MUTATION-SELECTION BALANCE


Supposing there is selection against a deleterious allele. Eventually, it will be lost from the population. However, new deleterious alleles arise by mutation. This leads to a balance between what goes in:-
Mutation, 
and what goes out:-
Selection, s
Supposing we have a recessive deleterious allele, a:
Genotypes                          AA       Aa      aa
fitnesses                           1        1      1-s
frequency before selection         p2      2pq       q2
genotype freqs after selection     p2      2pq     q2(1-s), as before
and the mutation rate is given as 

The loss rate of awhen q is small (see selection and the single gene).

The gain rate of a because .

So, if mutation which produces a and selection which removes a are balanced, we have an equilibrium gene frequency, q* between mutation and selection, so that:

EXAMPLE: Tay Sachs, an autosomal recessive genetic disease in humans has a frequency (q2, assuming random mating) of about 2x10-6; assuming random mating, therefore, the frequency of the Tay-Sachs allele, q is about 1.4x10-3 . Tay-Sachs sufferers usually die within two years (). If this disease is at mutation-selection balance, we can estimate that the mutation rate, .

Some lethal or nearly lethal diseases (for example sickle-cell anaemia, especially among West Africans, or cystic fibrosis (q ~ 1/20 among Europeans) are rather common.  This implies that something else is going on, possibly SELECTION for the mutant alleles in heterozygotes?



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