# Genotype frequency

Jump to: navigation, search

Genetic variation in populations can be analyzed and quantified by the frequency of alleles. Two fundamental calculations are central to population genetics: allele frequencies and genotype frequencies.[1] Genotype frequency in a population is the number of individuals with a given genotype divided by the total number of individuals in the population.[2] In population genetics, the genotype frequency is the frequency or proportion (i.e., 0 < f < 1) of genotypes in a population.

Although allele and genotype frequencies are related, it is important to clearly distinguish them.

Genotype frequency may also be used in the future (for "genomic profiling") to predict someone's having a disease[3] or even a birth defect.[4] It can also be used to determine ethnic diversity.

## Numerical example

As an example, let's consider a population of 100 four-o-'clock plants (Mirabilis jalapa) with the following genotypes:

• 49 red-flowered plants with the genotype AA
• 42 pink-flowered plants with genotype Aa
• 9 white-flowered plants with genotype aa

When calculating an allele frequency for a diploid species, remember that homozygous individuals have two copies of an allele, whereas heterozygotes have only one. In our example, each of the 42 pink-flowered heterozygotes has one copy of the a allele, and each of the 9 white-flowered homozygotes has two copies. Therefore, the allele frequency for a (the white color allele) equals

\begin{align} f({a}) & = { (Aa) + 2 \times (aa) \over 2 \times (AA) + 2 \times (Aa) + 2 \times (aa)} = { 42 + 2 \times 9 \over 2 \times 49 + 2 \times 42 + 2 \times 9 } = { 60 \over 200 } = 0.3 \\ \end{align}

This result tells us that the allele frequency of a is 0.3. In other words, 30% of the alleles for this gene in the population are the a allele.

Compare genotype frequency: let's now calculate the genotype frequency of aa homozygotes (white-flowered plants).

\begin{align} f({aa}) & = { 9 \over 49 + 42 + 9 } = { 9 \over 100 } = 0.09 = (9\%) \\ \end{align}

Allele and genotype frequencies always sum to less than or equal to one (in other words, less than or equal to 100%).

The Hardy–Weinberg law describes the relationship between allele and genotype frequencies when a population is not evolving. Let's examine the Hardy–Weinberg equation using the population of four-o'clock plants that we considered above:
if the allele A frequency is denoted by the symbol p and the allele a frequency denoted by q, then p+q=1. For example, if p=0.7, then q must be 0.3. In other words, if the allele frequency of A equals 70%, the remaining 30% of the alleles must be a, because together they equal 100%.[5]

For a gene that exists in two alleles, the Hardy–Weinberg equation states that (p2) + (2pq) + (q2) = 1
If we apply this equation to our flower color gene, then

$f(\mathbf{AA}) = p^2$ (genotype frequency of homozygotes)
$f(\mathbf{Aa}) = 2pq$ (genotype frequency of heterozygotes)
$f(\mathbf{aa}) = q^2$ (genotype frequency of homozygotes)

If p=0.7 and q=0.3, then

$f(\mathbf{AA}) = p^2$ = (0.7)2 = 0.49
$f(\mathbf{Aa}) = 2pq$ = 2×(0.7)×(0.3) = 0.42
$f(\mathbf{aa}) = q^2$ = (0.3)2 = 0.09

This result tells us that, if the allele frequency of A is 70% and the allele frequency of a is 30%, the expected genotype frequency of AA is 49%, Aa is 42%, and aa is 9%.[6]

A de Finetti diagram. The curved line is the expected Hardy–Weinberg frequency as a function of p.

Genotype frequencies may be represented by a De Finetti diagram.

## References

1. ^ Brooker R, Widmaier E, Graham L, and Stiling P. Biology (2011): p. 492
2. ^ Brooker R, Widmaier E, Graham L, and Stiling P. Biology (2011): p. G-14
3. ^ Janssens et al. "Genomic profiling: the critical importance of genotype frequency". PHG Foundation.
4. ^ Shields et al. "Neural Tube Defects: an Evaluation of Genetic Risk" (PDF).
5. ^ Brooker R, Widmaier E, Graham L, and Stiling P. Biology (2011): p. 492
6. ^ Brooker R, Widmaier E, Graham L, and Stiling P. Biology (2011): p. 493

## Notes

• Brooker R, Widmaier E, Graham L, and Stiling P (2011). Biology (2nd ed.). New York: McGraw-Hill. ISBN 978-0-07-353221-9.