Calculate the frequencies of the genotypes in future generations if the initial

Question

Calculate the frequencies of the genotypes in future generations if the initial population consists of the following genotype frequencies:

0.7AA, 0.1Aa, and 0.2aa and meets the requirements of the Hardy–Weinberg relationship.

1. What will be the frequency of AA in the first generation?  

2. What will be the frequency of Aa in the first generation?  

3. What is the frequency of aa in the first generation?

4. What will be the frequency of AA in the second generation?  

5. What will be the frequency of Aa in the second generation?  

6. What will be the frequency of aa in the second generation?

Explanation / Answer

To find out genotype frequencies, we must employ the well know HW equation:

p^2+2pq+q^2=1

According to question in this population. 70% (0.7) have the AA genotype, 10% (0.1) the Aa genotype, and 20% (0.2) the aa genotype. This works out to around 7 (of 10) individuals possessing two AA alleles, 1 (of 10) individuals possessing both an A and "a" allele, and 2 (of 10) individuals possessing 2 aa alleles. From simple math, we can calculate that the frequency of A= 0.75, and the frequency of a = 0.25. We substitute these values into our equation.

Therefore, in the second generation:
p^2+2pq+q^2=1
(0.75)^2+2(0.75)(0.25)+(0.25)^2=1.

p^2 = frequency of homozygous AA genotype= 0.56
2pq = frequency of heterozygous Aa genotype = 0.38
q^2 = frequency of homozygous aa genotype = 0.06

Now thinking this abide HW relationship, mating is completely random. any time in any generation we would expect to end with the frequencies listed above.

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