DOMINANCE AND OVERDOMINANCE 283 



In most situations, the hypotheses of dominance and overdominance lead 

 to the same expectations. In either case there is a decrease of vigor on in- 

 breeding and a gain on outcrossing. Wright (1922c) has shown that with the 

 dominance hypothesis the decline in vigor is proportional to the decrease in 

 heterozygosis, regardless of the relative number of dominant and recessive 

 genes and of the degree of dominance. The same decline in vigor with de- 

 creasing heterozygosity is true with overdominance. 



It is usually impossible in a breeding experiment to differentiate between 

 true overdominance in a pair of alleles, and pseudo-overdominance due to 

 the effects of two pairs of alleles closely linked in the repulsion phase. Only 

 in special circumstances, such as when a mutation has recently occurred in 

 an isogenic stock, can the experimenter be reasonably certain that the effect 

 is due to a single allelic difference. Furthermore, there is the possibility of 

 heterosis due to borderline situations, such as might arise in pseudoalleles 

 with a position effect, which could not even theoretically be classified as due 

 to dominance of linked genes or overdominance. Finally, it should be noted 

 that the various hypotheses may not be equally important in all situations. 

 For example, it is reasonable to expect that overdominance would be more 

 important in determining differences between inbred lines of corn pre- 

 viously selected for general combining ability than in lines not so selected. 



If the two hypotheses are not mutually exclusive, neither are they col- 

 lectively exhaustive. There is no reason to think that multiple factors are 

 any less complex in their interactions than factors concerned with qualitative 

 differences. With the number of genes involved in heterosis, and with the 

 complexity of interactions known to exist in cases where individual gene 

 effects have been isolated and studied, there must surely be all sorts of com- 

 plex interactions in heterosis. Therefore no single theory can be expected to 

 account for the entire effects of heterosis. Although it is difficult to separate 

 by statistical methods the effects of dominance and epistasis, it may be 

 possible to construct simple models which are of some utility. 



DOMINANCE 



Davenport (1908) was the first to point out the now well-recognized fact 

 that in most cases the dominant character is beneficial to the organism pos- 

 sessing it, while the recessive has a weakening effect. He noted that this could 

 help explain the degeneration that usually follows inbreeding. Davenport 

 was thinking of relatively few factors with individually large effects, whereas 

 at present, more emphasis is given to multiple factors. But he was close to 

 the ideas now held. 



Keeble and Pellew (1910) found that hybrids between two pure varieties 

 of peas were taller than either parent. In this case, two different dominant 

 factors were involved — one resulting in longer internodes and the other in- 



