The Hardy-Weinberg principleAQA A-Level Biology: Revision notes

Section 1

Populations, gene pools and allele frequency

A population is a group of organisms of the same species, living in a particular place at a particular time, that can potentially interbreed. A species may exist as one population or as several separate ones.

The gene pool is the complete set of alleles of all the genes in a population at a given time. The allele frequency is how common one allele is in the gene pool, written as a proportion between 0 and 1 (or a percentage). For example, if 30 of the 100 copies of a gene in a population are allele A, the frequency of A is 0.30.

Genotype frequency and phenotype frequency are different from allele frequency. They are the proportions of individuals with a given genotype or phenotype.

Key termspopulationgene poolallele frequency

Exam tip

Every diploid individual carries two alleles of each gene, so a population of 400 individuals has 800 copies of the gene.

Section 2

The Hardy-Weinberg principle

The Hardy-Weinberg principle is a mathematical model. It predicts that allele frequencies will not change from generation to generation, provided certain conditions apply:

the population is large, so chance has little effect
mating is random
there are no mutations
there is no selection: all genotypes are equally likely to survive and reproduce
there is no migration (no gene flow) into or out of the population

Real populations rarely meet every condition perfectly. The model is useful because it gives a baseline: if observed allele frequencies change, one or more of the conditions is not being met.

Key termsHardy-Weinberg principlerandom mating

Common mistake

The principle does not say that evolution never happens. It describes what happens when no evolutionary forces act, and shows how to detect change when they do.

Section 3

The equations

Consider one gene with a dominant allele (frequency $p$ ) and a recessive allele (frequency $q$ ). There are only two alleles, so

$p + q = 1$

Random mating produces three genotypes, whose frequencies are given by

$p^2 + 2pq + q^2 = 1$

$p^2$ = frequency of the homozygous dominant genotype
$2pq$ = frequency of the heterozygous genotype (carriers of the recessive allele)
$q^2$ = frequency of the homozygous recessive genotype

The homozygous recessive individuals are the only ones whose genotype can be known from their phenotype, so calculations usually begin with $q^2$ .

Key termspq2pq

Section 4

Worked example

A recessive condition affects 1 person in 1600. Calculate the frequency of carriers.

$q^2 = 1/1600 = 0.000625$
$q = \sqrt{0.000625} = 0.025$
$p = 1 - 0.025 = 0.975$
Carriers $= 2pq = 2 \times 0.975 \times 0.025 = 0.04875$

So about 4.9% of the population, or about 1 in 20, are carriers. To find numbers of individuals, multiply a frequency by the population size.

Exam tip

Find $q^2$ from the phenotype, take the square root for $q$ , subtract from 1 for $p$ , and only then calculate $2pq$ .

Common mistake

Using $q^2$ as if it were $q$ . If 1 in 1600 are affected, the allele frequency is 0.025, not 0.000625.

Section 5

When the principle does not hold

Each condition that is broken explains a way allele frequencies can change:

selection: some genotypes survive and reproduce more, so their alleles become more common
mutation: creates new alleles or changes existing ones
migration: individuals moving in or out change the gene pool
small population size: chance events cause random changes in allele frequency
non-random mating: changes genotype frequencies even if allele frequencies stay the same

In an exam, link the broken condition to the effect on allele frequency. For example, if people with a recessive disorder are less likely to reproduce, the recessive allele is passed on less, so $q$ falls and the model's prediction fails.

Key termsgene flow

That's the notes covered.

Carry on to the next subtopic.

Exam questions on The Hardy-Weinberg principle

A conservation biologist is studying rabbits living on a small island. She records the alleles present in the rabbit population for a gene controlling fur colour and wants to predict the allele frequencies in future generations.
State two conditions that must apply for the biologist's prediction, based on the Hardy-Weinberg principle, to be valid.2 marks
Cystic fibrosis is a human genetic disorder caused by a recessive allele, f. The dominant allele, F, is normal. In one population the incidence of cystic fibrosis is 1 in 2500 births. Assume that the Hardy-Weinberg principle applies to this population.
Many people with cystic fibrosis die young or do not have children. Explain why the Hardy-Weinberg principle may not predict the frequency of carriers accurately in future generations.2 marks
A population of 800 plants of one species has two alleles for flower colour. The allele for red flowers, R, is dominant to the allele for white flowers, r. In the population, 128 of the plants have white flowers. The population is assumed to be in Hardy-Weinberg equilibrium.
Calculate the frequency of the allele R and the number of heterozygous plants in the population. Show your working.3 marks

See the full worksheet

Written by the Exaim team, led by Shaun Daswani (Head of Upper Secondary, Improve ME Institute; MSc Financial Mathematics, Imperial College London; BSc, UCL) and Jason Daswani (operational lead, Improve ME Institute; LSE).