No. 635] SHORTER ARTICLES AND DISCUSSION 541 



total inbreeding. This proportion can be found by determining 

 the proportion of the area included by the actual inbreeding 

 curve in percentage of the area included by the maximum in- 

 breeding curve. The area of the latter can be calculated by inte- 

 gration. The actual curve is usually so irregular that no inte- 

 gration is possible. To get an approximate value the series of 

 values for Z is simply summed. The formula for the total in- 

 breeding coefficient is then the following: 



the 2 denoting the summation of all values between and includ- 

 ing the limits indicated, and F Tn is the area included 'by the 

 maximum curve, the same number of generations being involved. 2 



A question of considerable genetic bearing is the degree of 

 relationship between the parents of the individual, whose pedi- 

 gree is being examined. Relationship is indicated by the reap- 

 pearance of individuals from the pedigree of one individual in 

 the ancestry of another. 



As a measure of degrees of relationship Pearl proposed a co- 

 efficient of relationship. This is calculated in two slight ly dif- 

 ferent ways according to whether it is measured with the coeffi- 

 cient of inbreeding, where the relationship of the sire and dam 

 of the inbred individual is being calculated, or separately, when 

 relationship of any two individuals is measured. The formulae 



m „ _ 100(pn + i — qn . ,) - (-Zn _, • sp.i + <M n • ,ip n 



W 1/2P* + , 



(2) Kn = 1 oo ( „ +l)> 



where a prefixed s or d indicates that the following letter refers 

 to the sire's or the dam's pedigree only, and (p n+1 — r n+1 ) means 

 the number of common ancestors for both pedigrees in the 

 n -f- 1st generation. 



As a measure of the proportion of the actual inbreeding due 

 to relationship between the sire and dam of the individual Pearl 

 has proposed to give a series of jxirt'uil inbreeding indices cal- 

 culated according to the formula 



50(Kn 



KZ„=^p. 



:, "Studies on Inbreeding," VIII, 



