Question

4. In a population that is in Hardy-Weinberg equilibrium, 49% of the individuals are recessive homozygotes for a
certain trait. In a population of 14500, calculate the number of homozygous dominant individuals and
heterozygous individuals.
Choose the correct option.
(1) 6090, 7105
(2) 1305, 6090
(4) 7395, 6090
(3) 7105, 1305​

Answer 1

Answer:

The numbers of homozygous dominant individuals and heterozygous individuals are 1305 and 6090, respectively. So option (2) is the correct option.

To calculate the number of homozygous dominant individuals and heterozygous individuals, we must use the Hardy-Weinberg equation.

Explanation:

What is Hardy–Weinberg equilibrium in population genetics?

The Hardy–Weinberg equilibrium states that the genetic variation in a population will remain constant in the absence of disturbing influences.

What is the Hardy-Weinberg equation in population genetics?

The Hardy-Weinberg equation is the mathematical expression that is most commonly used to describe the genetic variation of a population at equilibrium. This equation is given below.

$p^{2} +2pq+q^{2} =1$

$p+q=1$

Here,

• p is the frequency of the dominant allele
• q is the frequency of the recessive allele
• $p^{2}$ is the frequency of homozygous dominant genotype
• $q^{2}$ is the frequency of recessive genotype
• 2pq is the frequency of heterozygous genotype

Given:

Percentage of recessive homozygotes = 49%

Total population = 14500

• Step 1. Calculate the frequency of the recessive allele:

Therefore, $q^2= 0.49$

Frequency of the recessive allele,

$q = \sqrt{0.49}\\q= 0.7$

• Step 2. Calculate the frequency of the dominant allele:

We know that, $p+q = 1$

Frequency of the dominant allele,

$p+0.7=1\\p=0.3$

• Step 3. Calculate the number of homozygous dominant individuals:

Frequency of homozygous dominant genotype,

$p^2 = (0.3)^2\\p^{2} =0.09$

Number of homozygous dominant individuals = Total population x frequency of homozygous dominant genotype

$= 0.09 \times 14500\\= 1305$

• Step 4. Calculate the number of heterozygous individuals:

Frequency of heterozygous genotype,

$2pq= 2 \times 0.7 \times0.3\\ 2pq= 0.42$

Number of heterozygous individuals = Total population x  frequency of heterozygous genotype

$=14500 \times0.42\\= 6090$

Therefore, the numbers of homozygous dominant individuals and heterozygous individuals are 1305 and 6090, respectively. So option (2) is the correct option.

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