The Gene Pool; Equilibrium Factors 



203 



zygous (A^a-j)', since homozygous children 

 die, a-2 is a recessive lethal mutant. Affected 

 individuals are found with a frequency of 

 one per 100,000, or .00001. What is the 

 frequency of a 2 in the gene pool? As shown 

 in Figure 15-3, the frequency of a^a% indi- 

 viduals at equilibrium is equal to q-. Ac- 

 cordingly, the frequency of a- 2 (q) must be 

 equal to Vq 12 , or V .00001, or about .003, 

 whereas the frequency of A\ must be one 

 minus .003. or .997. Note that heterozy- 

 gotes (carriers) are 600 times more fre- 

 quent than afflicted homozygotes. What is 

 the mutation frequency from A x to a-P. As- 

 sume that the gene pool is at equilibrium; 

 in other words, the frequency with which 

 a> enters the population by mutation equals 

 the frequency with which it leaves the pop- 

 ulation in flotfo homozygotes. Accordingly, 

 the mutation frequency to a 2 must be .00001. 

 The selection coefficient for normal indi- 

 viduals (A X A X and A^a^) is zero, and for 

 a 2 a-2 it is one. We see, therefore, that at 

 equilibrium the frequency of a recessive 



GENOTYPE 

 PHENOTYPE 



FREQUENCY AT 

 EQUILIBRIUM 



A, A, 



A,a : 



Normal Normal Dies 

 P 5 2pq q* 



u = Mutation rate from A, — a, 



q ="U u/s Here s = 1, hence q ="\| 



u = 10~ 5 = 0.000,01 Hence q =M 0.000,01 = 0.003 



OtQ 



DtO 



(WSSd 



lolorioo 



figure 15-3. Juvenile amaurotic idiocy. {See 

 text for explanation.) 



figure 15—4. Pedigree showing the occur- 

 rence of phenylketonuria among the offspring 

 of cousin marriages {denoted by thick marriage 

 lines). 



mutant in the gene pool can be expressed as 

 q = Vii s, where s = 1 for a recessive 

 lethal. When the homozygous recessive 

 mutant is detrimental without being lethal, 

 s becomes less than one (but more than 

 zero) and the frequency of the mutant in 

 the gene pool increases. Thus, if s were 

 Y 4 instead of one, q would be twice as large. 



* Nonrandom Matings 



In deriving the types and frequencies of 

 genotypes in a population at equilibrium, 

 we assumed that marriages were random 

 with respect to the genotypically-determined 

 trait under consideration. Such a randomly- 

 mating population is said to be panmictic 

 or to undergo panmixis. What happens if 

 the different genotypes do not marry at ran- 

 dom? Consider the disease phenylketonuria 

 (Figure 15-4) which involves a type of 

 feeblemindedness in individuals who are 

 homozygous for a recessive gene, and who 

 metabolize the amino acid phenylalanine to 

 phenylpyruvic acid, which is toxic. The 

 frequency in the gene pool of the normal 

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



