OxfordAQA International AS and A-level Biology: Allele frequencies, drift and Hardy-Weinberg (9610)

This guide covers sections 3.3.7.1 and 3.3.7.2 of the OxfordAQA International AS and A-level Biology (9610) specification, Version 5.1, for International A-level exams May/June 2018 onwards. Both sections sit in Unit 3, Populations and genes, which the specification lists under the International A-level assessments. The International AS covers Units 1 and 2 only. Course pages: the OxfordAQA A-level Biology hub, the printable checklist and the free diagnostics. Next steps: the revision notes and the practice questions.

What the specification asks for

Section	What you must be able to do
3.3.7.1	Define a population; explain gene pool and allele frequency; describe the influence of selection for high-yielding breeds and cultivars; explain genetic bottlenecks; explain genetic drift and why it has a larger effect when an allele has few copies
3.3.7.2	State the Hardy-Weinberg principle and the conditions under which it applies; use p² + 2pq + q² = 1 to calculate allele, genotype and phenotype frequencies from appropriate data

Evolution as a change in allele frequencies is met in section 3.3.8. For the genetic diversity this unit builds on, see the diversity of living organisms study guide.

Populations, gene pools and allele frequency

A population is made up of organisms of one species that could interbreed with each other and that live in the same place at the same time. “Potentially” matters: they do not all have to mate, but nothing prevents them from doing so.

The gene pool contains every allele of a gene that is present in one population. Each diploid organism carries two alleles of a gene, so a population of N individuals holds 2N copies of that gene.

The allele frequency is the fraction of the genes in the gene pool that is a particular allele. It is a proportion between 0 and 1, and the frequencies of all the alleles of one gene add up to 1. Do not confuse it with genotype frequency (the fraction of individuals with a given genotype) or phenotype frequency (the fraction showing a given characteristic).

Worked example 1: allele frequency from counts

A survey of 200 flowering plants records a gene for petal colour with two codominant alleles, C^R (red) and C^W (white). There are 90 C^R C^R, 100 C^R C^W and 10 C^W C^W plants.

• Copies of the gene in the gene pool = 2 × 200 = 400.
• Copies of C^R = (2 × 90) + 100 = 280.
• Frequency of C^R = 280 ÷ 400 = 0.70.
• Copies of C^W = (2 × 10) + 100 = 120, so frequency of C^W = 120 ÷ 400 = 0.30.
• Check: 0.70 + 0.30 = 1.

Count alleles, not individuals. Heterozygotes contribute one copy of each allele.

Selection for high-yielding breeds

In domesticated animals and cultivated plants, people choose which individuals breed. Breeders select parents with the phenotype they want, such as a high milk yield, more grain per plant or fast growth, and breed only from them. Individuals with the unwanted phenotype are not allowed to reproduce.

Over many generations:

• The frequency of alleles associated with the high yield rises, because those alleles are passed on more often.
• The frequency of other alleles falls, and some may be lost altogether.
• The gene pool of the breed becomes smaller and less varied, especially if breeders use only a few individuals or a few related lines as parents.

The gain is a population that reliably gives a high yield. The cost is reduced genetic variety. A population in which most individuals share the same alleles has less variation for selection to act on if conditions change, for example if a new disease appears, so many individuals may be susceptible at once. Breeders also have to watch for mating between close relatives, which makes homozygous recessive genotypes (including harmful ones) more likely. Be ready to give one advantage and one disadvantage in the same answer.

This is artificial selection by people, but it changes allele frequencies in the same way natural selection does.

Genetic bottlenecks

A genetic bottleneck is a severe reduction in population size caused by an environmental event, such as a drought, fire, flood or disease outbreak, or by human activities, such as hunting or habitat destruction. The survivors are a small sample of the original gene pool. This reduces the genetic variety in the gene pool. Alleles that were already rare may be absent from the survivors, and the allele frequencies in the survivors may differ from those in the original population simply because the sample is small.

Even if the population later recovers in number, the next generations descend from the few survivors. The variety lost in the bottleneck is not restored, except slowly by new mutations. The recovered population is therefore genetically uniform, which makes it vulnerable to disease and to environmental change.

A well-documented example is the northern elephant seal, which was hunted to very small numbers in the nineteenth century and has since recovered in number but not in genetic variety.

Worked example 2: what a bottleneck can do to a rare allele

A population of 5000 animals has a rare allele with frequency 0.02. A drought leaves 8 survivors, chosen with respect to this gene purely by chance.

• Copies of the allele before the drought = 2 × 5000 × 0.02 = 200.
• The survivors carry 2 × 8 = 16 copies of the gene.
• Expected copies of the rare allele among them = 16 × 0.02 = 0.32.
• Probability that none of the 16 copies is the rare allele = 0.98¹⁶ = 0.72, so there is about a 72% chance the allele is lost completely.
• Probability that it survives = 1 − 0.72 = 0.28.

The bottleneck has changed the allele frequency (up or down) without any advantage or disadvantage of the allele being involved.

Genetic drift

Genetic drift is a change in the frequency of alleles in a population due to chance. In each generation, only some individuals breed, and the gametes that form zygotes are a random sample of the gametes produced. By chance, an allele may be passed on more or less often than its frequency predicts. The change is random in direction and is not linked to the allele being useful.

The effect is larger when there are few copies of an allele, which is the case in small populations or for rare alleles. In a large population, each random event is a small fraction of the whole and the effects average out. A bottleneck is an extreme case where drift acts strongly because the population is small.

Worked example 3: the same chance event, two population sizes

An allele has a frequency of 0.05 in each of two populations. Population A has 10 individuals and population B has 500. Assume the next generation’s gene copies are a random sample of the same size from the current gene pool.

	Population A	Population B
Copies of the gene (2N)	20	1000
Copies of the allele now	1	50
Probability that the allele is absent in the next generation (0.95^2N)	0.36	about 5 × 10⁻²³

In A, one copy of the allele is lost with probability 0.36 in a single generation. The frequency would then be 0, and with no mutation or migration it could never return. In B the allele is, for practical purposes, certain to remain. Drift matters most in small populations because there are few copies to lose.

Drift reduces genetic variety. It acts alongside natural selection, not instead of it.

The Hardy-Weinberg principle

The Hardy-Weinberg principle is a mathematical model. It predicts that, from one generation to the next, allele frequencies stay the same. This holds only under certain conditions. The standard conditions are:

• The population is large, so drift is negligible.
• Mating is random: no mate preference, and no inbreeding.
• There is no mutation creating or changing alleles.
• There is no migration (no gene flow) into or out of the population.
• There is no selection: all genotypes are equally likely to survive and reproduce.

The specification asks for “the conditions” without listing them, so learn these five and be able to say what happens when each is broken. If the conditions hold, allele frequencies stay constant and genotype frequencies reach fixed values in one generation of random mating. A real population that differs from these predictions is changing, and the equation gives a baseline for detecting that change.

The Hardy-Weinberg equation

Take a gene that has two alleles. Let p be the frequency of one allele (usually the dominant one) and q the frequency of the other (usually the recessive one).

• p + q = 1 (allele frequencies).
• p² + 2pq + q² = 1 (genotype frequencies).
• p² = homozygous for the first allele; 2pq = heterozygous; q² = homozygous for the second allele.
• Phenotype frequencies follow from the genotypes. With complete dominance, the recessive phenotype has frequency q², and the dominant phenotype has frequency p² + 2pq (which equals 1 − q²).

The usual method:

1. Identify the genotype you can count directly. With complete dominance this is the homozygous recessive, because the recessive phenotype shows only in that genotype.
2. Set q² equal to its frequency (number ÷ total).
3. Take the square root to get q, and subtract from 1 to get p.
4. Calculate 2pq and p² as required.
5. To get a count of individuals, multiply the frequency by N, the number in the population.

Worked example 4: from the recessive phenotype

In a population of 1600 mice, coat colour is controlled by one gene. Grey (G) is dominant to white (g). There are 100 white mice. Assume Hardy-Weinberg conditions hold.

• q² = 100 ÷ 1600 = 0.0625.
• q = √0.0625 = 0.25, so p = 1 − 0.25 = 0.75.
• Homozygous grey (GG) = p² = 0.5625, so 0.5625 × 1600 = 900 mice.
• Heterozygous (Gg) = 2pq = 2 × 0.75 × 0.25 = 0.375, so 0.375 × 1600 = 600 mice.
• Check: 900 + 600 + 100 = 1600.
• Grey phenotype frequency = 0.5625 + 0.375 = 0.9375, which is 1 − 0.0625.

You cannot tell the 900 GG mice from the 600 Gg mice by looking at them.

Worked example 5: testing whether a population fits the model

Return to the plants in worked example 1, where p (C^R) = 0.70 and q (C^W) = 0.30. With codominance each genotype shows its own phenotype, so all three frequencies can be counted directly. If Hardy-Weinberg conditions held, in 200 plants we would expect:

Genotype	Expected	Observed
C^R C^R	0.70² × 200 = 98	90
C^R C^W	2 × 0.70 × 0.30 × 200 = 84	100
C^W C^W	0.30² × 200 = 18	10

There are more heterozygotes and fewer of both homozygotes than expected. The population is not in Hardy-Weinberg equilibrium for this gene. Possible reasons include non-random mating (for example, pollinators preferring to move between unlike flowers), selection favouring heterozygotes, or migration. State the difference, then give a reason that fits the context.

Common errors

• Using a recessive phenotype frequency as q instead of q². “One in 400 affected” means q² = 1/400.
• Counting individuals instead of alleles when finding allele frequency.
• Forgetting the 2 in 2pq.
• Giving the dominant phenotype frequency as p² only. It is p² + 2pq.
• Using the equation for a population that clearly breaks the conditions (small, isolated, or under strong selection) without commenting.
• Describing drift as “survival of the fittest”. Drift is chance and is not about advantage.
• Saying a bottleneck “kills the weak”. It reduces variety by chance sampling, whatever the survivors’ alleles are.

For worked questions in exam style, use the practice set, and for a one-page recap, the revision notes.

Official syllabus

OxfordAQA International AS and A-level Biology (9610), Version 5.1, for International AS exams May/June 2017 onwards and International A-level exams May/June 2018 onwards, published by OxfordAQA. Sections 3.3.7.1 and 3.3.7.2.