(7) 



360 C. R. HENDERSON 



non-random environment and expressed as deviations about the population 

 mean. The next step is to solve the following set of equations for Ci, . . . , Cp. 

 In these equations h denotes heritability and r denotes repeatability. 



Cianh-\-C-2 (FoJH j + • • • -hCpG^ph = 5*2 



* • 



Cia^pJi -\-C2a2ph + . . . +Cp [Fp -\ 'A = Vp 



If all available records are to be used in the estimation procedure just de- 

 scribed, the number of equations to be solved for the C's is large. It might ap- 

 pear, in fact, that the number is too great for the method to have any value. 

 However, the equations are ideally suited to an iterative solution. The reason 

 for this is that the diagonal elements of the left members of the equations are 

 very large compared to the off-diagonal elements thereby making the itera- 

 tive solution a particularly rapid one. On the basis of our experience with a 

 few herds a solution to sufficient accuracy can be obtained in three or four 

 rounds of iteration. 



Once the C's have been computed the estimate of gt, additive genetic value 

 of the iXh. animal, is 



gi = h (Cifli, -\-C2a2i + . . . +Cpap,) . 



If the iih animal had one or more records included in the computation of 

 the C's the estimate can be computed more easily, for 



-^ ^ . _^ 1 + ("> - 1) >' - n, h 



The estimate of the real producing ability of a tested animal is even more 

 simple to express. The estimated real producing ability is 



y'i—Ci . 



It should be pointed out that this estimate differs from the one presented by 

 Lush (1945) since his method does not utilize records on relatives. 



Valuable characteristics of the method just described, in addition to its 

 ease of computation and its use of all available information, is that the inclu- 

 sion of the records of the contemporaries of the ancestors of the animals being 

 appraised automatically eliminates the troublesome problem of what effect 

 selection has had on the phenotypic and genetic variances of the selected 

 group of ancestors. Also changes in additive genetic variances and covari- 



