Li: MUTATION, SELECTION, AND POPULATION FITNESS 37 



Equating this loss to the gain through mutation, viz., p u id, we 

 obtain the equilibrium condition (in terms of the recessive propor- 

 tion in population) 



sR — u, or R — ujs. 



In populations with inbreeding, 



-F + y/F 2 + 4(l-F)u/s 

 R = (l-F)q 2 + F q = u/s, q = . - 



20 -F) 



In populations without inbreeding, 



R = q 2 = ujs, q = sjujs 

 The equilibrium value of q with inbreeding is always lower than 

 that without inbreeding. But, with mutation rate and selection 

 coefficient fixed, the recessive proportion in the population is the 

 same, with or without inbreeding. The equilibrium condition 

 R = ujs is stable. 



III. Selectional Balance 

 D. General Formula 



The second broad category of equilibrium is that maintained 

 by selectional forces alone, without introducing new mutations into 

 the population each generation. Referring to the general procedure 

 outlined in Table 2, we see that equilibrium will be achieved when 

 the new gene frequencies (p' and q') after selection are equal to the 

 old ones (p and q) before selection. Substituting D = p- + Fpq, etc. 

 (Table 1) in the equation q' = q and simplifying, we obtain the 

 equilibrium condition (11) 



(\ — F) (w 2 — u'i) + F(w 3 — u'i) 

 q = 



(1 -F)[(w 2 -w 1 ) + (w 2 -w 9 )] 

 That is, when q assumes the value indicated above, the differen- 

 tial selective fitness of the genotypes does not change the gene fre- 

 quencies. In other words, the population remains the same inspite 

 of the selective operation. Note that when W\ — iv 3 , the equilibrium 

 condition is q = i/ 2 , with or without inbreeding. 



In order to make q a positive fraction in the expression above, the 

 quantities w 2 — w^ and w 2 — w 3 must be both positive (w 2 >Wi and w 2 > 

 w 3 ) or both negative and the inbreeding coefficient F not too high (see 



