The forward mutation rate for an allele is 43x105 mutationsg

The forward mutation rate for an allele is 4.3x10^-5 mutations/generations and back mutation occurs at a rate of 6.7x10^-7 mutations/generations. Assume that the frequency of the variant allele starts at 0.05.
   (a) What is the expected allele frequency after one generation?
   (b) What is the expected allele frequency after two generations?
   (c) What is the expecred equilibrium allele frequency? Does this depend on initial allele frequency?

Solution

Answer a) we are given that the variant allele frequency (say q) is 0.05, so the frequency of wild type allele will be 0.095 (p = 1-q).

and we have a forward mutation rate (u; from A to a allele) = 4.3 x 10^-5 and reverse mutation rate (v; from a to A allele) = 6.7x10^-7

we have a formula for calculating the change in allele frequency of variant allele as q₁ = q_o + mp_o - nq_o,

where mp denotes the fraction of allele which changes from A to a and nq denotes the fraction of allele which reverted to a from A. and p_o = frequency of wild type allele in parental generation q_o = frequency of variant allele in parental generation and q₁ = frequency of variant allele in next generation.

so q₁ = 0.05 + 4.3x10^-5 (0.95) - 6.7x10^-7 (0.05)

= 0.05 + 4.085x10^-5 - 0.335x10^-7

= 0.05 + 10^-5 (4.085- 0.00335)

= 0.05 + 10^-5 (4.08 2)

= 0.05 + 0.00004

= 0.05004

so, the expected frequency of variant allele after one generation will be 0.05004

Answer b) Similarly solve the allele frequency for second generation.

here, the parental allele frequencies will be allele frequencies obtained after one generation.4

if q₁ = 0.05004, so p₁ =.94996

and the formula will be rewritten as q₂ = q₂ + up₁ - vq₁

now solve this as following;

q₂ = 0.05004 + 4.3x10^-5 (0.94996) - 6.7x10^-7 (0.05004)

= 0.05004 + 4.0848x10^-5 - 0.3352x10^-7

= 0.05004 + 10^-5(4.0848 - 0.0033)

= 0.05004 + 10^-5(4.0815)

= 0.05004 + 0.00004

= 0.05008

hence, the expected variant allele frequency after two generations will be 0.05008

Answer C) We have a formula that expected allele frequency at equilibrium will be p = v/u+v

p = 6.7x10^-7 / 4.3x10^-5 + 6.7x10^-7

= 6.7x10^-7 / 10^-7(6.7+430)

= 6.7x10^-7/436.7x10^-7

= 0.015

and q = 1-0.015 =0.985, this is because the rate of forward mutation is much higher than the rate of reverse mutation. and this is nowhere related to the initial allele frequency but is related to the prevalence/rate of forward and reverse mutations.