Question

Explain the Hardy-Weinberg principle with the help of an algebric equation.

Hint:

Allele frequencies stay the same in every generation if nothing disturbs the gene pool, as shown by p^2 + 2pq + q^2 = 1.

Answer 1

Step 1: State the principle:
The Hardy-Weinberg principle says that allele and genotype frequencies in a population stay constant from one generation to the next.
This holds only when the population is not disturbed, so the gene pool is stable. This is called genetic equilibrium.

Step 2: Write the equation:
Let \( p \) be the frequency of allele \( A \) and \( q \) the frequency of allele \( a \) in a diploid population.
The alleles of a gene together make up the whole gene pool, so \( p + q = 1 \).
Random mating gives the genotype frequencies by squaring the sum.
\[ (p + q)^2 = p^2 + 2pq + q^2 = 1 \]
Here \( p^2 \) is the frequency of \( AA \), \( 2pq \) of \( Aa \) and \( q^2 \) of \( aa \).

Step 3: Factors that disturb equilibrium:
The frequencies change if there is gene migration (gene flow), genetic drift, mutation, genetic recombination or natural selection.
A change in allele frequency over generations means evolution is taking place.

Final Answer:
Allele frequencies stay constant across generations if nothing disturbs the gene pool: \( p^2 + 2pq + q^2 = 1 \), where \( p + q = 1 \). A departure from this shows evolution.