Explain the Hardy-Weinberg law of genetic equilibrium and give its algebraic expression. At a locus with a dominant and a recessive allele in Hardy-Weinberg equilibrium, 16% of the individuals are homozygous for the recessive allele. What is the frequency of the dominant allele in the population? (IFS 2019, 15 Marks)

Introduction

The Hardy-Weinberg law of genetic equilibrium is a fundamental principle in population genetics that describes the relationship between allele frequencies and genotype frequencies in a population that is not evolving. It states that in a large, randomly mating population with no selection, mutation, migration, or genetic drift, the frequencies of alleles and genotypes will remain constant from generation to generation.

Hardy-Weinberg Law of Genetic Equilibrium.

• Conditions for Hardy-Weinberg Equilibrium:
  
  • No mutation occurs.
  • No migration or gene flow occurs.
  • The population is large (no genetic drift).
  • Mating is random (no sexual selection).
  • No natural selection affects the alleles.

Algebraic Expression of the Hardy-Weinberg Law

The Hardy-Weinberg equilibrium is expressed algebraically using the following formula:

• p² + 2pq + q² = 1

Where:

• p is the frequency of the dominant allele (A).
• q is the frequency of the recessive allele (a).
• p² represents the frequency of homozygous dominant individuals (AA).
• 2pq represents the frequency of heterozygous individuals (Aa).
• q² represents the frequency of homozygous recessive individuals (aa).

Problem Analysis

Given:

• 16% of individuals are homozygous recessive (aa). This means that q² = 0.16.
• We need to find the frequency of the dominant allele p.

Solution

• Determine q (frequency of recessive allele):
  
  • Since q² = 0.16, we take the square root to find q.
  • q = 0.16 = 0.4q 
• Find p (frequency of dominant allele):
  
  • We know that p + q = 1 (since the total allele frequency in the population is 1).
  • So, p = 1− q = 1 − 0.4 = 0.6 

Conclusion

The frequency of the dominant allele in the population is 0.6. This calculation demonstrates the application of the Hardy-Weinberg law in determining allele frequencies in a population under genetic equilibrium.