Question

7) A rare dominant genetic disorder has an allele frequency of 0.00002. It is estimated to reduce the fitness of affected individuals by 50%. Under mutation-selection balance affecting a dominant, the mutation rate is predicted to be about half the equilibrium allele frequency, or 0.00001. We’ll assume this is the case here.

A) What is the frequency of affected individuals? (You could calculate an exact answer, but try getting a simple approximation using the fact that homozygotes for the mutant allele would be exceptionally rare, and the frequency of the wild-type allele is very close to 1)

B) Suppose a medical treatment for the disorder was developed that, although extremely expensive, allowed affected individuals to live normal lives. If everyone who needed it received the treatment, there would no longer be any selection against the mutant allele. What would be the allele frequency after 10 generations in this case? (You need your calculator for an exact answer, but you are encouraged to try to come up with a good approximation first, using your intuition and pencil and paper. Then check it with a calculator).

C) What would be the predicted frequency of affected individuals after 10 generations? How would this compare to the original frequency?

D) In your opinion, would the answer to (C) make you pause before recommending that the treatment be made available to anyone who needs it, at government expense? Why or why not?

Answer 1

Ans:

Answer 7A:)

Let, allele frequencies p and q, then due to the mutation, allele frequency should be like below:

P' = (p-p x u) x S

S is the selection.

Due to mutation the selection = 1- Fitness Fitness is 50% or 0.5.

Therefore, Selection = 0.5

P' is the new allele frequency and u is the mutation.

P' = (p- p x 0.00002) x S

If the allele frequency of wild type allele is close to 1 or supposing it is 1, the new allele frequency would be like below:

P' = (1- 0.00002) x 0.5

P' = 0.99998 x 0.5

P' = 0.49999

Answer 7B:) If persons are treated, then there would be no genetic loss of the allele frequency in the next generation. The next generation will have two alleles one is treated and the other one is wild type. And hence the next generation allele frequency would be =

P'2 = 0.49999 x 0.9

P'2 = 0.449991

Therefore, in each next generation, one wild type allele should cross with the previous allele.

Answer 7C:) Mutation after 10 generations = rate/generations Mutation after 10 generations = 0.00001/10 Mutation after 10 generations = 0.000001

After 10 generations, the allele frequency would be = Pt = (p0(1-u)t) x St

P' = 0.99999(1-0.00001)10 x 0.510

After 10 years, it would be nearly 0.

Answer 7D:) If people are suffering from a disease whether it is genetic, the government should provide them the treatment even on their cost. After 10 years, without treatment, the allele frequency would lose too much to an extent.