Balance between gain of homozygotes versus loss of heterozygotes with inbreeding

In the presence of inbreeding to the extent F, the frequency of homozygotes increases, and the frequency of heterozygotes decreases, as:

f(AA) = (1 - F)(p2)  +  Fp  

f(AB) = (1 - F)(2pq)    

f(BB) = (1 - F)(q2) + Fq


HOMEWORK: Show that the increased frequency of AA & BB homozygotes equals the decreased frequency of AB heterozygotes.
 

Text material © 2019 by Steven M. Carr