110 I The Process of Evolution 



Therefore, if SaP > Sgq, then Aq is positive and the frequency of a 

 is increasing, and if SaP < Saq, then Aq is negative and the frequency 

 of a is decreasing. When SaP = Saq, Aq = 0, and the frequency of a 

 is at equihbrium. In this situation, then, the equihbrium value of 

 q (q — "'q hat" ) is determined solely by the magnitude of the selec- 

 tion coefficients: 



SaP = Saq Sa{1 — q) — Saq = Sa — SAq — Saq = 



A . A A , . . A Sa 



Sa = SAq -{-Saq = q{SA-\-Sa) q = — ^r^ 



Sa -J- Sa 



Similarly, 



A Sa 



p = 



Sa + Sa 



If the adaptive values of the three genotypes remain constant, the 

 equilibrium value will also remain constant. If some incident, such 

 as the arrival of a group of migrant individuals, shifts the gene fre- 

 quency away from the equilibrium value, the selective forces will 

 restore the equilibrium. Therefore, we refer to this as a "stable" 

 equilibrium. 



Balanced Polymorphism and the Retention of Variability 



The selective system in which the heterozygotes are superior to 

 either homozygote results in the retention of both alleles in the 

 population rather than a trend toward fixation of one or the other. 

 A situation in which two or more forms of an organism persist in the 

 same population, with the rarest form in a frequency too high to be 

 accounted for by mutation alone, is known as pohjmorphism. When 

 heterozygotes are favored over homozygotes, the establishment of a 

 gene-frequency equilibrium creates a balanced polymorphism. This 

 type of polymorphism is important in evolution in part because it 

 permits a certain amount of variability to be retained in the popu- 

 lation. This means that the population may be able to react very 

 rapidly to an environmental change and thus avoid extinction. For 

 example, suppose that a certain locust living in a semiarid environ- 

 ment shows the following array of adaptive values at a locus: 

 BB, .50; Bb, 1.00; bb, .40. The heterozygotes are physiologically 

 superior to either homozygous type, and the BB nymphs are slightly 

 more resistant to desiccation than the bb nymphs. In such a popu- 

 lation the gene frequency would reach a stable equilibrium at 



^ ^ Si>^Sb ^ .60 +.50 ^ -^^^ 



