THE PROBLEM OF INBREEDING 155 



two individuals, a and 6, which mated together 

 produce the individual x, are of the same zygotic 

 constitution in respect of any one or more char- 

 acters, when they have 1, 2, 3, 4, . . . m common 

 ancestors in the nth ancestral generation? 



This I believe to be the crucial outstanding 

 problem of Mendelian mathematics in relation to 

 inbreeding. Its solution ought to be in principle 

 simple, if somewhat tedious in the carrying out. 

 As has already been pointed out (p. 145, supra), it 

 seems likely on a priori grounds that this probabil- 

 ity will be found always to bear a definite relation 

 to the coefficients of relationship. If this be true, 

 it will be of great help practically in studying 

 inbreeding, since it is always a simple matter to 

 determine coefficients of relationship. 



Finally, to summarize briefly this rather ex- 

 tended discussion of the logical aspects of the 

 problem of inbreeding, it may be said that in this 

 paper has been presented, first, a general method 

 of measuring the intensity or degree of the in- 

 breeding practiced 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 con- 

 trary, 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 criterion which distinguishes an inbred 



