FURTHER DATA ON THE MEASUREMENT OF INBREEDING. 239 



These facts will possibly be made clearer to those not actually 

 working much with pedigrees by Pedigree Table IV, which 

 gives the first four ancestral generations^ of the pedigree of 

 King Melia Rioter 14th. 



Generalizing the above reasoning we get the following result. 

 In As, and higher ancestral generations, 2-4 = 50.00 per cent. 



of the dam's ancestors are animals which are also ancestors 



of the sire. 

 In A4, and higher ancestral generations, 5-8 = 62.50 per cent. 



of the dam's ancestors are animals which are also ancestors 



of the sire. 

 In A5, and higher ancestral generations, 12-16 == 75 -oo per cent. 



of the dam's ancestors are animals which are also ancestors 



of the sire. 

 In As, and higher ancestral generations, 28-32 = 87.50 per cent. 



of the dam's ancestors are animals which are also ancestors 



of the sire. 

 In At, and higher ancestral generations, 59-64 =: 92.19 per cent. 



of the dam's ancestors are animals which are also ancestors 



of the sire, and so on. 



These percentages are quantities of a good deal of interest. 

 They measure the degree in which King Melia Rioter I4th's 

 sire and dam were related to each other. Community of ances- 

 try is the basis of kinship. 



Percentages derived in the way shown above, from cross 

 pedigree elimination tables, I have proposed to call coefficients 

 of relationship, and to designate by the letter K, with appro- 

 priate sub-numbers referring to the generation. These relation- 

 ship coefificients are, with some limitations, independent of the 

 inbreeding coefficients in the values they may take, though the 

 two will usually be correlated to some degree. It is, however, 

 possible to have a high value of Z with K = o. 



"In the study of pedigrees stress is naturally laid on the ancestral gen- 

 erations, rather than on the filial, as in breeding experiments. It becomes 

 very convenient to have a brief designation for ancestral generations, in 

 the same way that Fj, Fj, etc., are used to denote filial generations. I 

 would suggest the use of the letter A with sub-numbers for this purpose. 

 We then have Ai denoting the parental generation, A, the grandparental, 

 A3 the great-grandparental, etc. 



