DOMINANCE AND OVERDOMINANCE 289 



This has the sokition, R = u/s. (For a more pedantic demonstration of this, 

 see Crow, 1948.) 



The average reduction in selective value of the population due to a detri- 

 mental factor will be the product of the selective disadvantage of the factor 

 and the proportion of individuals possessing the factor. This amounts to 

 (s) (ti/s), or, simply, u, the mutation rate. Hence, the effect of a detrimental 

 gene on the selective value of the population is equal to the mutation rate to 

 that gene, and is independent of the selective disadvantage which that factor 

 causes, as was first pointed out by Haldane (1937). This fact, which at first 

 appears paradoxical, is readily understandable when one notes that a mildly 

 deleterious mutant persists much longer in the population, and hence affects 

 many more individuals than one which has a greater harmful effect. 



The total effect on the population of all the loci capable of mutating to 

 deleterious recessives is simply the sum of the individual mutation rates as 

 long as the gene effects are additive. If there are n such loci with an average 

 mutation rate of u, the net reduction in selective value due to all homozygous 

 detrimental recessives at all loci in which they occur is nil. This is also ap- 

 proximately correct if the factors are multiplicative, provided the individual 

 effects are small. 



The product ml is probably in the vicinity of .05 (Crow, 1948). This means 

 that if all the deleterious recessives were replaced by their dominant alleles, 

 the selective advantage of an equilibrium population would be increased by 

 about this amount. This could be considered as the maximum average im- 

 provement in vigor, as measured in terms of selective advantage, that could 

 occur due to hybridization. This means that the dominance hypothesis can- 

 not, under the conditions postulated, account for average increases of more 

 than a few per cent in vigor. 



There are several reasons why the 5 per cent figure given above may be 

 too large. One is that many deleterious factors considered to be recessive 

 may not be completely recessive. Stern and Novitski (1948) and Muller 

 (1950) have shown that the majority of lethals and detrimentals that occur 

 in laboratory cultures of Drosophila are not completely recessive. Even if the 

 detrimental effect of the heterozygote is much less than that of the homozy- 

 gote, the greatest selection effect will still be on heterozygotes because of 

 their much greater frequency in the population. Thus, from the population 

 standpoint, these factors would be acting more like dominants than reces- 

 sives. This means that each locus would have a detrimental effect of 2u in- 

 stead of u (since a dominant gene would be responsible for twice as many 

 "genetic deaths" as a recessive), but the locus would be unimportant for 

 heterosis. Since the n in the formula refers only to the number of loci which 

 are capable of mutating to a completely recessive allele, its value may be 

 smaller than previously assumed and the product nu proportionately less. 



It has been assumed that the parent populations are at equilibrium be- 



