A large population of beetles has 396 red individuals and 557 tan individuals. R

Question

A large population of beetles has 396 red individuals and 557 tan individuals. Red is recessive.

Calculate the following:
The frequency of the “A” allele: __________
The frequency of the “a” allele: : __________
The frequency of the homozygous dominant genotype: __________
The frequency of the homozygous recessive genotype: __________
The frequency of the heterozygous genotype: __________
The frequency of the dominant phenotype: __________
The frequency of the recessive phenotype: __________
The number of individuals who are heterozygous: __________

Assume that conditions are good, and in the following generation, there are now a total of 1,245 beetles. Hardy-Weinberg Equilibrium is in effect. Predict the following:

How many individuals in generation 2 will be red? __________
How many individuals in generation 2 will be tan? __________

Explanation / Answer

This problem is based on Hardy- Weinberg equation. As per this law, the allelic frequency in a given population remains constant from generation to generation.

To solve these questions lets consider "A" as the dominant allele for tan phenotype and "a" as the recessive allele for the phenotype red.

Two formulas are used for the calculation of allelic frequency. They are

p + q = 1 and p2 + q2 + 2pq = 1

where,

p = allelic frequency of the dominant allele

q = allelic frequency of the recessive allele

p2 = percentage of dominant individuals in a given population

q2 = percentage if recessive individuals in a given population

2pq = percentage of heterozygous individuals in a given population.

1. Now let us solve the first question The frequency of the "A" alleleT

Total number of beetles in the given populations is 396 + 557 = 953

To calculate the frequency of the dominant allele, first, we have to find out the percentage of red individuals in the given population. This is calculated as follows:

396/953 = 0.41 or 41%. We will use 0.41 for further calculation.

As I mentioned earlier "q2" is the percentage of recessive individuals.

So, in this case q2 = a2 = 0.41.

To find out the allelic frequency of recessive allele, we have to do the following calculation

a2 = 0.41

a = 0.41 = 0.645

So, based on the above calculation, the frequency of the recessive allele is 0.645

Now the frequency of dominant allele can be calculated as follows:

p + q = 1. In this case, it will be A + a = 1

By substitution, we get

A + 0.645 = 1

A = 1 - 0.645

A = 0.355

So, the answer to the first question The frequency of the "A" allele is 0.355

2. From the above calculation, the answer to the question The frequency of "a" allele is 0.645

3. The frequency of homozygous dominant genotype will be AA = A2 = (0.355)2 = 0.126

4. The frequency of homozygous recessive genotype will be aa = a2 = (0.645)2 = 0.416

5. The frequency of heterozygous genotype will be 2Aa = 2 X 0.345 X 0.645 = 0.458

6. The frequency of dominant phenotype

Dominant phenotype comprises two genotypes. They are AA and Aa.

So the frequency of dominant phenotype = frequency of dominant allele A + frequency of heterozygous dominant allele Aa

= 0.126 + 0.458

= 0.584

So, the answer to this question is 0.584

7. The frequency of recessive phenotype is 0.416 which is obtained from the first question.

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