Investigations to mimic the effects of?random sampling?on?allele frequencies?in a population can be devised using coloured beads, marbles or even sweets

An example of one such investigation is described below

Apparatus

24 beads in one colour and 24 beads in a different colour

Jar or container

Paper

Pencil

Calculator

Method

Place 24 red beads and 24 white beads in a container

Red beads represent a?dominant?allele (R)

White beads represent a?recessive?allele (r)

Shake the container to ensure the beads are well mixed

Carry out a?random?'mating' by drawing out two beads?without looking

Each pair of beads drawn represents the fusing of a pair of?sex cells?containing either?red?or?white?alleles

Carry out 24 of these random 'matings' and note down the?genotype?of each offspring

Ensure you place the beads?back into the container?after each draw

The theoretical offspring genotype ratio (also known as the expected genotype ratio) if thousands of draws are made and there is no genetic drift should be?1:2:1

RR?=?25%?(chance of drawing two red beads in a row)

Rr?=?50%?(chance of drawing a red bead then a white bead or a white bead then a red bead)

rr?=?25%?(chance of drawing two white beads in a row)

A table of these theoretical results (for 24 random 'matings') is shown below:

Results

However, the?chances?of drawing exactly six double red beads (RR), twelve red and white beads (Rr) and six double white beads (rr), as shown in the table above, are?very small

The effects of?chance?can mean that the offspring genotype ratio is likely to?differ?from the?theoretical?1:2:1?offspring genotype ratio

This change in the expected offspring genotype ratio that occurs in a small breeding population is known as?genetic drift

The table below shows some?example results?from 24 random '"matings"

If these results now represent the alleles in a?new population, the ratio of red and white alleles are different from the 24 red alleles and 24 white alleles in the original population:

Number of red alleles in new population = 5 x 2 (from RR) + 7 (from Rr) = 17

Number of white alleles in new population = 12 x 2 (from rr) + 7 (from Rr) = 31

As the?white?allele frequency has?increased?to 31 and the?red?allele frequency has?decreased?to 17,?genetic drift?has occurred

If 24 more random 'matings' are now carried out from the?new population?(i.e. by placing 17 red beads and 31 white beads in the container), the effect of genetic drift on the?allele frequencies?in the population can become?even greater

The table below shows some example results from this second round of 24 random 'matings'

Number of red alleles in new population = 4 x 2 (from RR) + 5 (from Rr) = 13

Number of white alleles in new population = 15 x 2 (from rr) + 5 (from Rr) = 35

As the?white?allele frequency has now?further increased?to 35 and the?red?allele frequency has now?further decreased?to 13,?an even greater amount of genetic drift has occurred

Using some simple maths, experiments like the one described above can be used to demonstrate genetic drift by?calculating?how?allele frequencies change?in a small population over?multiple generations

For example, it is possible to calculate how the?percentage frequency?of the alleles in the population changes?between generations:

In the first generation (original population) there were 24 red alleles and 24 white alleles. This means the percentage allele frequencies were:

(24 ÷ 48) × 100 =?50% red?alleles

(24 ÷ 48) × 100 =?50% white?alleles

In the?second?generation (after the first round of 'matings') there were 17 red alleles and 31 white alleles. This means the percentage allele frequencies were:

(17 ÷ 48) × 100 =?35.4% red?alleles

(31 ÷ 48) × 100 =?64.6% white?alleles

This means that in one generation the frequency of red alleles?decreased?by?14.6%?and the frequency of white alleles?increased?by?14.6%

In the?third?generation (after the second round of 'matings') there were 13 red alleles and 35 white alleles. This means the percentage allele frequencies were:

(13 ÷ 48) × 100 =?27.1%?red?alleles

(35 ÷ 48) × 100 =?72.9% white?alleles

This means that in two generations (i.e. compared to the starting population before any 'matings' were carried out) the frequency of red alleles?decreased?by?22.9%?and the frequency of white alleles?increased?by?22.9%