The Theory of Population Genetics I 109 



Table 6.8 



Homozygotes Inferior to Heterozygotes 



As a final detailed example of selection models, consider the case 

 in which both homozygous genotypes are inferior (i.e., the locus 

 shows overdominance with respect to fitness) to the heterozygotes so 

 that 



Genotype AA 



Adaptive value 1— Sa 



Aa 

 1 



aa 



l—Sa 



The proportions after one generation of selection will then be 

 P~{1 — Sa) aa, 2pq Aa, and q-(l — Sa) aa out of a total of 

 1 — SaP~ — Saq-. The latter quantity, obtained by summing the 

 values for the three genotypes and simplifying, is thus 



f{l-s.,)-\-2pq-{-qHl-Sa) 



Since the initial gene frequency is qo = pq -^ q~, qi (the frequency 

 of a genes after one generation of selection) is 



pq + q-(l - Sa) _ pq ^ q~ - s^q- _ q - s^q^ 



1 - SaP'- - Saq- 1 - SaP'- - Saq- 1 - SaP'- - Saq'' 



Then the change in q per generation is 

 q - Saq- 



Aq = 



q - Saq- - q-h Sxp-q + S gq-jl 



q = i ' 



-P) 



1 - SaP- - Saq- ' J- - s.ip- - Saq 



-Saq- + SAp-q + Saq- - Sgpq- ^ pq ( SaP - Sgq ) 

 1 - SAp- - Saq- 1 - SaP- - Saq- 



