Genotype Frequency
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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.

## Numerical example

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

{\displaystyle {\begin{aligned}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{aligned}}}

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).

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

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

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

If p=0.7 and q=0.3, then

${\displaystyle f(\mathbf {AA} )=p^{2}}$ = (0.7)2 = 0.49
${\displaystyle f(\mathbf {Aa} )=2pq}$ = 2×(0.7)×(0.3) = 0.42
${\displaystyle f(\mathbf {aa} )=q^{2}}$ = (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. (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.
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, Stiling P (2011). Biology (2nd ed.). New York: McGraw-Hill. ISBN 978-0-07-353221-9.