Studies in Milk Secretion 103 



•q n+1 the actual number of different individuals involved in these 

 matings, and Z n is the inbreeding coefficient for the n+i the 

 ancestral generation. 



The amount of inbreeding may be expressed as a single 

 numerical quantity by referring the inbreeding as expressed 

 for each generation to the maximum possible inbreeding of a 

 brother and sister mating. The formula by which this single 

 measure of inbreeding is determined is 



Z T 



where 2 denotes summation of all values between the inclusive 

 limits indicated, Ft is the total area of the maximum brother 



n 



x sister curve up to and including the n-f-ith generation. Zt q 

 is the measure of the inbreeding. 



A state or condition of relationship or kinship between 

 two organisms exists when these organisms have one or more 

 common ancestors. The degree, intensity or closeness of the 

 relationship is, in general, proportional to the number of dif- 

 ferent ancestors which the two individuals have in common, out 

 of the whole number they might possibly have in common. 



The degree or amount of relationship, in accordance with 

 the above definition, is numerically measured by relationship 

 coefficients, one for each ancestral generation. The coefficients 

 are calculated in two slightly different ways according to 

 whether they are being evaluated in connection with inbreeding 

 coefficients, which will usually be the case, or independently. 



When calculated in connection with inbreeding coefficients, 

 a relationship coefficient is calculated in accordance with the 

 following equation : 



Kn _ (pn+i — qn-j-i) — (sZn — i sPn + dZn — i dPn) 

 ioo y 2 Pn-j-i 



where the letters have the same significance as in the above 

 equation with the additions that K denotes a relationship co- 

 efficient, a prefixed subscript s means that letters following it 

 refer to the pedigree of the sire only, and a prefixed subscript 



