ESTIMATION OF AVERAGE DOMINANCE OF GENES 503 



tion as it became available. Then if loose linkages were of much importance 

 in the first estimate, one would antici]:)ate a downward trend in the estimates 

 of a as more and more advanced generations were employed. Natural selec- 

 tion too weak to have much effect on results when the F2 is used could be the 

 source of significant changes in gene frequencies over a period of generations. 

 Hence the effects of recombination and of shifting gene frequencies would be 

 confounded in trends observed using either Experiment I or II. 



Fortunately, E.xperiment III does not depend on any assumption about 

 gene frequencies. Letting q symbolize the population frequency of any gene 

 and 1 — ^ that of its allele, the genetic interpretation of al, and 0-^,; can be 

 expressed more generally than in Table 30.4 as ^2^(1 — q)u'' and l.qil — 

 q)a-ii~, respectively. One possible weakness of the proposal is apparent. If 

 shifts in gene frequency are variable by loci the weighting of individual c's in 

 a- is shifted slightly since it is now relative to ^(1 — q)u' rather than ur. 

 However, barring shifts greater than .2 which are unlikely unless a gene has 

 a very important effect, shifts in weights will be of minor magnitude since 

 q{\ — q) varies only between .21 and .25 as q varies from .3 to .7. Further- 

 more, shifts in weight are not a source of bias unless degree of dominance 

 (size of a) is correlated with importance of the gene. While this weakness 

 should not be overlooked, it appears of minor consequence. A partial check 

 could be made by accumulating seed of each generation for a yield compari- 

 son of the successive generations. If major gene frequency trends have oc- 

 curred at important loci they should be evidenced in higher yields by the 

 later generations. 



The suggested extension of Experiment III is intrinsically the same sort of 

 technic as Mather (1949) has outlined for investigating linkage effects on 

 genetic variances. 



DERIVATION OF GENETIC INTERPRETATIONS OF COMPONENTS 

 OF VARIANCE BETWEEN PROGENIES 



The genetic constitution of a?„ and al,i of Experiment III will be derived 

 as examples. Derivations for components of the other two experiments are 

 given elsewhere (Comstock and Robinson, 1948). Initial assumptions will in- 

 clude only the following: regular diploid behavior at meiosis, no multiple 

 allelism, no epistasis. Restrictions are not being placed on gene frequencies 

 or linkage. To that extent the derivations to be given below are more general 

 than those cited above which assumed absence of linkage and gene frequen- 

 cies all equal to one-half. 



The population sampled in Experiment III is outlined in Table 30.5. It 

 consists of an infinity of pairs of backcross progencies, one pair for each vari- 

 able parent that might be chosen from the F2 or a later generation from cross- 

 ing the two homozygous lines. Expected genetic values of each progeny are 

 indicated symbolically. Because all progenies must be of finite size, there will 



