Biology 334
Proof of the inbreeding equilibrium formula
Use the following thought experiment:
“Assume the population is divided into 2 parts
A proportion F exclusively selfs
A proportion 1F mates randomly.”
Among the selfers, we know that eventually there will be only homozygotes: a proportion p of AA and q of aa.
Among the random maters there will be p2 AA, 2pq Aa and q2 of aa.
Therefore there will be
From the selfers F p of AA and F q of aa.
From the outbreeders there will be (1F) p2 of AA
(1F) 2pq of Aa
(1F) q2 of aa
Hence in total AA = F p + (1F) p2
Aa = (1F) 2pq
aa = F q + (1F) q2
