Consider a rare, recessive,
deleterious
allele a
f(a) = q
<<
1 & f(A) = p ~ 1
f(Aa)
= 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 - s2)
µ - s2
[since p 1 ]
s2 =µ
So
= (µ / s)(1/2)