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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 1-F 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 (1-F) p2 of AA

                                                             (1-F) 2pq of Aa

                                                         (1-F) q2 of aa

Hence in total             AA = F p + (1-F) p2

                            Aa = (1-F) 2pq

                                   aa = F q + (1-F) q2



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