Consider a rare, recessive, deleterious
allele a
f(a) = q <<
1 & f(A) = p ~ 1
f(A
a)
= µ
mutation rate (# new mutant alleles /
gamete / generation)
The value of q is an equilibrium
between loss of a due to selection
& replacement of a by new mutation
change in f(a) due to selection:
qs=
-spq2 / (1 - sq2)
change in f(a) due to mutation:
qµ=
µp
Then
qs
+
qµ=
µp - spq2 / (1 -
sq2)
µp - spq2
[since (1 - sq2)
1 if q<<p ]
= p (µ - sq2)
At equilibrium (
)
:
q = 0 =
p (µ - s
2)
µ - s
2
[since p
1 ]
s
2 =µ
So
= (µ / s)(1/2)