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Q.
A population is in Hardy- weinberg equilibrium for a gene
with only two alleles. If the gene frequency of an allele A is
$0.7$, the genotype frequency of $Aa$ is
Evolution
Solution:
For a gene with two alleles, $A$ (dominant) and $a$ (recessive), if the frequency of $A$ is $p$ and the frequency of $a$ is $q$, then the frequencies of the three possible genotypes ( $A A, A a$, and $a a$ ) can be expressed by the Hardy-Weinberg equation:
$p^2+2 p q+q^2=1$
where, $p^2=$ frequency of $A A$ (homozygous dominant) individuals, $2 p q=$ frequency of $Aa$ (heterozygous) individuals and $q^2=$ frequency of $a a$ (homozygous recessive) individuals. The equation can be used to calculate allele frequencies if the numbers of homozygous recessive individuals in the population is known.
Here, $p=0.7$ and $q=0.3$ (given)
$\therefore 2 p q$ (frequency of heterozygote)
$=2 \times 0.7 \times 0.3=0.42$