Zoology · Evolution

Hardy–Weinberg Principle

The Hardy–Weinberg principle is the algebraic null hypothesis of population genetics. It predicts that, in an idealised population, allele and genotype frequencies stay constant generation after generation — a state called genetic equilibrium. Any observed deviation from p² + 2pq + q² = 1 is read as evidence of evolution. Sitting in NCERT §6.7, the topic supplies at least one direct NEET question almost every alternate year, and the five disturbing factors are textbook fodder for one-line MCQs.

NCERT grounding

NCERT Class 12 Biology, Chapter 6 (Evolution), §6.7, fixes the syllabus boundary. The book states that allele frequencies in a population are stable and constant from generation to generation, calls this state genetic equilibrium, and identifies the gene pool as the total of all genes and their alleles in a population. NIOS Lesson 1, §1.2.5, supplements this with the term panmictic population — a sexually reproducing population in which mating is random — and credits the principle to G. H. Hardy and W. Weinberg working independently in 1908.

"Allele frequencies in a population are stable and constant from generation to generation. The gene pool remains a constant. This is called genetic equilibrium."

NCERT Class 12, Chapter 6, §6.7

The principle and its equation

Consider one autosomal locus in a sexually reproducing diploid population with two alleles: A (dominant) at frequency p and a (recessive) at frequency q. Because every allele in the population must be either A or a, the two frequencies must sum to one:

p + q = 1

Allele-frequency identity

The sum of all allelic frequencies at a locus is always 1. For two alleles this gives q = 1 − p, a step NEET problems demand before squaring.

Now ask: under random mating, with what probability do two A alleles meet in a zygote? Each gamete carries an A with probability p. Sampling two gametes independently, the probability of an AA zygote is p × p = . The probability of an aa zygote is q × q = . A heterozygote Aa can arise in two ways — an A egg meeting an a sperm (p × q) or an a egg meeting an A sperm (q × p) — giving a combined probability of 2pq. The three genotype frequencies must again exhaust the population:

p² + 2pq + q² = 1 (p + q)²

Hardy–Weinberg expansion

The genotype frequencies are simply the binomial expansion of (p + q)². NCERT highlights this explicitly: "This is a binomial expansion of (p + q)²."

Figure 1 Allele × allele combination producing p² + 2pq + q² How (p + q)² generates the three genotype frequencies SPERM EGG A (p) a (q) A (p) a (q) AA Aa pq Aa qp aa SUM AA: Aa: pq + qp = 2pq aa: Total = p² + 2pq + q² = 1

Figure 1. Random union of gametes treats A and a as samples drawn with probabilities p and q. The four cells partition the offspring gene pool into the three genotype classes, recovering Hardy–Weinberg's algebra.

Reading the equation backwards

Most NEET problems give you one observable — typically the frequency of the recessive phenotype — and demand the rest. Because aa is the only genotype that displays the recessive phenotype (AA and Aa share the dominant phenotype), the trick is to set the observed recessive frequency equal to q², take the square root to recover q, and then back-fill p, p², and 2pq. This single workflow handles the 2019 PYQ, the standard sickle-cell carrier estimate, and any "X% albinos — what fraction are carriers?" question the examiner can write.

Five assumptions of equilibrium

Hardy–Weinberg's prediction holds only when an idealised set of conditions is met. Memorise these as a checklist — every NEET trap is built by flipping exactly one of them.

Large population

Effectively infinite size so sampling chance is negligible.

Violation → genetic drift.

Random mating

Population is panmictic — no genotype-based mate choice.

Violation → assortative mating skews 2pq.

No mutation

No new alleles A→a or a→A created.

Violation → mutation adds raw variation.

No gene flow

No migration in or out of the population.

Violation → allele frequencies shift in both donor and recipient.

No selection

All genotypes have equal fitness; survival and reproduction are independent of genotype.

Violation → favoured alleles rise in frequency.

When all five assumptions are met simultaneously, the gene pool is locked in place and the population is, by definition, not evolving. This is the inverted way population geneticists define evolution: any allele-frequency change across generations is microevolution. NCERT writes it bluntly — "Disturbance in genetic equilibrium, or Hardy–Weinberg equilibrium, i.e. change of frequency of alleles in a population would then be interpreted as resulting in evolution."

Five factors that disturb equilibrium

NCERT names five forces capable of changing allele frequencies, and the NEET 2024 paper directly asked students to identify the one that does not disturb equilibrium. Lock the list down.

  1. 01

    Gene migration / gene flow

    Movement of individuals between populations transfers alleles. Repeated migration = gene flow.

  2. 02

    Genetic drift

    Random change in allele frequency in small populations. Sub-cases: founder effect, bottleneck effect.

  3. 03

    Mutation

    Heritable change in DNA introduces a new allele. Rate ≈ 10⁻⁵–10⁻⁸ per locus per generation.

  4. 04

    Genetic recombination

    Crossing-over during gametogenesis shuffles existing alleles into new combinations.

  5. 05

    Natural selection

    Differential reproductive success of genotypes. Outcomes: stabilising, directional, disruptive.

How each factor moves the algebra

Drift vs. selection — both change p, but for different reasons

Genetic drift

Random

non-directional

  • Allele-frequency change due to sampling error.
  • Strongest in small populations.
  • Can fix or lose alleles even if neutral.
  • Founder & bottleneck effects are special cases.
VS

Natural selection

Directional

fitness-driven

  • Allele-frequency change due to differential fitness.
  • Operates in populations of any size.
  • Tends to increase fit alleles, decrease unfit ones.
  • Three modes: stabilising, directional, disruptive.

Genetic drift: founder & bottleneck

Two well-named sub-cases of drift sit on the high-yield list. NEET 2021 directly asked which factor produces the founder effect — the answer is genetic drift, not selection or recombination.

Figure 2 Founder effect vs. bottleneck effect Founder effect Bottleneck effect Source population few founders disperse New colony (skewed gene pool) Before catastrophe disaster / epidemic Survivors (skewed gene pool)

Figure 2. Both founder and bottleneck effects are forms of genetic drift, but the trigger differs. Founder effect — a small group leaves the parent population. Bottleneck effect — a large population is reduced in place. In both, the post-event gene pool is a non-random sample of the original.

NCERT closes the discussion with a striking line: "Sometimes the change in allele frequency is so different in the new sample of population that they become a different species. The original drifted population becomes founders and the effect is called founder effect." Drift can therefore, in principle, drive speciation without any role for selection — a key point because students reflexively credit speciation to natural selection alone.

Worked examples

Worked example 1

Q. A gene locus has two alleles A and a. If the frequency of dominant allele A is 0.4, what are the frequencies of homozygous dominant, heterozygous and homozygous recessive individuals?

Solution. Given p(A) = 0.4, so q(a) = 1 − 0.4 = 0.6. Apply p² + 2pq + q² = 1. AA frequency = p² = (0.4)² = 0.16. Aa frequency = 2pq = 2 × 0.4 × 0.6 = 0.48. aa frequency = q² = (0.6)² = 0.36. Check: 0.16 + 0.48 + 0.36 = 1.00. This is the exact algebra of NEET 2019 Q.61.

Worked example 2

Q. In a population of 10,000, 1% express a recessive phenotype (e.g. an autosomal recessive disorder). Assuming Hardy–Weinberg equilibrium, how many heterozygous carriers exist?

Solution. The recessive phenotype is shown only by aa, so q² = 0.01. Therefore q = √0.01 = 0.1, and p = 1 − 0.1 = 0.9. Carrier (heterozygote) frequency = 2pq = 2 × 0.9 × 0.1 = 0.18. In a population of 10,000, expected carriers = 0.18 × 10,000 = 1,800 individuals. Notice the asymmetry: 100 affected, but eighteen times that number silently carry the allele — the standard "hidden reservoir" argument used in medical-genetics MCQs.

Worked example 3

Q. A bird population is in Hardy–Weinberg equilibrium for a wing-colour locus with q = 0.3. A storm wipes out 80% of the population at random. Predict the new q immediately after the storm and explain.

Solution. If the kill is genuinely random with respect to genotype, the expected q remains 0.3 — selection has not acted. But because the population has been bottlenecked to a small size, the observed q in the survivors will deviate from 0.3 by sampling chance. This is the bottleneck effect, a form of genetic drift. The smaller the surviving population, the larger the expected deviation — and the alleles that happen to be over-represented may even be neutral or mildly deleterious.

Worked example 4

Q. In a Hardy–Weinberg population the frequency of heterozygotes is 0.42. What is the maximum possible value of 2pq, and at what allele frequencies is it attained?

Solution. The function 2pq with p + q = 1 reaches its maximum when p = q = 0.5, giving 2pq = 2 × 0.5 × 0.5 = 0.5. So at most half the population can be heterozygous at a two-allele locus. The given 0.42 is achievable; setting 2p(1 − p) = 0.42 gives p² − p + 0.21 = 0, with p ≈ 0.7 or p ≈ 0.3 — both valid solutions, mirror images of each other.

Common confusion & NEET traps

NEET PYQ Snapshot — Hardy–Weinberg Principle

Direct questions on the principle, its equation, and its disturbing factors — NEET 2019, 2021, 2024.

NEET 2024

Which one of the following factors will not affect the Hardy–Weinberg equilibrium?

  1. Genetic recombination
  2. Genetic drift
  3. Gene migration
  4. Constant gene pool
Answer: (4)

Why: The five factors that disturb equilibrium are gene migration, drift, mutation, recombination and selection. A "constant gene pool" describes the equilibrium itself, not a force that perturbs it.

NEET 2021

The factor that leads to founder effect in a population is:

  1. Genetic drift
  2. Natural selection
  3. Genetic recombination
  4. Mutation
Answer: (1)

Why: The founder effect is the change in allele frequency that occurs when a few individuals colonise a new area. Because the founders are a small random sample of the parent gene pool, this is a special case of genetic drift.

NEET 2019

A gene locus has two alleles A, a. If the frequency of dominant allele A is 0.4, then what will be the frequency of homozygous dominant, heterozygous and homozygous recessive individuals in the population?

  1. 0.36(AA); 0.48(Aa); 0.16(aa)
  2. 0.16(AA); 0.24(Aa); 0.36(aa)
  3. 0.16(AA); 0.48(Aa); 0.36(aa)
  4. 0.16(AA); 0.36(Aa); 0.48(aa)
Answer: (3)

Why: p = 0.4, so q = 0.6. AA = p² = 0.16; Aa = 2pq = 2(0.4)(0.6) = 0.48; aa = q² = 0.36. Direct plug-and-chug into the binomial expansion.

NEET 2019

Variations caused by mutation, as proposed by Hugo de Vries, are:

  1. random and directional
  2. random and directionless
  3. small and directional
  4. small and directionless
Answer: (2)

Why: De Vries' mutation theory (1901) describes evolution by discontinuous, random and directionless variations arising from sudden gene mutations. Mutation supplies raw material; natural selection supplies the direction.

FAQs — Hardy–Weinberg Principle

Equation interpretation, panmixis, drift sub-cases, and the line between assumptions and disturbances.

What does the Hardy–Weinberg principle state?

In a large, randomly mating sexual population with no mutation, no selection, no gene flow and no genetic drift, allele and genotype frequencies remain constant from one generation to the next. Algebraically, p + q = 1 for allele frequencies and p² + 2pq + q² = 1 for genotype frequencies, a state called genetic equilibrium.

What is the meaning of p² + 2pq + q² = 1?

It is the binomial expansion of (p + q)². For a locus with two alleles A (frequency p) and a (frequency q), p² is the expected frequency of homozygous dominant AA individuals, q² is the expected frequency of homozygous recessive aa individuals, and 2pq is the expected frequency of heterozygous Aa individuals. The three genotype frequencies must sum to 1.

What are the five factors that disturb Hardy–Weinberg equilibrium?

NCERT lists five factors that change allele frequencies and therefore violate the equilibrium: (1) gene migration or gene flow, (2) genetic drift, (3) mutation, (4) genetic recombination during gametogenesis, and (5) natural selection. Any deviation of observed frequencies from the predicted p² + 2pq + q² values is read as evidence of evolution.

What is the difference between founder effect and bottleneck effect?

Both are forms of genetic drift acting on small populations. The founder effect occurs when a few individuals leave a large population and start a new one — the new population's gene pool reflects only the alleles those founders happened to carry. The bottleneck effect occurs when an existing population is drastically reduced (by disease, disaster or hunting), and the survivors' allele frequencies differ from those of the original population.

If the frequency of allele A is 0.4, what is the frequency of AA, Aa and aa?

Let p = 0.4 (allele A). Then q = 1 − p = 0.6 (allele a). Frequency of AA = p² = 0.16. Frequency of Aa = 2pq = 2 × 0.4 × 0.6 = 0.48. Frequency of aa = q² = 0.36. Check: 0.16 + 0.48 + 0.36 = 1.00. This is the standard form tested in NEET 2019 Q.61.

Why is mutation called the raw material of evolution but not the main driver?

Mutations create new alleles that did not previously exist in the gene pool, so they are the ultimate source of variation. However, mutation rates are extremely low (about 10⁻⁵ to 10⁻⁸ per gene per generation), and most mutations are random and directionless. Mutation alone changes allele frequencies very slowly; large-scale evolutionary change requires natural selection or drift to amplify favourable mutations.

What is a panmictic population?

A panmictic population is one in which mating is completely random — individuals do not preferentially choose mates based on genotype. Random mating is one of the five assumptions of Hardy–Weinberg equilibrium. NIOS gives the example of human blood groups: most marriages are not arranged with reference to ABO blood type, so humans are panmictic with respect to that locus.