Gene pool and allele frequency
A population is a group of the same species living in one area and breeding together. Its gene pool is every allele of every gene in all its members.
Allele frequency = copies of that allele ÷ total copies of the gene. Each diploid individual has 2 copies.
Example: 10 plants: 4 AA, 4 Aa, 2 aa. Copies of A = 4×2 + 4 = 12; copies of a = 4 + 2×2 = 8; total = 20. So p = 12/20 = 0.6 and q = 0.4. Always p + q = 1.
In the biological species concept a species is a group of populations that can interbreed and produce fertile young, so a species shares one gene pool. (This concept does not fit asexual organisms or fossils well.)
The Hardy–Weinberg principle and calculations
In 1908 G. H. Hardy and Wilhelm Weinberg showed that in an ideal population allele and genotype frequencies stay constant generation after generation. Random mating is like drawing two alleles from the pool:
p² + 2pq + q² = 1 (AA + Aa + aa)
Five assumptions
- Very large population (no drift)
- Random mating
- No migration (no gene flow)
- No mutation
- No natural selection
Standard method
Start from the recessive phenotype, because aa individuals are the only ones you can recognise: q² = fraction showing the recessive trait → q = √q² → p = 1 − q → carriers = 2pq.
If observed genotype numbers differ clearly from p², 2pq, q², at least one assumption is broken and the population is evolving. A chi-square test is used to check if the gap is bigger than chance.
What changes allele frequencies
- Genetic drift: random change, strongest in small populations. Bottleneck effect: a disaster leaves a few survivors (e.g. cheetahs, northern elephant seals have very low variation). Founder effect: a few individuals start a new population (e.g. high rates of some disorders in isolated island or community groups).
- Gene flow: migrants bring or take alleles; makes populations more similar.
- Mutation: the original source of new alleles; slow on its own.
- Natural selection: alleles that help survival and reproduction become more common. It can be directional, stabilising or disruptive.
- Non-random mating: e.g. choosing similar mates or inbreeding; changes genotype frequencies (more homozygotes).
How new species form: speciation
Speciation is the splitting of one gene pool into two that can no longer mix. The key is reproductive isolation:
- Pre-zygotic barriers (before fertilisation): different habitat, breeding season, courtship behaviour, body parts that don't fit, or gametes that don't fuse.
- Post-zygotic barriers: hybrids die, or are sterile (a mule from horse × donkey).
Allopatric speciation ("other homeland")
A geographic barrier (river change, mountain rise, sea level, island colonisation) separates populations. Mutation, drift and different selection make the gene pools drift apart. Example: squirrels on the two rims of a deep canyon.
Sympatric speciation ("same homeland")
New species form in the same area. Most often in plants by polyploidy: an error doubles chromosome sets (2n → 4n), and the 4n plant cannot make fertile offspring with 2n parents. Bread wheat arose by polyploidy. Animals may split by habitat or mate preference, such as cichlid fish in African lakes.
Adaptive radiation, divergence and convergence
Divergent evolution: related species become different as they adapt to different ways of life. They keep homologous structures (same origin, different use), like the forelimbs of human, whale and bat.
Adaptive radiation is fast divergence from one ancestor into many niches: Darwin's finches in the Galápagos (seed-crushing, insect-eating beaks) or Australian marsupials.
Convergent evolution: unrelated species evolve similar features because they face similar problems. These are analogous structures (different origin, same use): wings of bird and insect, streamlined bodies of shark and dolphin, eyes of octopus and human.
Key formulas and definitions
- p + q = 1
- p² + 2pq + q² = 1 (AA + Aa + aa)
- Allele frequency = copies of allele ÷ (2 × number of individuals)
- q = √(frequency of recessive phenotype); p = 1 − q; carriers = 2pq
- Hardy–Weinberg assumptions: large population, random mating, no migration, no mutation, no selection
- Allopatric = geographic barrier; sympatric = same area (polyploidy, behaviour, habitat)
- Divergence → homologous structures; convergence → analogous structures
Worked examples
1. In a population of 500 people, 320 are AA, 160 are Aa and 20 are aa. Find p and q.
Copies of A = 2×320 + 160 = 800. Total copies = 2×500 = 1000. p = 800/1000 = 0.8. q = 1 − 0.8 = 0.2. (Check: copies of a = 160 + 2×20 = 200 → 0.2.)
2. Is the population above in Hardy–Weinberg equilibrium?
Expected AA = p² × 500 = 0.64 × 500 = 320; Aa = 2pq × 500 = 0.32 × 500 = 160; aa = q² × 500 = 0.04 × 500 = 20. Observed equals expected, so yes, it is in equilibrium.
3. Albinism (recessive) appears in 1 out of 400 people in a region. What fraction are carriers?
q² = 1/400 = 0.0025 → q = 0.05. p = 0.95. Carriers = 2pq = 2 × 0.95 × 0.05 = 0.095, about 9.5% (roughly 1 in 10).
4. In a flock of 1,000 sheep, 90 have black wool (recessive bb). How many are expected to be heterozygous?
q² = 90/1000 = 0.09 → q = 0.3, p = 0.7. 2pq = 2 × 0.7 × 0.3 = 0.42 → 0.42 × 1000 = 420 heterozygous sheep.
5. Next generation the same flock has p = 0.75. What does this tell you?
p changed from 0.7 to 0.75, so allele frequencies are not constant: at least one Hardy–Weinberg assumption is broken (for example farmers choosing white sheep = selection). The population is evolving.
6. A storm leaves only 5 birds of a large island population; 4 carry only allele R. Why might R become fixed even if it gives no advantage?
This is a bottleneck. With so few individuals, chance decides which alleles pass on (genetic drift). R starts at a high frequency (about 0.8 or more), so by chance it may reach 1.0 (fixed) while other alleles are lost, without any selection.
Common mistakes
- Taking q from the dominant phenotype: always start from the recessive phenotype, q² = aa fraction.
- Forgetting to take the square root: if q² = 0.16 then q = 0.4, not 0.16.
- Thinking dominant alleles automatically become more common; in Hardy–Weinberg, dominance does not change frequency.
- Mixing allopatric (separated by a barrier) and sympatric (same place) speciation.