472 FRED H. HULL 



is at equilibrium for one locus when gene frequencies are (1 + k)/2k in both, 

 and k> 1. It is conceivable that gene frequencies of the two crossbreds may 

 wander in the zone of low heritability through many cycles of reciprocal selec- 

 tion, but they must eventually separate on opposite sides to approach aa and 

 AA respectively with increasing velocities. When the two gene frequencies 

 are on opposite sides of the equilibrium initially, reciprocal selection will tend 

 to drive them farther apart. If they are on the same side both will tend to ap- 

 proach equilibrium. Comstock's statement here that the one nearest equilib- 

 rium may approach it more rapidly and continue beyond to reverse the trend 

 of the other, thus obtaining a quick separation, seems good. I had overlooked 

 this point and hope it may be experimentally verified. 



Gametes with critical gene frequencies in the present model are aAAA, 

 AaAA, AAaA, AAAa. A general tester composed of the four homozygous 

 lines producing these four gametes respectively will provide zero heritability. 

 So also will a crossbred tester for every locus where gene frequency is f . One 

 of the homozygous lines alone as a specific tester provides mean bp = — 

 [f + 3( — 1)]/4. But here the individual values of bp for each locus are at 

 maximum, | for the aa locus, and — | for each A A locus, providing maximum 

 heritability in selection to a homozygous tester. 



Defining phenotypes of aa, aA, A A alternatively as 1 — .y, 1 — hs, 1, pro- 

 vides bp = \ — h — {I — 2h)v. Then with // = — | for the same degree of 

 dominance as the present model, bp = ^3) — 2v again. The only inconsist- 

 ency between the two systems of defining phenotypes which may be encoun- 

 tered here, I think, is failure to distinguish between physical values and selec- 

 tive values, e.g., body weight and number of offspring surviving to breed. 



It seems fairly clear that overdominance of the degree considered here may 

 provide considerable variation of heritability within a finite sample, a herd 

 or a variety on one farm. Mean bp may be positive and fairly large, yet bp = 

 near the upper range of gene frequency in the sample. Moreover, the degree 

 of dominance for selective values might be appreciably greater than for the 

 physical trait. For these reasons, selection indexes made up with average 

 heritabilities of physical traits could be misleading. 



Parallel operations of the foregoing breeding plans with heavy dosages of 

 mutagenic agents in addition might provide significant information on pro- 

 gressive improvement, where the objectives respectively are the superior 

 homozygote, the mean of the population, and the superior heterozygote. 

 This proposal will be subject to criticism by those who are convinced that it 

 is only in gene-by-gene analysis that real advances in knowledge of genetics 

 can be obtained. I have no quarrel with that viewpoint except that where 

 many genes with minute efliects may be involved the gene-by-gene approach 

 still seems fairly remote. 



Recurrent selection in prolific species such as corn, chickens, mice, and 

 Drosophila may soon build up very large selection intensities, perhaps to re- 



