# Genotype frequency

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.

Genotype frequencies may be represented by a De Finetti diagram.

## Numerical example[edit]

As an example, 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

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).

Allele and genotype frequencies always sum to one (100%).

### Equilibrium[edit]

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 **( p^{2}) + (2pq) + (q^{2}) = 1**.
If we apply this equation to our flower color gene, then

- (genotype frequency of homozygotes)
- (genotype frequency of heterozygotes)
- (genotype frequency of homozygotes)

If **p**=0.7 and **q**=0.3, then

- = (0.7)
^{2}= 0.49 - = 2×(0.7)×(0.3) = 0.42
- = (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]}

## References[edit]

**^**Brooker R, Widmaier E, Graham L, and Stiling P.*Biology*(2011): p. 492**^**Brooker R, Widmaier E, Graham L, and Stiling P.*Biology*(2011): p. G-14**^**Janssens; et al. "Genomic profiling: the critical importance of genotype frequency". PHG Foundation.**^**Shields; et al. (1999). "Neural Tube Defects: an Evaluation of Genetic Risk".*American Journal of Human Genetics*.**64**(4): 1045–1055. doi:10.1086/302310. PMC 1377828. PMID 10090889.**^**Brooker R, Widmaier E, Graham L, and Stiling P.*Biology*(2011): p. 492**^**Brooker R, Widmaier E, Graham L, and Stiling P.*Biology*(2011): p. 493

## Notes[edit]

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