INBRED LINES FOR HETEROSIS TESTS? 343 



mentary lines to be used in production of commercial hybrids. Comstock 

 et al. (1949) have compared expected effectiveness of Hull's plan with that 

 for reciprocal selection for cross performance between two foundation stocks 

 of divergent origin, avoiding inbreeding in both stocks. The}' point out that 

 the potential limits of improvement are the same for the two methods, except 

 for loci exhibiting only partial dominance {k < 1), where the use of a tester 

 homozygous for any of the less favorable alleles would reduce potential hy- 

 brid performance. Existence of important epistatic effects also would tend to 

 make limits lower for use of a homozygous tester. 



There is no reason to expect initial cross performance to differ between 

 reciprocal and homozygous tester selection, other than because of the per- 

 formance of the inbred tester line itself (inbreeding effects on maternal en- 

 vironment of the litter in swine). If anything, it would be easier to find a 

 population differing materially in gene frequency at individual loci from a 

 homozygous tester than to find two similarly complementary non-inbred 

 populations. 



Relative rates of improvement expected from the two plans depend on (1) 

 selection pressure applied, and on (2) size of regression of gene frequency in 

 the material under selection on performance of test-cross progeny. Hull's 

 homozygous tester plan limits selection to only one of the parental stocks. 

 Hence selection applied will be only | as great as in reciprocal selection. 

 However, as long as frequencies of the more favorable alleles {q) are any- 

 where near their expected equilibrium of (1 + k)/2k, progress toward com- 

 plementary gene frequencies (toward maximum proportion of heterozygous 

 loci in the cross) per cycle of selection will be far less for reciprocal than for 

 homozygous tester selection. 



Comstock (1949) has shown that improvement in performance of random 

 crosses between two segregating populations per generation of selection, at a 

 given locus, is: 



AP.= [^qA^ + k-2kq.i) -{-Aq2{l + k-2kqi) - Ik- Lq,- Aq^] d (1) 



The change in gene frequency at a given locus within each of the two selected 

 populations (A^i and Ag2, respectively) will be determined by (1) the in- 

 tensity of selection based on the test-cross progeny means {s = selection dif- 

 ferential in a units), (2) the correlation between qi and the mean progeny 

 performance (P), and (3) the size of aq^ among the tested individuals, as 

 follows: 



Avi = s r,,,.a„ = , Cov,...^ 5^^ q,{\-q,){\ + k -2kq.^ (2) 



0" P 2<T p 



Hence, as Comstock indicates, improvement in cross performance from 

 one cycle of reciprocal selection and for any one locus is: 



APr = ^[qi{\-q,)(l + k-2kq,)^-+q2i\-q2)il + k-2kq,)^ ^^^ 



— 2k'Aqi-\q-2 



