Question

I really want to understand this, please help step by step

Cystic fibrosis is a Mendelian recessive disease of humans caused by defects in ion transport (OMIM 602421). Until the 1950's when antibiotics were first used to treat CF patients, most newborns with CF died at an early age. Yet CF is relatively common in Caucasians, with a frequency of an allele that is lethal to homozygotes. There is no agreement on the reason for this high frequency.

a) Suppose that an allele that causes CF is maintained by mutation-selection balance. What would be the mutation rate necessary for that allele to have a frequency of 0.02?

b)Suppose that an allele that causes CF is maintained by heterozygote advantage. In order for the equilibrium frequency to be 0.02, what would the difference between the viabilities of the homozygote and the heterozygote have to be?

Answer 1

a) Lets assume the selection rate for the deleterious mutation, s = 0.1

Mutation rate, u =?

q*= 0.02

q* =sqrt(u/s) - from mutation selection balance

u=0.00004

b) lets say the viabilities are v1 and v2.

At equilibrium pv1=qv2 and p+q=1

so,q*=v1/(v1+v2)

q* =0.02

2/100= v1/(v1+v2)

reciprocating 50=1+(v2/v1)

=v2/v1=49