Gene Frequencies 537 



lation of large numbers of recessive lethal and other mutations 

 and has prevented the recombinations of numerous genes with 

 the concomitant origin of many genetic types upon which natural 

 selection can act. Interracial hybrids do not occur frequently 

 and, when they do, those with a circle of fourteen are perpetuated 

 indefinitely as true-breeding types. In the Oenotheras, a large 

 number of forms has arisen, but they do not behave in the way 

 that they would in a freely interbreeding population. 



Apparently the balanced lethal mechanism which renders 

 some complex heterozygotes permanently true-breeding also en- 

 sures them of the advantages of heterosis. In all the "half 

 mutants," where the loss of one lethal allows homozygotes to 

 be formed, these homozygotes are quite markedly inferior to 

 the corresponding complex heterozygotes. 



Gene Frequencies 



We showed in Chapter 6 that if a heterozygote, Aa, is self- 

 fertilized, it will produce an offspring whose genotypic ratio is 

 lAA : 2Aa : laa. This was predicated upon several assump- 

 tions. It assumed that any egg could be fertilized by any sperm, 

 that each type of egg was equally frequent, that each type of 

 sperm was equally frequent, and that all possible types of off- 

 spring could be formed and would be viable. We demonstrated 

 this graphically in Fig. 28 by the checkerboard method. That 

 none of the eggs or sperm was preceded by any number that 

 would denote their frequency indicated that the A and a eggs 

 were present in a ratio of 1 : 1 or that each had a frequency 

 of 0.5, and that this was also true of the sperm. In other words, 

 if each type of egg and each type of sperm were present in equal 

 frequency, the offspring would be present in a ratio of 1 homozy- 

 gous dominant : 2 heterozygous : 1 recessive. 



The genotypic ratio that is obtained in the Fi by selfing a 

 heterozygote is the same as the ratio found in the offspring of a 

 population of organisms that reproduce sexually, provided that 

 in both sexes the gametes bearing the dominant allele and those 

 bearing the recessive allele are equally frequent, and provided 

 furthermore that theoretically any egg can be fertilized by any 

 sperm. The additional assumptions must also be made that 

 the homozygous dominant, heterozygous, and recessive types all 



