SPECIFIC AND GENERAL COMBINING ABILITY 357 



the right member of the equation pertaining to the particular b to be esti- 

 mated is 1 rather than 0. 



An easier solution to the problem of unknown 6's often can be obtained 

 by regarding the model as, 



where the d are independently distributed with mean zero and variance al^ 

 and the z's are observable parameters. For example, ^i might rei)resent the 

 general combining ability of inbred line A, di the general combining ability 

 of line B, and di a specific effect peculiar to the cross A X B. The observable 

 parameters z would have the following values: Zi = 1 when line A is one 

 of the parents, = otherwise; Z2 = 1 when line B is one of the parents, = 

 otherwise; and Zs = 1 when ji is an observation on the cross A X B ox 

 B X .1, = otherwise. Now the joint estimates of 6's and 0's are the joint 

 solution to the subsets of equations (3), (4), and (5). 



<^i< +C2V. +• • • +C,^_,^. = y,- b,x^, - ... - 6^x,, 



'. . (3) 



C,a +C,(7 +...+C,.(72 =y -hx -. . .-h X 



1 i/,y_Y ' 2 y„yx A y^ ' -V 1 UV p p.-v 



1 1 j/j9[ A y^v'i 



(4) 



"? 



where 



b,Sx\ + . . . + bpSx.Xj, + ^i^.vi si + • . . + ^,5.vi2, = 5.viy 



'. . (5) 



Si5:*;iXp + . . . + 6p5.Vp + diSXp zi + . . . + ^,>SXp z, = Sxj,y , 



S.v;=2:#. 5.v,.v.= 2:^?^, etc. 



These equations can be solved by the following steps. First solve for the C's 

 in equations (3). The results will be in terms of the sample observations and 

 the 6's. Second, substitute values of these C's in equations (4) to obtain ^'s 

 in terms of the sample and the b's. Third, substitute these values of the ^'s 

 in equations (5) and solve for the 6's. Fourth, substitute the computed values 

 of the S's in (4) and solve for the ^'s. 



