor" of an inbred pair 

 belongs. 



In developing a general measure of the intensity of inbreed- 

 ing we may well start from the conception set forth in the pre- 

 ceding 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 reduced number of dift'erent ancestors 

 is found, and the extent to which these generations are removed 

 (in the sense of Lehndorff mentioned above) from the indi- 

 vidual or 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 reduc- 

 tion in successively earlier generations, and fb) the rate of this 

 reduction ever any specified number of generations. 



Both of these demands are met by taking as a measure of 

 the intensity of inbreeding in any generation the proportionate 

 degree to which the actually existent number of different ances- 

 tral individuals fails to reach the maximum possible number. 



