114 I The Process of Evolution 



occurred in heterozygotes, while at loci not showing such over- 

 dominance they would be "all bad." ) 



Heterozygotes Inferior to Homozygotes 



When selection is against the heterozygotes, an unstable equilibrium 

 point exists at p = q = .50. Any deviation from this value leads to 

 extinction of the allele that is made less frequent by the deviation. 

 As shown by the values given in the discussion of selection against 

 recessive homozygotes (p. 107), the rarer an allele is, the larger is 

 the proportion of that allele in the heterozygotes. Therefore when 

 selection is against the heterozygotes, the less frequent allele is at a 

 disadvantage which increases as it becomes rarer. This means that 

 there is no tendency to return to the equilibrium point, once a 

 deviation has occurred; rather, the situation proceeds to fixation of 

 one allele or the other. 



MIGRATION AND POPULATION 

 STRUCTURE 



When a population is not completely isolated from other popula- 

 tions, its gene frequencies are subject to alteration through the in- 

 corporation of migrants which, as a group, have gene frequencies 

 deviating from that of the recipient population. At any locus the 

 change in gene frequency per generation is given by the expression 



Aq = -m(q - q,„) = -mq-]-mq,„ 



where m is the number of migrant individuals divided by the popu- 

 lation size of the recipient population, q is the gene frequency in the 

 recipient population, and q,„ is the gene frequency in the migrant 

 group. Manipulating the right-hand side of this equation by adding 

 and subtracting the quantity mq^q, we get 



—mq-\-mq,„q-^mq„, — mq„,q = —mq(l — q,„) -\-mq,„(l — q) 

 = —mq{p,„) -^mplq,,,) 



This final equation is in the same form as the expression for A^ in 

 the discussion of the action of mutation and back mutation (p. 101); 

 indeed, the situations are analogous. 



Figure 6.4 shows how the distribution of gene frequencies changes 

 with changes in m or N, where the gene frequency of the migrants 

 is .50. Diagrams such as Fig. 6.4 are known as stationary frequency 



