36 MUTATION AND PLANT BREEDING 



Table 2. — General Procedure of Calculating Selection Effect. 



Geno- 

 type 



Frequency 



Fitness 



w 



Selected 

 fw 



New gene frequency 



W\ 



Wo 



Wz 



D wi 



H w-i 

 R w 3 



{Dwi + }4Hwi) I w = p' 

 (Rw 3 + }4Hwi) I w = q ' 



Total 



1 



w 



1 



A. Selection against dominant mutant gene A' 



D 1 D 



[D+ y 2 H(\-s)] I (\-Hs) 

 H \-s H(\-s) 



y 2 H(\-s) I (l-Hs) 

 



A A 

 A A' 

 A' A' 



P' 



q' 



Total 



1 



w 



= l-Hs 



1 



AA 



B. Selection against the recessive genotype 



1 D 



(D + y 2 H) / (1 - Rs) = p' 

 1 H 



(R-Rs + y 2 H)/{\ -Rs) = q' 

 \-s R(ls) 



D 

 H 

 R 



Total 



1) = 1 - Rs 



w 



1 



dominants are nonexistent in the population, so that D + H = 1 

 and q - \/ 2 H is the frequency of the dominant mutant gene. The 

 change in gene frequency due to selection is Ag = q' — q = —s q 

 (\—H)/(l —Hs) = —sq (\—H). Again, if u is the mutation rate from 

 the type gene A to dominant mutant A', there will be up' = u 

 (1 — H + \/ 2 H (1 +s)) new mutations. Equating the loss due to selection 

 and the gain due to new mutation, we obtain the approximate equi- 

 librium condition that could be written in various forms as follows: 

 S q = u , q = l/ 2 H = u\s, H = 2ujs, u = l/ 2 Hs. 

 When the mutant is dominant in its deleterious effect, the bal- 

 anced condition q = u/s is of the same form as that of gametic 

 selection. 



Table 2B gives the result of selection against the recessives. 

 The change in freqfrt) in one generation is 



q — Rs 

 Aq = q' — q = - - q = — s p R/w 



1 -Rs 



