Population genetics and Hardy-Weinberg

Gene pools and allele frequency

A population has a gene pool: every allele of every gene in every member. For a gene with two alleles, A and a, the allele frequencies are:

📖 Allele frequencies

p = frequency of A, q = frequency of a, p + q = 1

Each individual carries two alleles, so each allele appears in two copies per diploid individual. Frequencies are always proportions of all gene copies in the population.

The Hardy-Weinberg equation

📖 Hardy-Weinberg

p² + 2pq + q² = 1

p² = frequency of AA (homozygous dominant); 2pq = frequency of Aa (heterozygous); q² = frequency of aa (homozygous recessive).

A population is in Hardy-Weinberg equilibrium when its allele frequencies stay the same from one generation to the next. This needs five conditions: no mutation, no migration, no natural selection, a very large population, and random mating.

Why these five? Mutation adds alleles, migration brings or removes them, selection favours some alleles, small populations drift by chance, and non-random mating changes genotype frequencies. Each one breaks equilibrium.

Worked example: finding p, q and carriers

✏️ Worked example

1In a population, 9% of people show a recessive trait (aa). Recessive phenotype = q² = 0,09.

2q = √0,09 = 0,3.

3p = 1 − q = 1 − 0,3 = 0,7.

4Carriers (heterozygotes, Aa) = 2pq = 2 × 0,7 × 0,3 = 0,42, so 42% of the population carry the allele without showing the trait.

5Check: p² + 2pq + q² = 0,49 + 0,42 + 0,09 = 1,00 ✓

Blood groups and change in gene pools

The ABO blood groups are controlled by three alleles: I^A, I^B and i. Surveys of different populations show different frequencies of the blood groups, which means the allele frequencies differ between groups. Such differences come from isolation, migration, drift or selection in different environments. Hardy-Weinberg is the baseline: a difference between the observed and expected genotype frequencies is evidence that one of the five conditions is not met.

Answer in your exercise book, then open each memo to mark your work.

Question 1 · (3 marks)

Define the term gene pool. Explain why allele frequencies are expressed as proportions of all gene copies rather than of individuals.

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Gene pool: all the alleles of all the genes in a population ✓.
Each diploid individual carries two copies of each gene ✓, so an allele's frequency must be counted out of all 2N gene copies, not out of the N individuals ✓.

Question 2 · (5 marks)

In a population, 16% of individuals show a recessive phenotype. Calculate (a) q, (b) p, (c) the percentage of heterozygous carriers. Show all working.

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(a) q² = 0,16 ✓, so q = √0,16 = 0,4 ✓
(b) p = 1 − q = 0,6 ✓
(c) 2pq = 2 × 0,6 × 0,4 = 0,48 ✓, so 48% are carriers ✓.

Question 3 · (4 marks)

Name FOUR of the five conditions required for Hardy-Weinberg equilibrium and, for each, explain how it would change the allele frequencies.

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Any FOUR, condition with its effect (1 mark each):
• No mutation — mutations create new alleles ✓
• No migration — gene flow adds or removes alleles ✓
• No natural selection — selection makes favoured alleles more common ✓
• Very large population — in small populations chance (genetic drift) changes frequencies ✓
• Random mating — non-random mating changes genotype frequencies ✓

Question 4 · (4 marks)

A survey finds fewer heterozygotes in a small, isolated population than the Hardy-Weinberg equation predicts. Suggest TWO possible reasons and link each to a condition of equilibrium.

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Any TWO, each with its link (2 marks each):
• Inbreeding / non-random mating ✓ increases homozygotes and reduces heterozygotes — breaks the random-mating condition ✓
• Genetic drift ✓ — chance loss of alleles in a small population breaks the large-population condition ✓
• Selection against heterozygotes ✓ — breaks the no-selection condition ✓