460 FRED H. HULL 



predicted frequency of heterozygosity in succeeding generations of inbreeding. 

 Since the considerable body of data on inbreeding effects on yield of corn 

 fails to show any such non-linearity at all, I have been inclined to dismiss in- 

 teraction of dominance with other gene effects. Since, in addition, back- 

 crosses of Fi's to homozygous parent lines fail to show significant non-line- 

 arity I have been inclined to dismiss epistasis in general as an appreciable 

 part of the explanation of the disparity of yields of homozygous and cross- 

 bred corn. 



Overdominance alone is an adequate explanation of the disparity. Pseudo- 

 overdominance from random linkage is not an adequate explanation by itself 

 since the totals of gene effects are independent ( f linkage (Hull, 1945a). 



REGRESSION OF Fi YIELD ON YIELDS OF PARENT LINES 



Corn breeders have frequently chosen a small sample (usually 10) of in- 

 bred lines and have made all or most of the specific crosses. Comparable 

 yield records on parent lines and Fi's have become available now in 25 sets 

 of data. F2 records are included with 3 of them. None of these data are 

 mine. Some of them were analyzed in part by simple regression of yield of Fi 

 on yield of parents, which would seem to provide the significant information 

 from the general combinability viewpoint. Interaction of parents is mostly 

 neglected. 



Within each column or each row of a (10 X 10) table as described are nine 

 Fi's or nine F2's with one common parent. The common parent is the tester 

 of the other nine lines. Each line serves as the tester of one such group. 



On the assumption that the partial regression of offspring on parent with- 

 in a group having one common parent is a relative measure of heritability 

 within the group, or of efficiency of the common parent as a tester, it has 

 seemed worth while to calculate all of the regression coefficients for individual 

 columns of the twenty-five Fi and three Fo tables. We tacitly accept that 

 yield may be a heritable character. Beyond this we need no fine-spun theory 

 nor any genetic theory at all to warrant direct regression analysis of the data. 

 However, Mendel's final test of his theory was with backcrosses to aa and 

 A A separately. He noted essentially that with completely dominant charac- 

 ters the expected regression of offspring phenotype on gene frequency of par- 

 ent gamete was unity with the aa tester and zero with the ^.4 tester. We may 

 be dealing with multiple factor cases of such testcrosses and of course with 

 different degrees of dominance at the several loci. The significant differentia- 

 tion of our homozygous testers may be in relative frequencies of aa and ^.4 at 

 the fli, ai, a^ — a„ loci. 



Results with the first two examples are shown in Table 28.1. Yield of the 

 tester parent (P) is in bushels per acre. Directly below are the partial regres- 

 sion coefficients (bp) for the respective testers. Since there are apparently 

 negative trends of bp with respect to P, the second order regression (62) of 



