Q.A population is in genetic equilibrium/Hardy-Weinberg equilibrium for a gene with 2 alleles (dominant allele is 'A' and recessive allele 'a'). If the frequency of allele 'A' is 0·6, then the frequency of genotype 'Aa' is : (A) 0·21 (B) 0·42 (C) 0·48 (D) 0·32

The core idea here is the Hardy-Weinberg principle, which describes the genetic makeup of a population that is not evolving. It states that allele and genotype frequencies in a population remain constant from generation to generation in the absence of other evolutionary influences.

1. Let p be the frequency of the dominant allele 'A' and q be the frequency of the recessive allele 'a'.
2. We are given that the frequency of allele 'A' (p) is 0.6. …

The question asks us to find the frequency of the heterozygous genotype 'Aa' in a population that is in genetic equilibrium, also known as Hardy-Weinberg equilibrium. This concept is fundamental to population genetics, as it describes a theoretical state where allele and genotype frequencies remain constant from generation to generation in the absence of evolutionary influences.

Concept and Intuition

The Hardy-Weinberg principle is a mathematical model that describes how genetic variation is maintained in a population under specific ideal conditions. These conditions include:

1. No mutation
2. No gene flow (migration)
3. Random mating
4. No genetic drift (large population size)
5. No natural selection

When these conditions are met, the population is said to be in genetic equilibrium. For a gene with two alleles, typically denoted 'A' (dominant) and 'a' (recessive), we use specific symbols to represent their frequencies:

• Let p be the frequency of the dominant allele 'A'.
• Let q be the frequency of the recessive allele 'a'.

Since these are the only two alleles for this gene in the population, their frequencies must sum to 1:

This equation represents the allele frequencies in the gene pool.

When individuals in this population mate randomly, the probability of forming different genotypes can be predicted. Imagine drawing two alleles at random from the gene pool to form a diploid individual.

• The probability of drawing 'A' and 'A' (forming 'AA') is p × p = p^2.
• The probability of drawing 'a' and 'a' (forming 'aa') is q × q = q^2.
• The probability of drawing 'A' and 'a' (forming 'Aa') is p × q.
• The probability of drawing 'a' and 'A' (forming 'aA') is q × p. Since 'Aa' and 'aA' represent the same heterozygous genotype, the total frequency of heterozygotes is pq + qp = 2pq.

Therefore, the frequencies of the three possible genotypes in the population must also sum to 1:

Here:

• p^2 represents the frequency of the homozygous dominant genotype 'AA'.
• 2pq represents the frequency of the heterozygous genotype 'Aa'.
• q^2 represents the frequency of the homozygous recessive genotype 'aa'. …