DOMINANCE AND OVERDOMINANCE 291 



tional increase in selective value. Thus any conclusions about maximum i)ro- 

 portional increase in selective value would hold a forliori for yield. Fisher 

 (1949) reaches a similar conclusion when he says: "If the chance of survival is 

 equated to the yield, as is reasonable with grain crops." 



Another assumption is that the hybrids are compared with equilibrium 

 populations. There is room for question, particularly with domestic plants 

 and animals, as to whether selection has been occurring long enough and its 

 direction has been consistent enough for a gene frequency equilibrium to have 

 been attained. Another point that must be remembered in discussions of 

 maize is that commercial hybrids are not random combinations of inbred 

 lines, but highly select combinations. An average hybrid may have a yield 

 very close to that of a randomly mating population. Thus the argument of 

 this section may not be relevant for corn. But it can hardly be true that the 

 high yield of certain corn hybrids is due to the elimination of deleterious 

 recessives during inbreeding. 



The quantitative limit placed on average improvement on hybridization 

 with the dominance hypothesis does not hold for overdominant loci. A locus 

 at which the homozygote A A has a selective disadvantage of .y with respect 

 to the heterozygote, and the homozygote A' A' has a disadvantage of /, will 

 come to equilibrium with gene frequency of A equal to t/(s + 0, and the 

 frequency of A' equal to s/(s + /) (Wright, 1931b; Crow, 1948). The average 

 reduction in selective advantage of the population due to the two homozy- 

 gous genotypes comes out to be st/{s + /). The loss in fitness of the popula- 

 tion is of the order of magnitude of the selection coefficients, as Haldane 

 (1937) has first shown, whereas with a detrimental recessive, the loss is of 

 the order of the mutation rate. Hence a single overdominant locus has a 

 tremendously greater effect on the population fitness than a single locus with 

 dominance or intermediate heterozygote. If such loci are at all frequent they 

 must be important. The question is: how frequent are they? 



Even with overdominance it is difficult to understand large average in- 

 creases in selective advantage of hybrids between equilibrium populations. 

 Such populations should be somewhere near their optimum gene frequencies, 

 which means that the hybrids would be about the same as the parents. It 

 may be that, on the average, hybrids do not greatly exceed their parents in 

 selective advantage, and that the cases of increased size observed in variety 

 crosses and occasionally in species crosses are nothing but luxuriance. If so, 

 they are much less difficult to explain. 



As Bruce showed in 1910, if the parents differ at all in gene frequencies, 

 the hybrids will be more heterozygous. If both parents are at equilibrium 

 they should have, for additive genes, approximately the same frequencies. 

 But what differences there are — due to chance, for example — will amount to 

 much more in an overdominant than in a dominant locus because the former 

 has a gene frequency much nearer .5. 



