No. 573] 



STUDIES ON INBREEDING 



521 



of a continued brother by sister breeding. Clearly K 

 would be 0, since no animal on one half of the pedigree 

 could even appear on the other. The values of the suc- 

 cessive coefficients of inbreeding (Z's) in such a case are 

 shown in Table VI, where they are compared with the 

 coefficients of inbreeding in complete continued brother 

 X sister mating, where K = 100. 5 



From this it appears that an individual may be inbred 

 in 10 generations to within two tenths of one per cent as 



his sire and dam are in no wait related, as he would he if 

 his sire and dam were brother and sister. But clearly the 

 germinal constitution of the individual produced would, 

 except by the most remote chance, be quite different in the 

 two cases. This point is so evident as to need no elab- 

 oration. It has been brought out by East and Hayes. 6 



The values of the Tl's for a particular pedigree evi- 

 dently furnish a rough index of the probability that the 



alik/in their constitution. This will follow because of the 

 fact that the probability of likeness of germinal constitu- 

 tion in two individuals must tend to increase as the num- 

 ber of ancestors common to the two increases. Just what 

 is the law of this increase in probability is a problem in 

 Mendel ian mathematics which has not yet been worked 

 out. The general fact, however, seems quite sure. 



From the above discussion it seems plain that in reach- 

 ing a numerical measure of the degree of inbreeding it is 

 not sufficient to consider coefficients of inbreeding alone. 

 The coefficients of relationship must also be taken into 

 account. 



It is suggested that the two constants be written to- 

 gether for each generation, the coefficient of inbreeding 

 being followed bv the coefficient of relationship in brackets. 

 Thus we have 



