What is Hardy-Weinberg's law? Give examples to establish its validity and limitations.

The Hardy-Weinberg Law: A Detailed Explanation

The Hardy-Weinberg equilibrium is based on several key assumptions:

• No mutation: The rate of mutation must be negligible.
• Random mating: Individuals must mate randomly, without any preference for certain genotypes.
• No gene flow: There should be no migration of individuals into or out of the population.
• No genetic drift: The population must be large enough to avoid random fluctuations in allele frequencies.
• No natural selection: All genotypes must have equal survival and reproductive rates.

Mathematically, the Hardy-Weinberg principle is expressed by two equations:

p + q = 1, where:

• p = frequency of the dominant allele
• q = frequency of the recessive allele

and

p² + 2pq + q² = 1, where:

• p² = frequency of the homozygous dominant genotype
• 2pq = frequency of the heterozygous genotype
• q² = frequency of the homozygous recessive genotype

Establishing Validity: Examples

While perfectly adhering to all assumptions is rare in natural populations, certain scenarios approximate Hardy-Weinberg equilibrium. Consider a hypothetical population of butterflies where wing color is determined by a single gene with two alleles: B (black) and b (white). If the population meets the Hardy-Weinberg assumptions, and we observe that the frequency of the 'b' allele (q) is 0.2, then:

• The frequency of the 'B' allele (p) would be 1 - q = 0.8
• The expected genotype frequencies would be:
• BB (p²) = 0.64
• Bb (2pq) = 0.32
• bb (q²) = 0.04

If, upon sampling the population, the observed genotype frequencies closely match these expected frequencies, it supports the validity of the Hardy-Weinberg principle in this case. Another example is in populations exhibiting balanced polymorphism, where heterozygotes have a selective advantage, maintaining both alleles in the population.

Limitations: Factors Disrupting Equilibrium

In reality, populations rarely meet all the assumptions of the Hardy-Weinberg principle. Several factors can disrupt the equilibrium, leading to evolutionary change:

• Mutation: Introduces new alleles, altering allele frequencies.
• Gene Flow (Migration): Can introduce or remove alleles, changing allele frequencies. For example, pollen flow between different plant populations.
• Genetic Drift: Random fluctuations in allele frequencies, particularly significant in small populations. The founder effect and bottleneck effect are examples of genetic drift.
• Non-random mating: Assortative mating (individuals with similar phenotypes mate more frequently) and inbreeding can alter genotype frequencies.
• Natural Selection: Differential survival and reproduction of genotypes, leading to changes in allele frequencies. Sickle cell anemia provides a classic example of balancing selection.

The following table summarizes the factors disrupting Hardy-Weinberg equilibrium and their effects:

Disrupting Factor	Effect on Allele/Genotype Frequencies
Mutation	Introduces new alleles, alters existing frequencies
Gene Flow	Homogenizes allele frequencies across populations
Genetic Drift	Randomly alters allele frequencies, especially in small populations
Non-random Mating	Alters genotype frequencies, but not allele frequencies
Natural Selection	Increases frequency of beneficial alleles, decreases frequency of detrimental alleles