SPECIFIC AND GENERAL COMBINING ABILITY 359 



somewliat if they appear totally unreasonable. At any rate the estimation 

 procedure serves to point out what additional information is needed if an 

 intelligent job of selection is to be accomplished. 



SELECTION FOR ADDITIVE GENETIC VALUES IN INDIVIDUALS 

 As our first application of the methods described above, consider the esti- 

 mation of additive genetic values of individuals with respect to a single trait 

 (the single trait might be net merit) from a set of records all made in the 

 same herd or flock. It will be assumed for the present that the population 

 mean is known and that records can be corrected satisfactorily for all non- 

 random environmental factors. For example, the records might represent 

 all of the 305 day, mature equivalent butterfat records made in a herd during 

 the past ten years. It is desired on the basis of these records to decide which 

 cows should be culled, which heifers should be selected for replacements, and 

 which bull calves should be grown out for possible use as herd sires. 



In the usual approach to this selection problem by use of the selection 

 index, one would decide what particular subset of the records would con- 

 tribute most to the estimate of the value of each animal under consideration 

 and would then construct separate indexes. The method to be presented here 

 employs all available records in estimating the value of each animal. That is, 

 no prior decision is made concerning which records to use to construct the 

 index for each animal, but instead all available ones are used. 



The first step in the procedure is the computation of what Emik and Ter- 

 rill (1949) have called a numerator relationship chart and Lush (1948) has 

 called genie variances and covariances for all animals whose records are to be 

 used in the index or whose breeding values are to be estimated. In terms of 

 Wright's (1922) coefficients of relationship and inbreeding, the genie variance 

 of the iih animal is 1 -|- Fi, where Fi is the inbreeding coefficient of the ith 

 animal, and the genie co variance between the ith. andjth animal is 



i?oV(l+F,)(l-|-Fy), 



where i?,, is the coefficient of relationship between the two animals. The nu- 

 merator relationship or genie eovariance, which we shall denote by a.y, is the 

 numerator of the fraction representing relationship. That is 



7? - ^'' 



Vd+FJd-fF,) 



The computation of ||a,_,|| is a routine procedure if it is done systematically as 

 described by Emik and Terrill and by Lush. 



Next we need an estimate of heritability of the trait, and if more than one 

 record is available on a single animal, as would be true of butterfat produc- 

 tion, an estimate of repeatability. Now let yi, yz, ■ ■ • , yp be the mean of the 

 ■Hi records of each of p animals, these records having been corrected for 



