Genetic Drift: Random Sampling

Genetic Drift

Genetic drift is the random sampling of alleles in a population. That is to say, the frequency of a particular allele in relation to its counterpart is not determined by natural selection, but by chance.

In population genetics,

• evolution is defined as as the change in allele frequencies in a population over generations. Two evolutionary mechanisms are:
  • natural selection, defined  as the change in allele frequencies in a population over generations as a result of their fitness for reproduction.
  • genetic drift, defined as the change in allele frequencies in a population over generations due to random sampling, leading to loss of genetic variation.

Genetic drift occurs in all non-infinite populations, but its effects are more clearly apparent in small populations. The 'drift' in genetic drift can be explained most easily with an example:

Given two alleles of a gene coding for fur colour, B and b, either may move (drift) towards:

• Fixation — only B survives (or vice-versa).
• Loss — b becomes extinct (or vice-versa).

To reiterate: whichever allele drifts to fixation or loss is a matter of chance, not of natural selection. The surviving allele could be detrimental or beneficial (or neither) towards the adaptability of the phenotype to its environment.

Causes

As mentioned, genetic drift occurs most markedly in small populations. The events that produce small populations are of two main kinds:

1) The Bottleneck Effect

Some kind of catastrophic event occurs, killing off a large percentage of a population. Subsequent generations will have a much smaller allele pool to draw from, and chance events (e.g. reproductory success) can lead to the disappearance of a particular allele from the population within a few generations.

2) The Founder effect

A small part of a population breaks off from the main body and becomes isolated from it. The frequencies of the alleles in this much reduced allele pool will now be subject to chance and, as in the bottleneck effect, their drift towards fixation or loss in subsequent generations will become more likely.

An Example

Assumption: after each round of reproduction, the previous generation dies out.

Generation One (following a bottleneck or founder effect)

A small population of 10 rabbits is made up of:

• 8 individuals with black fur (genotype BB or Bb) and
• 2 individuals with brown fur (genotype bb).

• P (B allele frequency) = 0.5
• q (b allele frequency) = 0.5

Generation 2

The population is now made up of:

• 9 individuals with black fur (genotype BB or Bb) and
• 1 individual with brown fur (genotype bb).

• P (B allele frequency) = 0.65
• q (b allele frequency) = 0.35

Generation 3

The population is now made up of:

• 10 individuals with black fur (genotype BB or Bb) and
• 0 individuals with brown fur (genotype bb).

• P (B allele frequency) = 1
• q (b allele frequency) = 0

The fact that five pairs of rabbits reproduced in the first generation and only one pair reproduced in the second was purely a matter of chance.

However, if the first generation population had been much larger, say a thousand rabbits rather than ten, there would have initially been two hundred rabbits with the bb genotype rather than two, and the likelihood that none of these rabbits would have passed on their genes to the third generation would have been much smaller.

The drift towards the fixation or loss of alleles in small populations reflects the law of large numbers.

The law of large numbers

The law of large numbers states that in the long run random events tend to average out at the expected value.

Example: tossing a coin

There are two sides to a coin so the probability of heads landing is 50% and the probability of tails landing is also 50%. The expected value is therefore 0.5.

However, if we tossed the coin only ten times, we wouldn't be surprised if heads landed 70% of the time and tails 30% of the time, or even 100% and 0% of the time.

On the other hand, if we tossed the coin a million times, we would be very surprised if we obtained these ranges of values. It is much more likely that the result would be very close to 50% for either side, i.e. close to the expected value of 0.5. (As up to ten simulations can be run at the same time, drifting to both fixation and loss may be seen as possible outcomes in the same chart.)

Returning to the earlier example, if the rabbit population size had been made up of hundreds of thousands of individuals, instead of only ten, the initial frequencies of 0.5 for the P (B allele) and q (b allele) would have shown little variation over many generations.

Simulating Genetic Drift

The charts simulate the possible frequencies of one allele, B, having an initial frequency of 0.5, over a selected number of generations at different population sizes. Allele B's corresponding allele, b, is not shown but its fate can be inferred from the results:

• If the line goes to the top of the x-axis (1.0) and flattens out, B has drifted to fixation (it is the only surviving allele) and b has drifted to loss (it has gone extinct),
• If the line goes to the bottom of the x-axis (0.0) and flattens out, B has drifted to loss and b has drifted to fixation.

Sample Results

Below are three screenshots of charts showing ten simulations with different population sizes, over fifty generations.

Population: 20

Population: 200

Population: 2000