The Theory of Population Genetics 1 101 



1 percent selective advantage over its wild-type allele. These prob- 

 abilities are reproduced in Table 6.5, which shows that a new muta- 

 tion has virtually no chance of survival in a population unless selec- 

 tion counteracts the decay of variability. 



MUTATION 



Mutations are changes in genetic information and as such have been 

 discussed in Chap. 3. Mutation will now be considered as one of the 

 systematic pressures tending to cause deviation from the Hardy- 

 Weinberg equilibrium. If A is the "type gene" and a is the mutated 

 gene, u = mutation rate, A-^ a, and v = back mutation rate, A<—a. 

 Such a system has an equilibrium point, as shown in the following 

 calculations: 



Aq = up (gain) — vq (loss) 



A^ = at equilibrium point (p,q) 



A Av 



Therefore Aq = = u{l — q) — vq 



r\ A A 



= II — uq — vq 



— II = q( —II — v) 



A n 



9 = 



II ^ V 

 A , A 



p=l-q=l 



u u -^ V — U V 



?< + u w + t) u-\-v 



where p = gene frequency of A 

 q = gene frequency of a 

 p + q= l;q = l-p 

 Aq = change in q 

 ^ = equilibrium value (referred to as "q hat") 



A graphic representation of this equilibrium is shown in Fig. 6.3. 

 Note that Aq is the net change per generation in the frequency of a 

 and that A^ is positive when q < q, and Aq is negative when q > q. 

 The change at 1 (all a) is one-half as great as at (all A) since 

 A-^a = u = .00004 anda-^A = v= .00002. Thus we can see that, 

 in a population meeting all the requirements of Hardy-Weinberg 

 equilibrium except the absence of mutation, the equilibrium value 

 for the frequency of a gene is determined by the mutation rate and 

 back mutation rate at the locus in question. 



