344 



GORDON E. DICKERSON 



However, equation (3) is not applicable for evaluating Hull's (1945) plan 

 of recurrent selection for cross performance with a homozygous tester line. 

 Here, cross performance will improve as qi -^ for loci at which the more 

 favorable homozygote (A A) is fixed in the tester, and as Qj -^ 1 for loci at 

 which the tester is homozygous for the less favorable allele (aa). li qr repre- 



TABLE 21.2 



MEANS, VARIANCES, AND COVARIANCES FOR GENOT\TES OF 



SELECTED POPULATION AND PHENOTYPES OF TEST-CROSS 



PROGENIES FROM HOMOZYGOUS TESTER 



sents the proportion of loci segregating in the stock under selection that are 

 homozygous A A in the tester, then it can be shown (Table 21.2) that aver- 

 age progress in cross performance per locus is: 



AP,= [qT•^qA'^-k) + {\- qr) '^qJ{\ + k)]d (4) 



For loci fixed .4.4 in the tester: 



A^, = s- rpo^' >'G,„,-(rgi = —rr-—'q^ (I- q,)(l- k) (5) 



^ (T p 



Similarly for loci fixed aa in the tester: 



sd 



Aqj 



S ' r p(; • y a ,, ' a 



., ^,, . Vil-qr) 'qj{\-qj)il-\-k) (6) 



Z, (7 p 



