Blood type and population genetics.?

Question

In a sample of individuals from the population of humans in LA the following blood type frequencies are observed: A=0.53, B=0.13, O=0.26. What are the allele frequencies, genotype frequencies, and phenotype frequencies in this sample population.

Please someone give me a way to start this. Hardy weinberg wont work.....

Answer 1

Use these Hardy-Weinberg equations for 3 alleles:

p + q + r = 1

p^2 + 2pq + 2pr + q^2 + 2qr + r^2 = 1

In the first equation,

p is the frequency of the A allele.

q is the frequency of the B allele

r is the frequency of the O allele.

In the second equation,

p^2 is the frequency of the AA genotype.

2pq is the frequency of the AB genotype.

2pr is the frequency of the AO genotype.

q^2 is the frequency of the BB genotype.

2qr is the frequency of the BO genotype.

r^2 is the frequency of the OO genotype.

You've been given the phenotype frequencies for blood types A (which can be from AA or AO), B (from BB or BO) and O (OO). Since p^2 represents AA and 2pr represents AO, you can replace (p^2 + 2pr) by 0.53 in the second equation. Similarly, you can replace (q^2 + 2qr) by 0.13 for the frequency of the B blood type, and you can replace r^2 by 0.26 for the O blood type. This gives you the equation:

0.53 + 2pq + 0.13 + 0.26 = 1

Now you can work out the frequency of the AB blood type, since 2pq represents the AB genotype.

So, 2pq = 0.08.

Before you can work out the genotype frequencies of AA, AO, BB and BO, you need to work out the allele frequencies of A, B and O. Work out the allele frequency of O first:

r = square root of O genotype frequency (0.26)

r = 0.51

To work out the frequency of the A allele:

p^2 + 2pr = 0.53

Substitute in r = 0.51.

Then use the quadratic equation to solve for p (representative of the A allele). Do this for q^2 + 2qr = 0.13 to work out the frequency of the B allele also. You should get:

p = A = 0.38

q = B = 0.11

and r = 0.51

Now you can work out the genotype frequencies you don't already know (AA, AO, BB, BO), using the second equation!

AA = p^2 = 0.14

AO = 2pr = 0.39

BB = q^2 = 0.01

BO = 2qr = 0.11

and

AB = 0.08 (worked out above)

OO = 0.26 (given in the question).

If you add all these up they should give 1, as shown by the second equation. They all add up to give 0.99, and the mistake is somewhere in the BB and BO genotype frequencies because they only add up to give 0.12, not 0.13 as they should. I can't find where I've made the mistake.

All of the phenotype frequencies have already been given to you, except for the AB phenotype frequency. This will just be the same as the AB genotype frequency, 0.08.