Populations (A-level only)

What you'll learn

How a species, population, gene pool and allele frequency are linked.
Why populations are the unit where evolution is measured.
How the Hardy–Weinberg principle predicts allele, genotype and phenotype frequencies.
How to use $p^2 + 2pq + q^2 = 1$ in A-Level calculations.

Species and populations

A species can exist as one large population or as several separate populations in different places. For example, the same species of beetle might have one population in one woodland and another population in a different woodland.

Definition

Species and population

A species is a group of organisms that can reproduce with one another to produce fertile offspring. A population is a group of organisms of the same species occupying a particular space at a particular time that can potentially interbreed.

The phrase “particular space at a particular time” matters. Populations are not just defined by species; they are also defined by location and time. A population of limpets on one rocky shore in June is not automatically the same population as limpets on another shore in September.

Why populations matter

Evolution is usually described as a change in allele frequencies in a population over time. Individual organisms do not change their alleles during life, but the genetic make-up of the population can change between generations.

Example

Deciding whether organisms are one population

A biologist studies rabbits in two fields separated by a busy road. The rabbits are the same species, but they rarely cross the road.

Check the species: because the rabbits can potentially breed with each other and produce fertile offspring, they are members of the same species.
Check the space and interbreeding: if the road prevents regular breeding between the two fields, the rabbits in each field may form separate populations.
Make the conclusion: the species exists as at least two populations, each with its own local breeding group.

Gene pools and allele frequencies

An allele is a version of a gene. For example, a gene affecting flower colour might have one allele for purple flowers and one allele for white flowers.

Definition

Gene pool

The gene pool is the total collection of all the alleles of all the genes in a population at a particular time.

A population with lots of different alleles has a more varied gene pool. This genetic variation is important because natural selection can only act on variation that already exists, or on new variation produced by mutation.

Definition

Allele frequency

An allele frequency is the proportion of all copies of a gene in a population that are a particular allele.

For a diploid organism, each individual usually has two copies of each autosomal gene, one from each parent. So, if you are counting alleles for one gene, the total number of allele copies is usually twice the number of individuals.

gene\text{allele frequency} = \frac{\text{number of copies of the allele}}{\text{total number of allele copies for that gene}}

Allele frequencies are proportions, so they have no units. They can be written as decimals, fractions or percentages, but decimals are usually easiest for Hardy–Weinberg calculations.

Example

Calculating allele frequency from genotype counts

In a population of 100 diploid plants, 20 have genotype RR, 50 have genotype Rr and 30 have genotype rr. Calculate the frequencies of the R and r alleles.

Count the total allele copies: 100 plants each have two copies of the gene, so there are 200 allele copies in total.
Count R alleles: each RR plant contributes two R alleles and each Rr plant contributes one R allele, so $\times 20 + 50 = 90$ R alleles.
Calculate the R allele frequency: $\frac{90}{200} = 0.45$ .
Use the fact that the two allele frequencies must add to 1: $q = 1 - 0.45 = 0.55$ . The r allele frequency is 0.55.

Genotypes, phenotypes and notation

A genotype is the combination of alleles an organism has for a gene, such as AA, Aa or aa. A phenotype is the observable characteristic, such as purple flowers or white flowers.

A homozygous genotype has two identical alleles, such as AA or aa. A heterozygous genotype has two different alleles, such as Aa.

For Hardy–Weinberg questions, the allele frequencies are usually labelled:

$p$ = frequency of one allele, usually the dominant allele
$q$ = frequency of the other allele, usually the recessive allele

Because there are only two alleles in the simple A-Level model:

p + q = 1

Tip

Naming p and q

Always state what $p$ and $q$ represent in the question. The letters are just labels; the biology comes from linking them to the actual alleles.

The Hardy–Weinberg principle

The Hardy–Weinberg principle is a mathematical model. It predicts what happens to allele and genotype frequencies if nothing is causing them to change.

Definition

Hardy–Weinberg principle

The Hardy–Weinberg principle states that allele frequencies in a population will remain constant from generation to generation if certain conditions are met.

The model is useful because it gives a “no change” expectation. If real data do not match Hardy–Weinberg predictions, that suggests at least one assumption may not be true.

Hardy–Weinberg schematic showing a population, gene pool, allele frequencies p and q, genotype frequencies, and assumptions

Conditions for Hardy–Weinberg equilibrium

For the principle to apply, the population should have:

a large population size, so random chance has little effect
random mating, so all genotypes have an equal chance of mating
no natural selection, so no genotype has a survival or reproductive advantage
no mutation, so new alleles are not being produced
no migration, so alleles are not entering or leaving the population

Random changes in allele frequency due to chance are called genetic drift. Genetic drift has a stronger effect in small populations, which is why Hardy–Weinberg assumes a large population.

Key Idea

What equilibrium means

Hardy–Weinberg equilibrium means allele frequencies are not changing between generations. It does not mean every genotype is equally common.

The Hardy–Weinberg equation

If there are two alleles, A and a:

p + q = 1

When gametes combine at random, genotype frequencies are predicted by:

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

The three terms represent:

$p^2$ = frequency of homozygous dominant genotype, AA
$2 pq$ = frequency of heterozygous genotype, Aa
$q^2$ = frequency of homozygous recessive genotype, aa

The $2 pq$ term appears because a heterozygote can be formed in two equivalent ways: A from one parent and a from the other, or a from one parent and A from the other.

Example

Predicting genotype frequencies from allele frequencies

In a population, the frequency of allele A is 0.70 and the frequency of allele a is 0.30. Predict the genotype frequencies.

Assign the allele frequencies: $p = 0.70$ and $q = 0.30$ .
Substitute into the Hardy–Weinberg terms:
$p2=0.702=0.492pq=2×0.70×0.30=0.42q2=0.302=0.09\begin{aligned} p^2 &= 0.70^2 = 0.49 \\ 2pq &= 2 \times 0.70 \times 0.30 = 0.42 \\ q^2 &= 0.30^2 = 0.09 \end{aligned}$
Interpret the results: 0.49 of the population is predicted to be AA, 0.42 is predicted to be Aa and 0.09 is predicted to be aa.
Check the frequencies add to 1: $0.49 + 0.42 + 0.09 = 1.00$ .

Using phenotype data

In many questions, you are not given genotype counts directly. Instead, you may be told the frequency of an observable phenotype.

This is especially useful for recessive phenotypes. If a recessive phenotype only appears in homozygous recessive individuals, then the frequency of that phenotype is $q^2$ .

Tip

Start with the recessive phenotype

If the question gives the frequency of individuals showing a recessive characteristic, treat that frequency as $q^2$ , then square root it to find $q$ .

Example

Calculating carrier frequency from a recessive phenotype

In a population of 10,000 newborns, 25 have a recessive disorder caused by genotype aa. Estimate the number of heterozygous carriers.

The affected newborns are aa, so their frequency is $q^2$ :
$newborns=0.0025q^2 = \frac{25\ \text{newborns}}{10\,000\ \text{newborns}} = 0.0025$
The units cancel, so this is a dimensionless frequency.
Find $q$ and then $p$ :
$q=0.0025=0.05p=1−0.05=0.95\begin{aligned} q &= \sqrt{0.0025} = 0.05 \\ p &= 1 - 0.05 = 0.95 \end{aligned}$
Carriers are heterozygous, so use $2 pq$ :
$\times 0.95 \times 0.05 = 0.095$
Convert the frequency into a number of newborns: $0.095 \times 10\,000 = 950$ . The estimated number of carriers is 950 newborns.

Common Mistake

Using the dominant phenotype incorrectly

The dominant phenotype is not just $p^2$ . It includes both AA and Aa individuals, so its frequency is $p^2 + 2pq$ .

Collecting data from a population

You may be asked how phenotype frequencies could be collected from a single population. The key is to sample fairly from a defined population.

For example, if you were recording flower colour in a plant population, you should define the area, sample at the same time, choose individuals randomly where possible, and record a large enough sample to reduce the effect of chance.

Common Mistake

When the simple equation is not enough

The A-Level Hardy–Weinberg equation assumes one gene with two alleles. If there are more than two alleles, sex-linked inheritance, non-random mating or strong selection, the simple form may not apply reliably.

Exam technique

In the exam

Define $p$ and $q$ before calculating, then use $p + q = 1$ to find the missing allele frequency.
If you are given a recessive phenotype frequency, start with $q^2$ , not $q$ .
When interpreting real populations, mention the assumptions: large population, random mating, no selection, no mutation and no migration.

Self review

Check yourself

What is the difference between a species, a population and a gene pool?
If 9% of a population shows a recessive phenotype, what are $q$ , $p$ and $2 pq$ ?
Name two conditions needed for Hardy–Weinberg equilibrium and explain why each matters.

Populations (A-level only)

What you'll learn

How a species, population, gene pool and allele frequency are linked.
Why populations are the unit where evolution is measured.
How the Hardy–Weinberg principle predicts allele, genotype and phenotype frequencies.
How to use $p^2 + 2pq + q^2 = 1$ in A-Level calculations.

Species and populations

Definition

Species and population

Why populations matter

Example

Deciding whether organisms are one population

A biologist studies rabbits in two fields separated by a busy road. The rabbits are the same species, but they rarely cross the road.

Check the species: because the rabbits can potentially breed with each other and produce fertile offspring, they are members of the same species.
Check the space and interbreeding: if the road prevents regular breeding between the two fields, the rabbits in each field may form separate populations.
Make the conclusion: the species exists as at least two populations, each with its own local breeding group.

Gene pools and allele frequencies

An allele is a version of a gene. For example, a gene affecting flower colour might have one allele for purple flowers and one allele for white flowers.

Definition

Gene pool

The gene pool is the total collection of all the alleles of all the genes in a population at a particular time.

Definition

Allele frequency

An allele frequency is the proportion of all copies of a gene in a population that are a particular allele.

gene\text{allele frequency} = \frac{\text{number of copies of the allele}}{\text{total number of allele copies for that gene}}

Allele frequencies are proportions, so they have no units. They can be written as decimals, fractions or percentages, but decimals are usually easiest for Hardy–Weinberg calculations.

Example

Calculating allele frequency from genotype counts

In a population of 100 diploid plants, 20 have genotype RR, 50 have genotype Rr and 30 have genotype rr. Calculate the frequencies of the R and r alleles.

Count the total allele copies: 100 plants each have two copies of the gene, so there are 200 allele copies in total.
Count R alleles: each RR plant contributes two R alleles and each Rr plant contributes one R allele, so $\times 20 + 50 = 90$ R alleles.
Calculate the R allele frequency: $\frac{90}{200} = 0.45$ .
Use the fact that the two allele frequencies must add to 1: $q = 1 - 0.45 = 0.55$ . The r allele frequency is 0.55.

Genotypes, phenotypes and notation

A genotype is the combination of alleles an organism has for a gene, such as AA, Aa or aa. A phenotype is the observable characteristic, such as purple flowers or white flowers.

A homozygous genotype has two identical alleles, such as AA or aa. A heterozygous genotype has two different alleles, such as Aa.

For Hardy–Weinberg questions, the allele frequencies are usually labelled:

$p$ = frequency of one allele, usually the dominant allele
$q$ = frequency of the other allele, usually the recessive allele

Because there are only two alleles in the simple A-Level model:

p + q = 1

Tip

Naming p and q

Always state what $p$ and $q$ represent in the question. The letters are just labels; the biology comes from linking them to the actual alleles.

The Hardy–Weinberg principle

The Hardy–Weinberg principle is a mathematical model. It predicts what happens to allele and genotype frequencies if nothing is causing them to change.

Definition

Hardy–Weinberg principle

The Hardy–Weinberg principle states that allele frequencies in a population will remain constant from generation to generation if certain conditions are met.

The model is useful because it gives a “no change” expectation. If real data do not match Hardy–Weinberg predictions, that suggests at least one assumption may not be true.

Hardy–Weinberg schematic showing a population, gene pool, allele frequencies p and q, genotype frequencies, and assumptions

Conditions for Hardy–Weinberg equilibrium

For the principle to apply, the population should have:

a large population size, so random chance has little effect
random mating, so all genotypes have an equal chance of mating
no natural selection, so no genotype has a survival or reproductive advantage
no mutation, so new alleles are not being produced
no migration, so alleles are not entering or leaving the population

Random changes in allele frequency due to chance are called genetic drift. Genetic drift has a stronger effect in small populations, which is why Hardy–Weinberg assumes a large population.

Key Idea

What equilibrium means

Hardy–Weinberg equilibrium means allele frequencies are not changing between generations. It does not mean every genotype is equally common.

The Hardy–Weinberg equation

If there are two alleles, A and a:

p + q = 1

When gametes combine at random, genotype frequencies are predicted by:

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

The three terms represent:

$p^2$ = frequency of homozygous dominant genotype, AA
$2 pq$ = frequency of heterozygous genotype, Aa
$q^2$ = frequency of homozygous recessive genotype, aa

The $2 pq$ term appears because a heterozygote can be formed in two equivalent ways: A from one parent and a from the other, or a from one parent and A from the other.

Example

Predicting genotype frequencies from allele frequencies

In a population, the frequency of allele A is 0.70 and the frequency of allele a is 0.30. Predict the genotype frequencies.

Assign the allele frequencies: $p = 0.70$ and $q = 0.30$ .
Substitute into the Hardy–Weinberg terms:
$p2=0.702=0.492pq=2×0.70×0.30=0.42q2=0.302=0.09\begin{aligned} p^2 &= 0.70^2 = 0.49 \\ 2pq &= 2 \times 0.70 \times 0.30 = 0.42 \\ q^2 &= 0.30^2 = 0.09 \end{aligned}$
Interpret the results: 0.49 of the population is predicted to be AA, 0.42 is predicted to be Aa and 0.09 is predicted to be aa.
Check the frequencies add to 1: $0.49 + 0.42 + 0.09 = 1.00$ .

Using phenotype data

In many questions, you are not given genotype counts directly. Instead, you may be told the frequency of an observable phenotype.

This is especially useful for recessive phenotypes. If a recessive phenotype only appears in homozygous recessive individuals, then the frequency of that phenotype is $q^2$ .

Tip

Start with the recessive phenotype

If the question gives the frequency of individuals showing a recessive characteristic, treat that frequency as $q^2$ , then square root it to find $q$ .

Example

Calculating carrier frequency from a recessive phenotype

In a population of 10,000 newborns, 25 have a recessive disorder caused by genotype aa. Estimate the number of heterozygous carriers.

The affected newborns are aa, so their frequency is $q^2$ :
$newborns=0.0025q^2 = \frac{25\ \text{newborns}}{10\,000\ \text{newborns}} = 0.0025$
The units cancel, so this is a dimensionless frequency.
Find $q$ and then $p$ :
$q=0.0025=0.05p=1−0.05=0.95\begin{aligned} q &= \sqrt{0.0025} = 0.05 \\ p &= 1 - 0.05 = 0.95 \end{aligned}$
Carriers are heterozygous, so use $2 pq$ :
$\times 0.95 \times 0.05 = 0.095$
Convert the frequency into a number of newborns: $0.095 \times 10\,000 = 950$ . The estimated number of carriers is 950 newborns.

Common Mistake

Using the dominant phenotype incorrectly

The dominant phenotype is not just $p^2$ . It includes both AA and Aa individuals, so its frequency is $p^2 + 2pq$ .

Collecting data from a population

You may be asked how phenotype frequencies could be collected from a single population. The key is to sample fairly from a defined population.

Common Mistake

When the simple equation is not enough

Exam technique

In the exam

Define $p$ and $q$ before calculating, then use $p + q = 1$ to find the missing allele frequency.
If you are given a recessive phenotype frequency, start with $q^2$ , not $q$ .
When interpreting real populations, mention the assumptions: large population, random mating, no selection, no mutation and no migration.

Self review

Check yourself

What is the difference between a species, a population and a gene pool?
If 9% of a population shows a recessive phenotype, what are $q$ , $p$ and $2 pq$ ?
Name two conditions needed for Hardy–Weinberg equilibrium and explain why each matters.

Populations (A-level only)

What you'll learn

Species and populations

Why populations matter

Gene pools and allele frequencies

Genotypes, phenotypes and notation

The Hardy–Weinberg principle

Conditions for Hardy–Weinberg equilibrium

The Hardy–Weinberg equation

Using phenotype data

Collecting data from a population

Recap questions

You've reached the end

Populations (A-level only)

What you'll learn

Species and populations

Why populations matter

Gene pools and allele frequencies

Genotypes, phenotypes and notation

The Hardy–Weinberg principle

Conditions for Hardy–Weinberg equilibrium

The Hardy–Weinberg equation

Using phenotype data

Collecting data from a population

Recap questions

You've reached the end

Populations (A-level only)

What you'll learn

Species and populations

Why populations matter

Gene pools and allele frequencies

Genotypes, phenotypes and notation

The Hardy–Weinberg principle

Conditions for Hardy–Weinberg equilibrium

The Hardy–Weinberg equation

Using phenotype data

Collecting data from a population

Recap questions

You've reached the end

Populations (A-level only) Revision Guide

Populations (A-level only)

What you'll learn

Species and populations

Why populations matter

Gene pools and allele frequencies

Genotypes, phenotypes and notation

The Hardy–Weinberg principle

Conditions for Hardy–Weinberg equilibrium

The Hardy–Weinberg equation

Using phenotype data

Collecting data from a population

Recap questions

You've reached the end

Populations (A-level only) Revision Guide