Question

The forward mutation rate from allele Z to allele z is 0.00001 and the reverse mutation rate 0.0000001. What is the expected frequency of allele Z at mutational equilibrium?

Answer 1

Answer: let the frequency of Z be p

And the frequency of z be q

The rate of forward mutation (Z to z) be equal to ‘u’

u = 0.00001

the rate of backward mutation (z to Z) be equal ot ‘v’

v= 0.0000001

change in p is equal to subtracting loss from forward mutation i.e. ‘up’ from gain from reverse mutation i.e.’vq’

therefore change in p = vq –up (equation 1)

similarly change in q = up-vq

at equilibrium change in p is equal to change in q

change in p=0 and change in q=0

therefore vq-up = 0

but we know that p +q = 1, therefore q =1-p

Substituting this in above equation

v(1-p) –up = 0

therefore v-vp-up =0

therefore v= p(v+u)

therefore p= v/(v+u)

Substituting the values of mutation rate

p = 0.0000001/(0.0000001+0.00001)

p = 0.0000001/0.0000101

p = 0.0099

and q = 1-p = 1-0.0099 = 0.99(frequency of z allele at mutational equilibrium)

Hence the expected frequency of Z allele at mutational equilibrium is 0.0099