DOMINANCE AND OVERDOMINANCE 287 



epistatis is not important or else that there is some sort of cancelling out of 

 various effects. On the other hand, Stringfield (1950) found that in many 

 cases backcrosses showed consistently higher yields than the F2. This sug- 

 gests some sort of interaction, as if some of the gene combinations selected for 

 during the inbreeding process were active in the backcross, but were broken 

 in the F2. None of these data give any evidence as to the importance of 

 epistasis in determining the difference between an inbred line and a hypothet- 

 ical line with none of the favorable dominants, since the data do not extend 

 into this range. It is in this range where non-additivity might be expected 

 to be most pronounced. 



Hull's second argument is based on results obtained by the technique of 

 constant parent regression. The regression of Fi on one parent, with the other 

 parent held constant, has different expectations when there is overdominance 

 than when there is dominance. With overdominance the regression may be 

 negative when the constant parent is high-yielding, so the regression surface 

 is different from that expected with dominance. In this volume Hull gives 

 data which conform with this expectation. 



Overdominance is not the only possible explanation of such results, as 

 Hull has pointed out. In addition, the constant parent regression technique, 

 or any technique making use of yield data on inbred lines, is complicated by 

 the difficulty of obtaining consistent results with inbreds. Another possi- 

 bility is that the factors responsible for yield in inbreds are largely different 

 genes from those determining the yield in the hybrids. This possibility will 

 be considered later. 



For these reasons it is still not possible to be sure of the importance of 

 overdominance from Hull's methods. They are at least strongly suggestive, 

 and recent data from Robinson et al. (1949), obtained by an entirely differ- 

 ent procedure, also gave evidence of overdominance. 



MAXIMUM HETEROSIS WITH THE DOMINANCE HYPOTHESIS 



In this discussion several assumptions are made. Most of these have been 

 implicit in most discussions of heterosis, but it is best that they be clearly set 

 forth at the outset. The assumptions are: 



1. Genes concerned with vigor are dominant, and in each case the domi- 

 nant allele is beneficial and the recessive deleterious. This is an assumption 

 of convenience which does not alter the essential nature of the hypothesis. 

 The conclusions still hold if dominance is not complete. Also there are loci 

 in which the recessive is advantageous or in which the heterozygote is inter- 

 mediate; but these are of no consequence for heterosis and therefore can be 

 omitted from the discussion. 



2. There is complete additivity of effects between loci — no epistasis. 



3. There are no barriers to recombination that prevent each gene from 

 reaching its own equilibrium frequency independently of other loci. 



