292 JAMES F. CROW 



POPULATION VARIANCE 



The same considerations which show that an overdominant locus has a 

 much greater effect on average population fitness than a dominant locus also 

 show that an overdominant locus has a much greater effect on the population 

 variance. If the selective values of the three genotypes, AA,Aa, and aa are 1, 

 1, and 1 — s respectively, the frequency of aa genotypes is u/s and the aver- 

 age selective value 1 — u. The variance in fitness will be sii. On the other 

 hand, with an overdominant locus where the fitnesses of the three genotypes 

 are 1 — ^, 1, and 1 — ^, the mean fitness is 1 — s/2. The variance in fit- 

 ness is 5-/4. 



The ratio of these variances is s/4u, which means that an overdominant 

 locus causes a population variance s/4:U times as great as that resulting from 

 a recessive locus of the same selective disadvantage. If 4u is 10"^, this 

 amounts to 100 for ^ = .001, or is 1000 for s = .01. This makes an over- 

 dominant locus with these selective values equivalent to 100 or 1000 ordinary 

 loci in its effect on the population variance. Haldane (1950) has emphasized 

 the importance of loci with adaptively superior heterozygotes in increasing 

 the variance of natural populations. 



From this we must conclude that there doesn't have to be a very high 

 proportion of overdominant loci for overdominance to be the most important 

 factor in the genetic variance of the population. If much of the genetic vari- 

 ance of a population is due to overdominance, this would explain the great 

 slowness of selection. Characters with high genetic determination but low 

 parent-offspring correlation might be due to this cause. 



The facts of hybrid corn also are consistent with this. Ordinary selection 

 has not been effective. Yet there is a great deal of variation in an open- 

 pollinated variety. It has been relatively easy to find combinations of inbred 

 lines that have yields well above the open-pollinated averages. There appears 

 to be a relatively high degree of genetic determination of yield, but relatively 

 low heritability. These results are not impossible with dominant genes, es- 

 pecially with epistasis, but are precisely what would be expected if some of 

 the variance were due to overdominant loci. 



A population with many overdominant loci is always well below its maxi- 

 mum possible fitness. It is expected that such factors could eventually be 

 replaced in long evolutionary periods. This might occur by an appropriate 

 mutation, by duplication, or by modifiers. Or a population with too many 

 overdominant loci might disappear due to inter-population competition. But 

 at any particular time, a population may have a small proportion of such loci, 

 and it does not require many for these to be the major source of variation. 



DO THE SAME GENES DETERMINE VARIATION IN 

 INBREDS AND HYBRIDS? 



The rarer a recessive phenotype is in a population, the greater will be its 

 relative increase in frequency on inbreeding. If the frequency of the recessive 



