Hardy Weinberg’s Principle

Hardy–Weinberg's principle states that allele frequencies in a population are stable and constant from generation to generation in the absence of evolutionary forces.

• The total collection of all genes and their alleles in a population is called the gene pool.
• The gene pool remains constant across generations — this condition is termed genetic equilibrium.
• The sum total of all allelic frequencies is always 1.
• Evolution, in operational terms, is any change in allele frequency in a population over time.
• A population in Hardy–Weinberg equilibrium is therefore a non-evolving population.
• Also referred to as Hardy–Weinberg equilibrium law.

Notation

Let:

• p = frequency of dominant allele A
• q = frequency of recessive allele a

Allele Frequency Equation

Since A and a are the only alleles at the locus:

p + q = 1

Hardy–Weinberg Equation (Genotype Frequencies):

This is the binomial expansion of (p + q)²:

p² + 2pq + q² = 1

The probability that allele A (frequency p) appears on both chromosomes of a diploid individual = p × p = p². Similarly, q² for aa, and 2pq for Aa.

The equation is derived by considering all possible gamete combinations in a randomly mating population:

Total: p² + pq + pq + q² = p² + 2pq + q² = 1

Like allele frequencies, genotypic frequencies together also equal 1:

AA + 2Aa + aa = 1

All five conditions must be simultaneously satisfied:

1. Very large (infinitely large) population size - Eliminates random fluctuations in allele frequency.
2. Random mating - Every organism has an equal chance to mate with any other, with no preference for a particular genotype.
3. No mutation - No new alleles are generated by mutation; no genes are duplicated or deleted.
4. No gene flow - Neither individuals nor their gametes enter (immigration) or leave (emigration) the population.
5. No natural selection - All alleles are equally fit to survive and reproduce.

If any one of these conditions is not met, the population will not be in Hardy–Weinberg equilibrium and evolution will occur.

• Hardy–Weinberg principle provides a mathematical model of how genetic equilibrium can be maintained in a gene pool.
• It shows that a large proportion of recessive alleles in a population exist in carrier heterozygotes (2pq), not in homozygous recessive individuals (q²).
• The heterozygous genotype maintains a substantial potential source of genetic variability.
• Only alleles present in homozygous recessive organisms are expressed in the phenotype and thus exposed to environmental selection and possible elimination.
• Changes in allele frequency are the raw material of evolution; departures from equilibrium expose selection pressures operating on the population.
• When frequency measured differs from expected values, the direction of difference indicates the extent of evolutionary change.

Given: A large population of beetles. Allele 'A' determines colour.

• AA and Aa beetles are dark grey; aa beetles are light grey.
• Frequency of 'A' allele: p = 0.3
• Frequency of 'a' allele: q = 0.7
• Verify: p + q = 0.3 + 0.7 = 1

Step 1: Apply the Hardy–Weinberg equation:

(p + q)² = p² + 2pq + q²

Step 2: Calculate each genotype frequency:

Step 3: Verify: 0.09 + 0.42 + 0.49 =1

Interpretation: When beetles in this equilibrium reproduce, allele and genotype frequencies in the next generation remain the same (9% AA, 42% Aa, 49% aa), confirming no evolution has occurred.

• Gene migration or gene flow changes allele frequencies in both old and new populations.
• Genetic drift causes a change in allele frequency by chance, especially in a new sample of a population.
• A mutation introduces changes in genes and alleles.
• Genetic recombination contributes to variation in future generations.
• Natural selection alters frequencies by favouring heritable variations that improve survival and reproduction.
• The founder effect occurs when a drifted original population becomes the founders of a new population.

When migration of a section of population occurs repeatedly (gene flow), and the change in allele frequency in the new population is so marked that they become a different species - the original drifted population becomes founders and the effect is called the founder effect.

Natural Selection: Three Outcomes

Natural selection can lead to:

1. Stabilisation - More individuals acquire the mean character value.
2. Directional change - More individuals acquire a value other than the mean character value.
3. Disruption - More individuals acquire peripheral character values at both ends of the distribution curve.

Diagrammatic representation of the operation of natural selection on different traits: (a) Stabilising (b) Directional and (c) Disruptive

• Hardy–Weinberg’s principle states that allele frequencies in a population remain constant from generation to generation in the absence of evolutionary forces.
• The total collection of all alleles in a population is called the gene pool.
• Genetic equilibrium means no change in allele frequencies over time.
• If p is the frequency of dominant allele and q is the frequency of recessive allele, then
  p + q = 1.
• Genotype frequencies are expressed as:
  p² (AA) + 2pq (Aa) + q² (aa) = 1.
• Any deviation from Hardy–Weinberg equilibrium indicates that evolution is occurring.
• The principle helps in detecting the role of natural selection and other evolutionary forces.