THE PROBLEM OF INBREEDING 109 



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. 

 The statement is amplified and made more 

 precise in the following propositions : 



1. The production of the individual must be 

 the point of departure in any analytical considera- 

 tion of inbreeding, leading towards its measure- 

 ment. That is, the question to which one wants 

 an answer is : What degree of inbreeding was 

 involved in the production of this particular 

 animal ? 



2. It is therefore necessary practically to start 

 with the individual and work backwards into the 

 ancestry in measuring the inbreeding, rather than 

 to start back in the ancestry and work down 

 towards the individual. 



3. In the genetic passage from the n + 1th 

 generation to the nth, or in other words the con- 

 tribution of the matings of the ?i + 1th generation 

 to the total amount of inbreeding involved in the 

 production of an individual, the degree of inbreed- 

 ing involved will be measured by the expression, 



Pn+l (ill) 



where 2?n+i denotes the maximum possible num- 

 ber of different individuals involved in the 



