Dq = qn+1
- q n
Dq = [(1 - s)*q
n]/[1 - s*q n] - q n
(Substituted the equation of qn+1 for qn+1.)
Dq = [(1 - s)*q
n - (1 - s*q n)*q n] / [1 - s*q n]
(Brought q into the fraction by cross multiplication.)
Dq = [q n
- s*q n - q n - s*q n *q n]
/ [ 1 - s*q n]
Dq = [-s*q n
-s*q n *q n]/ [1 - s*q n]
Dq = -s*(q n
- q n *q n) / [ 1 - s*q n]
Dq = -s*q n
*(1 - q n) / [ 1 - s*q n]
Because p n + q n = 1, 1 -
q n = p n; therefor:
Dq = -s*p n *q n /[ 1 - s*q n]
Summary : The change in q due to 1 generation of selection is called
delta q (Dq) is given by the equation:
Dq = -s*p n *q
n /[ 1 - s*q n]
where s is the selection coefficient, p n is the frequency
of the more fit (increasing) allele, and q n is frequency of
the less fit (decreasing) allele.