How can we calculate allele and genotype frequencies in a population, and what conditions keep them constant?
Use the Hardy-Weinberg principle to calculate allele and genotype frequencies and state the conditions for equilibrium
A focused answer to the H2 Biology Inheritance and Evolution outcome on population genetics. The Hardy-Weinberg equations, calculating allele and genotype frequencies including carriers, the conditions required for equilibrium, and how departures indicate evolution.
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What this dot point is asking
SEAB wants you to use the Hardy-Weinberg principle to calculate allele and genotype frequencies (including carriers) in a population, to state the conditions under which frequencies stay constant, and to interpret a departure from equilibrium as evidence of evolution. It connects single-gene inheritance to whole populations.
The answer
The two equations
For a gene with two alleles, let p be the frequency of the dominant allele and q the frequency of the recessive allele.
The genotype frequencies are then:
where p squared is the frequency of homozygous dominant, 2pq is the frequency of heterozygotes (carriers), and q squared is the frequency of homozygous recessive.
Using the equations
A common task starts from the frequency of the recessive phenotype, which equals q squared (the homozygous recessive). Take its square root to find q, then p = 1 - q, then calculate carriers as 2pq and homozygous dominant as p squared.
The conditions for equilibrium
Allele frequencies stay constant (no evolution) only if:
- the population is large (so chance has little effect),
- there is no migration in or out,
- there is no mutation changing allele frequencies,
- mating is random, and
- there is no natural selection (all genotypes survive and reproduce equally).
Interpreting a departure
If observed genotype frequencies differ significantly from those predicted, one or more conditions is not met, so allele frequencies are changing: the population is evolving.
Examples in context
Example 1. Estimating carriers of a recessive disease. Public health workers use the Hardy-Weinberg equation to estimate how many people carry a recessive disease allele from the frequency of affected individuals, informing genetic counselling and screening programmes.
Example 2. Detecting selection. If a genotype is consistently rarer than Hardy-Weinberg predicts, it may be selected against; if commoner, it may be favoured. Comparing observed with expected frequencies is one way biologists detect natural selection acting on a gene in a population.
Try this
Q1. In the Hardy-Weinberg equation, state what the term 2pq represents. [1 mark]
- Cue. The frequency of the heterozygous genotype (the carriers).
Q2. A recessive phenotype has a frequency of 0.09 in a population at equilibrium. Calculate the frequency of the recessive allele. [1 mark]
- Cue. q = the square root of 0.09 = 0.3.
Q3. State two conditions required for a population to remain in Hardy-Weinberg equilibrium. [2 marks]
- Cue. Any two of: a large population, no migration, no mutation, random mating, no natural selection.
Exam-style practice questions
Practice questions written in the style of SEAB exam questions on this dot point, with worked answer explainers. The year tag is the paper they imitate, not the source.
Original5 marksIn a population, 1 in 400 individuals shows a recessive condition caused by a single autosomal recessive allele. Assuming Hardy-Weinberg equilibrium, calculate the frequency of the recessive allele and the proportion of the population that are carriers.Show worked answer →
The answer should use the two Hardy-Weinberg equations.
The recessive condition corresponds to the homozygous recessive genotype, with frequency q squared. So q squared = 1/400 = 0.0025.
The frequency of the recessive allele is q = the square root of 0.0025 = 0.05.
The frequency of the dominant allele is p = 1 - q = 1 - 0.05 = 0.95.
Carriers are heterozygotes, with frequency 2pq = 2 times 0.95 times 0.05 = 0.095.
So about 9.5 percent of the population are carriers.
Markers reward equating the affected frequency with q squared, finding q by taking the square root, finding p as 1 minus q, and calculating the carrier frequency as 2pq.
Original4 marksState the conditions that must be met for a population to remain in Hardy-Weinberg equilibrium, and explain what it means if the observed genotype frequencies depart from those predicted.Show worked answer →
The answer should list the conditions and interpret a departure.
For Hardy-Weinberg equilibrium the population must be large (so chance has little effect), there must be no migration into or out of the population, no mutation altering allele frequencies, random mating (no mating preference for particular genotypes), and no natural selection (all genotypes equally likely to survive and reproduce).
If the observed genotype frequencies differ significantly from those predicted by the equation, then one or more of these conditions is not being met. This indicates that the allele frequencies are changing, that is, the population is evolving (for example because selection or migration is acting).
Markers reward the five conditions (large population, no migration, no mutation, random mating, no selection) and the interpretation that a significant departure indicates the allele frequencies are changing and the population is evolving.
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