Question

In a random mating population frequency of recessive gene is 0.5, then what is the frequency of dominant phenotypes in population?

• A. 0.25
• B. .50
• C. 0.20
• D. 0.75

Answer 1

Answer: (D)

0.75

Answer 2

The problem can be solved using the Hardy-Weinberg principle, which describes the genetic equilibrium in a population.

Hardy-Weinberg Principle Formulas:

1. Allele Frequencies: $p + q = 1$
   • $p$ = frequency of the dominant allele
   • $q$ = frequency of the recessive allele
2. Genotype Frequencies: $p^2 + 2pq + q^2 = 1$
   • $p^2$ = frequency of homozygous dominant genotype
   • $2pq$ = frequency of heterozygous genotype
   • $q^2$ = frequency of homozygous recessive genotype

Given Information:

• Frequency of recessive gene (allele), $q = 0.5$

To Find:

• Frequency of dominant phenotypes in the population.

Step-by-step Solution:

1. Calculate the frequency of the dominant allele ($p$): Using the allele frequency equation: $p + q = 1$ $p + 0.5 = 1$ $p = 1 - 0.5$ $p = 0.5$

2. Identify genotypes contributing to the dominant phenotype: Individuals showing the dominant phenotype have either the homozygous dominant genotype ($AA$ or $p^2$) or the heterozygous genotype ($Aa$ or $2pq$).

3. Calculate the frequency of dominant phenotypes: The frequency of dominant phenotypes is the sum of the frequencies of the homozygous dominant and heterozygous genotypes: Frequency of dominant phenotypes = $p^2 + 2pq$

   Substitute the values of $p$ and $q$: $p^2 = (0.5)^2 = 0.25$ $2pq = 2 \times (0.5) \times (0.5) = 2 \times 0.25 = 0.50$

   Frequency of dominant phenotypes = $0.25 + 0.50 = 0.75$

   Alternatively: The total frequency of all genotypes in the population is 1. The frequency of the recessive phenotype is $q^2$. Frequency of recessive phenotypes = $q^2 = (0.5)^2 = 0.25$

   Since the population consists of dominant and recessive phenotypes, the frequency of dominant phenotypes can also be calculated as: Frequency of dominant phenotypes = $1 - \text{Frequency of recessive phenotypes}$ Frequency of dominant phenotypes = $1 - q^2$ Frequency of dominant phenotypes = $1 - 0.25 = 0.75$

Therefore, the frequency of dominant phenotypes in the population is 0.75.