Derivation of the Overdominance
case of the General Selection Model
Given:
genotype: AA
AB BB
phenotype: W0
< W1 > W2
or
1-s1
< 1 > 1-s2
Overdominance occurs
when fitness of the heterozygote is superior to that of either
homozygote. The result is that both alleles are maintained in the
population at an equilibrium frequency (
, read "q
hat", where 
q = 0) that
maximizes fitness. ["Overdominance" is an unfortunate term:
a superior AB phenotype cannot be said to be "dominant"
to either homozygote, as 'dominance' is a relationship
between alleles, and is unrelated to the relative 'value'
of the allele. Likewise the term 'underdominance' where AB
produces a phenotype inferior to either homozygote].
Recall from the numerator of the General Selection Equation that
q 
[(q)(W2 - W1)
+ (p)(W1 - W0)]
So, to find q at equilibrium () , we can
ignore the denominator and
set q = 0
= [(q)(1 - s2 - 1) + (p)(1 - 1 + s1)]
= -s2q + s1p
= s1(1
- q) - s2q
= s1 - s1q
- s2q
Then s1 = s1q
+ s2q = (q)(s1 + s2)
and
= (s1)/(s1 + s2)
Note
that for f(B) =, the numerator is the selection
coefficient associated with the alternative allele
A.
Homework: re-derive the above for "p" at
equilibrium