Is it correct to say: Taking q as the frequency of aa individuals?

The frequency of aa individuals is q². Take the square root to get the allele frequency q.

Is it correct to say: Writing the heterozygote frequency as pq?

It is 2pq, because an Aa individual can form in two ways (A from either parent).

Is it correct to say: Assuming the dominant allele must be the more common one?

Dominance decides the phenotype, not the frequency. A dominant allele can be rare (p < q).

Is it correct to say: Calling the forelimbs of whale and bat analogous?

They have the same basic structure but different functions, so they are homologous (divergent evolution). Analogous organs do the same job with different structures.

Is it correct to say: Confusing gene flow with genetic drift?

Gene flow is change in allele frequencies due to migration. Genetic drift is change by chance, which can lead to the founder effect.

Is it correct to say: Equating Darwinian fitness with physical strength?

Fitness means reproductive fitness — the ability to leave more progeny in a given environment.

📄 Formula sheet (PDF)

Evolution

Q: Is it correct to say: Calling the forelimbs of whale and bat analogous?

They have the same basic structure but different functions, so they are homologous (divergent evolution). Analogous organs do the same job with different structures.

Q: Is it correct to say: Confusing gene flow with genetic drift?

Gene flow is change in allele frequencies due to migration. Genetic drift is change by chance, which can lead to the founder effect.

Q: Is it correct to say: Equating Darwinian fitness with physical strength?

Fitness means reproductive fitness — the ability to leave more progeny in a given environment.

Origin of life, Miller's experiment, evidences for evolution, adaptive radiation, Darwinism and mutation theory, Hardy–Weinberg principle, types of natural selection and origin of man — NCERT Class 12 Biology Ch 6

📐 14 formulas✏️ 4 examples🎯 6 practice⚖️ Unit VII Genetics and Evolution: 20 marks (with Ch 4 and 5)🏫 CBSE📚 Class 12✓ 2025–26 syllabus

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Board Exam Tips

→In Hardy–Weinberg numericals, start from the homozygous recessive frequency: it equals q², so take the square root to get q, then p = 1 − q.
→Write the full statement before any numerical: allele frequencies in a population stay constant from generation to generation when no evolutionary force acts.
→Learn the five factors that disturb Hardy–Weinberg equilibrium as a list: gene flow, genetic drift, mutation, genetic recombination, natural selection.
→Homologous organs mean divergent evolution and analogous organs mean convergent evolution. Keep two NCERT examples ready for each.
→Draw the three distribution curves for stabilising, directional and disruptive selection. A clear sketch with the shifted peaks explains the answer at a glance.

📐 Formulas(14)

Time Scale of Life

Universe \approx 13.8 billion yr; Earth \approx 4.5 billion yr; life \approx 4 billion yr ago

Miller's Experiment (1953)★ Board fav

CH_{4} + H_{2} + NH_{3} + H_{2} O (vapour) electric discharge, 80 0^{\circ} C amino acids

Homology and Analogy★ Board fav

Homologous organs \Rightarrow divergent evolution; Analogous organs \Rightarrow convergent evolution

Adaptive Radiation

One ancestral stock (one area) \to many species adapted to different habitats

Industrial Melanism

1850s: white-winged > dark-winged; 1920: dark-winged > white-winged

Darwinian Fitness

Fitness = reproductive fitness (leaving more progeny)

Mutation Theory (de Vries)

Mutation: large, sudden, random, directionless (saltation) vs Darwinian variation: small, directional

Sum of Allele Frequencies

p + q = 1

Symbol	Meaning
$p$	Frequency of allele A (dimensionless, 0 to 1)
$q$	Frequency of allele a (dimensionless, 0 to 1)

Hardy–Weinberg Equation★ Board fav

p^{2} + 2 pq + q^{2} = 1

Symbol	Meaning
$p^{2}$	Frequency of homozygous dominant AA
$2 pq$	Frequency of heterozygous Aa
$q^{2}$	Frequency of homozygous recessive aa

Recessive Allele from Phenotype

q = q^{2} = frequency of aa

Symbol	Meaning
$q$	Frequency of the recessive allele a

Allele Frequency by Counting

p = \frac{2 N _{AA} + N _{A a}}{2 N}, q = \frac{2 N _{aa} + N _{A a}}{2 N}

Symbol	Meaning
$N_{AA}, N_{A a}, N_{aa}$	Number of individuals of each genotype
$N$	Total number of individuals

Factors Affecting Hardy–Weinberg Equilibrium★ Board fav

Gene flow, genetic drift, mutation, genetic recombination, natural selection

Types of Natural Selection

Stabilising (mean favoured); Directional (one extreme favoured); Disruptive (both extremes favoured)

Brain Capacity in Human Evolution

Homo habilis : 650 to 800 cc; Homo erectus \approx 900 cc; Neanderthal \approx 1400 cc

✏️ Solved Examples

1Solved Exampleeasy3 steps

In a population at Hardy–Weinberg equilibrium the frequency of allele A is 0.7. Find the frequency of allele a and of genotypes AA, Aa and aa.

Allele frequencies add to 1.

q = 1 - p = 1 - 0.7 = 0.3

2Solved Exampleboard4 steps

In a population of 1000 individuals at equilibrium, 160 show the recessive phenotype (aa). Calculate p, q and the expected number of heterozygotes and of homozygous dominant individuals. (3 marks)

Frequency of aa individuals equals q².

q^{2} = \frac{160}{1000} = 0.16

3Solved Exampleboard3 steps

A sample of 500 individuals has 245 AA, 210 Aa and 45 aa. Calculate the allele frequencies by counting and check whether the population is in Hardy–Weinberg equilibrium.

Count alleles: there are 2 × 500 = 1000 alleles in total.

p = \frac{2 ( 245 ) + 210}{1000} = \frac{700}{1000} = 0.7, q = \frac{2 ( 45 ) + 210}{1000} = 0.3

4Solved ExampleHOTS4 steps

A recessive disorder affects 1 in 100 people in a population at equilibrium. What percentage of people are carriers (Aa)? What fraction of all recessive alleles is present in carriers rather than in affected people?

Frequency of affected (aa) people is q².

q^{2} = 0.01 \Rightarrow q = 0.1, p = 0.9

⚠️ Traps & Common Mistakes

⚠️Common Mistakes6

1
Taking q as the frequency of aa individuals
✓The frequency of aa individuals is q². Take the square root to get the allele frequency q.
2
Writing the heterozygote frequency as pq
✓It is 2pq, because an Aa individual can form in two ways (A from either parent).
3
Assuming the dominant allele must be the more common one
✓Dominance decides the phenotype, not the frequency. A dominant allele can be rare (p < q).
4
Calling the forelimbs of whale and bat analogous
✓They have the same basic structure but different functions, so they are homologous (divergent evolution). Analogous organs do the same job with different structures.
5
Confusing gene flow with genetic drift
✓Gene flow is change in allele frequencies due to migration. Genetic drift is change by chance, which can lead to the founder effect.
6
Equating Darwinian fitness with physical strength
✓Fitness means reproductive fitness — the ability to leave more progeny in a given environment.

🎯 Practice Yourself

🎯Practice Yourself6 questions

Q1
In a population at equilibrium the frequency of aa individuals is 0.36. Find p and q.
Q2
If p = 0.8 in a population at equilibrium, what is the frequency of heterozygotes?
Q3
A population of 2000 has 720 AA, 960 Aa and 320 aa individuals. Find p and q by counting.
Q4
Name the five factors that affect Hardy–Weinberg equilibrium.
Q5
Which gases did Miller place in his flask, and what did he obtain?
Q6
Name the type of natural selection in which more individuals acquire extreme character values at both ends of the distribution.

📝 Notes

Evolution

The chapter moves from the origin of life to the mechanism of evolution and ends with the evolution of humans. Only one part is truly numerical — the Hardy–Weinberg principle — but the rest is full of paired concepts that boards like to contrast.

Evidence comes in pairs

Homology vs analogy: same structure with different functions (divergent evolution) vs same function with different structures (convergent evolution).
Darwin vs de Vries: small, directional variations acted on by natural selection vs large, sudden, directionless mutations (saltation).
Adaptive radiation vs convergent evolution: one radiation from a common ancestor (Darwin's finches) vs separate radiations in an isolated area that end up looking alike (Australian marsupials and placental mammals).

Industrial melanism and antibiotic or pesticide resistance are NCERT's examples of natural selection seen within human history.

Hardy–Weinberg in three moves

Find $q^2$ from the recessive phenotype frequency.
Get $q = \sqrt{q^2}$ and $p = 1 - q$ .
Compute $p^2$ , $2pq$ and $q^2$ , then check that they add to 1.

When genotype counts are given, count alleles directly: $p = (2N_{AA} + N_{Aa})/2N$ . If the observed genotype numbers differ from $p^2$ , $2pq$ and $q^2$ , the difference shows that evolution is taking place.

What breaks equilibrium

Gene flow, genetic drift, mutation, genetic recombination and natural selection all change allele frequencies. Natural selection can be stabilising, directional or disruptive — always draw the three curves with the original mean marked.

Human evolution

Learn the order in which NCERT presents the stages (Dryopithecus and Ramapithecus → Australopithecines → Homo habilis → Homo erectus → Neanderthal man → Homo sapiens) together with the brain capacities, since short-answer questions can ask for them.