DOMINANCE AND OVERDOMINANCE 293 



gene is q, the frequency of recessive homozygotes in a randomly mating 

 population is (f. With increasing amounts of inbreeding, the frequency 

 changes from q- to q. The smaller the value of q, the greater is the ratio of 

 q to q~. If a gene is highly deleterious it will be very rare in the population. 

 Hence the genotypes which are most deleterious are those which have the 

 greatest relative increase in frequency on inbreeding. 



These relationships are brought out in the following figures, based on a 

 mutation rate of 10~^. The ratio given is the ratio of homozygous recessives 

 in a homozygous population as compared with one which is mating at 

 random. 



Selective disadvantage (5) 0001 .001 .01 .1 lethal 



Gene frequency (?) 1 -032 .01 .003 .001 



Ratio (g/5=) 10 32 100 316 1000 



This means that highly deleterious recessives, which ordinarily have an 

 effect on the population only of the order of the mutation rate, become much 

 more important wdth inbreeding and may become the major factors in deter- 

 mining the fitness of an inbred population. This might to some extent be 

 offset by selection during the inbreeding process, but such selection would be 

 directed against factors which are of no consequence in a more heterozygous 

 population. 



The detrimental recessive factors referred to here include the lethals and 

 semilethals (such as chlorophyll deficiencies) that show up during inbreed- 

 ing. But more important are the larger number of factors, not individually 

 detectable, which collectively result in the loss of vigor with inbreeding de- 

 spite rigorous selection. 



On the other hand, the major part of the variance of a non-inbred popu- 

 lation may well be determined by genes of intermediate frequencies, from 

 .1 to .9. The effect of such factors in determining the population variance 

 in fitness would change only slightly with inbreeding. 



As an example, consider a hypothetical population mating at random 

 whose variance is made up of two components. Ninety per cent of the vari- 

 ance is due to relatively common loci with gene frequencies of the order of .5. 

 The other 10 per cent is due to loci with recessive gene frequencies of the 

 order of .01 or less. Now when this population is inbred without selection, 

 the variance due to the common genes will not change greatly but the vari- 

 ance due to the recessive loci will increase by a hundred fold or more. Thus 

 the factors which originally contributed only 10 per cent to the variance 

 may now contribute over 90 per cent of the variance between the various 

 inbred lines derived from the population. 



Gene frequencies of the order of .5 might result from several causes. They 

 might be genes which are advantageous in one geograj)hical location and 

 disadvantageous in another so as to form a cline. Or there might be seasonal 

 differences in selective value. They may be due to complex interactions with 

 other loci or be of extremely small selective advantage or disadvantage. But 



