THE PROBLEM OF INBREEDING 117 



(having an obligate bisexual type of reproduc- 

 tion) that its pedigree on analysis will give 

 Z 3 >87.5. If, therefore, the coefficients of Table 

 I are plotted, the result will be the maximum 

 limiting curve of inbreeding. This curve is shown 

 in Fig. 1. 



In all actually realized pedigrees except those in 

 which there has been continued brother X sister 

 breeding the curve of inbreeding found will lie 

 wholly or in part below the maximum curve 

 shown in Fig. 1. 



ILLUSTRATION II. PARENT X OFFSPRING BREEDING 



The next illustration of the application of 

 coefficients of inbreeding will be the general case 

 of back-crossing, that is, the mating of parent 

 X offspring. Such a case is illustrated in the 

 hypothetical pedigree, Table II. 



Here it will be seen that 6, the dam of y, is a 

 daughter of a, who is also the sire of y, and that in 

 each preceding generation every daughter is bred 

 back to her sire. Proceeding as before to calculate 

 the coefficients of inbreeding, we have, first, 



7 100 (g-g) 



z - - -o. 



In forming the expression for Z\ we are met 

 by the fact in determining q n+1 for generation 2 

 that the individual a has already appeared once 

 and been counted as a "different" ancestor in 



