Mutation and Selection — Mating and Heterosis 



231 



can be expressed as q = Vu/s, where 

 s = 1 in the case of a recessive lethal. If the 

 recessive mutant is detrimental without being 

 lethal, s becomes less than 1 (but more than 

 0) and the frequency of the mutant in the 

 gene pool becomes higher for the same muta- 

 tion rate. Thus, if in the present example, s 

 is Yi instead of 1 , q is twice as large. 



In deriving the types and frequencies of 

 genotypes in a population at equilibrium, it 

 was presumed that marriages were at random 

 with respect to the genotypically determined 

 trait under consideration. What happens if 

 the different genotypes do not marry at 

 random? Consider the disease phenylketo- 

 nuria (Figure 27-2) which involves a type of 

 feeblemindedness in individuals, homozygous 

 for a recessive gene, who cannot properly 

 metabolize the amino acid phenylalanine. 

 The frequency in the gene pool of the normal 

 gene (A) is .99, and of the abnormal gene (a) 

 is .01. In the population at equilibrium, 

 therefore, AA : Aa : aa individuals will have 

 frequencies of 



9801 10,000 : 198 10,000 : 1/10,000, 



respectively. Notice that Aa individuals are 

 198 times more frequent than aa, so that even 

 if every aa did not reproduce, only one 

 per cent of the a genes present in the gene 

 pool would be eliminated each generation. 

 This illustrates the inefficiency of selection 

 against homozygotes for rare recessive genes, 

 insofar as lowering the frequency of such 

 genes is concerned. AA and Aa individuals 

 apparently marry each other at random. 



FIGURE 27-2. Pedigree showing the 

 occurrence oj phenylketonuria among 

 the offspring oJ cousin marriages 

 {denoted by thick marriage lines) 



However, it is also true that feebleminded 

 people do not marry in the population at 

 random. But this has little effect on the dis- 

 tribution of genotypes in successive genera- 

 tions, since aa people have so few of all the a 

 genes present in the population. You can 

 see that it is only marriages between Aa indi- 

 viduals that are of consequence, since those 

 are the major source of aa offspring. 



The example of phenylketonuria shows 

 that, when a gene is rare and apparently 

 completely recessive, nonrandom marriage 

 has little influence upon its frequency, or the 

 diploid genotypes in which it is found in the 

 population. When the mutant is relatively 

 frequent in the population, however, it is 

 obvious that nonrandom marriages will raise 

 the frequencies of certain genotypes and 

 lower others. Moreover, if there are adap- 

 tive differences for the different genotypes, 

 the composition of the gene pool may be 

 changed in a different direction, or at a dif- 

 ferent rate, from what would be predicted 

 for a population mating at random. Con- 

 sider two ways in which mating may be non- 

 random. The first involves the tendency of 

 phenotypically similar individuals (disre- 

 garding the sex differences) to mate, and is 

 referred to as assortive mating. This kind of 



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