RECURRENT SELECTION AND OVERDOMINANCE 459 



homozygotes less for any locus with multiple alleles present in a crossbreed- 

 ing population. If heterozygosity should be of general advantage, multiple 

 alleles would provide more heterosis. East was at some pains to explain the 

 development of A 4 from A 1 by successive steps to the end of a superior hetero- 

 zygote. He apparently did not accept that hetero zygote superiority might be 

 general, with multiple alleles affecting vigor. I do not accept it either as a 

 likely proposition. 



It seems likely that production of grain, meat, eggs, or milk may consist 

 of main effects and interactions of many, perhaps most, of the genes of the 

 plant or animal. Main effects must be of many kinds and magnitudes. Where 

 inbreeding depression and heterosis are evident there must be bias of positive 

 dominance or interactions of alleles to provide a gain in heterozygotes over 

 the arithmetic mean of homozygotes. Whether the interaction is basically a 

 stimulation of unlike alleles in the heterozygote, an interfering depressing in- 

 teraction in the top homozygote, or some other kind of interaction is an im- 

 portant problem in gene physiology. Present concern, however, is only with 

 the magnitude and frequency of the effect without regard to its basic physi- 

 ology. 



Various writers have noted that dominance is not an absolute property. If 

 the phenotype is fruit size, degree of dominance is hardly the same for both 

 diameter and volume. The same genes might also affect stem length and ex- 

 hibit a third degree of dominance there. Gene effects are often greatly subject 

 to environmental fluctuations and to presence or absence of genes at other 

 loci. 



Within reasonable limits of soil fertility and climate, grain yield of selected 

 homozygous corn is about 30 per cent of the yield of crossbred corn. Seventy 

 per cent of the apparent yield of crossbred corn consists of dominance effects 

 and perhaps of interactions of dominance with other gene effects. The 30 per 

 cent yield of homozygous corn consists of main effects and epistatic interac- 

 tions of main effects. 



One difficulty in resolving the present situation without regard to how it 

 may have evolved is that the absolute zero of the genetic yield range cannot 

 be easily estimated. However, it might be assumed that it is less than zero on 

 our data scale. More specifically, the homozygotes with more than two-thirds 

 of the concerned loci aa or less than one-third AA may be inviable or have 

 an average yield potential of zero. The 100 per cent of measured yield then 

 would represent only the upper two-thirds of the total genetic range. With 

 dominance of high yield complete at each locus and the foregoing assumption 

 the present situation is adequately explained without resort to epistatis or 

 overdominance. 



LINEARITY OF INBREEDING DEPRESSION AND HETEROZYGOSITY 

 Any appreciable degree of interaction of dominance with other gene ef- 

 fects might be detectable in a non-linear relation of inbreeding depression to 



