Editing Genotype frequency

[[File:De Finetti diagram.svg|thumb|right|A [[De Finetti diagram]] visualizing genotype frequencies as distances to triangle edges x (AA), y (Aa) and z (aa) in a [[ternary plot]]. The curved line are the [[Hardy–Weinberg equilibrium|Hardy–Weinberg equilibria]].]]
[[File:Hardy–Weinberg law - Punnett square.svg|thumb|right|A [[Punnett square]] visualizing the genotype frequencies of a [[Hardy–Weinberg equilibrium]] as areas of a square. ''p'' (A) and ''q'' (a) are the [[allele frequencies]].]]
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.<ref>Brooker R, Widmaier E, Graham L, and Stiling P. ''Biology'' (2011): p. 492</ref> '''Genotype frequency''' in a population is the number of individuals with a given [[genotype]] divided by the total number of individuals in the population.<ref>Brooker R, Widmaier E, Graham L, and Stiling P. ''Biology'' (2011): p. G-14</ref>    
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<ref>{{cite web|last=Janssens|title=Genomic profiling: the critical importance of genotype frequency|url=http://www.phgfoundation.org/news/3740/|publisher=PHG Foundation|display-authors=etal}}</ref>  or even a birth defect.<ref>{{cite journal|last=Shields|title=Neural Tube Defects: an Evaluation of Genetic Risk|journal=American Journal of Human Genetics|volume=64|issue=4|pages=1045–1055|display-authors=etal|pmc=1377828|year=1999|pmid=10090889|doi=10.1086/302310}}</ref> It can also be used to determine ethnic diversity.

Genotype frequencies may be represented by a [[De Finetti diagram]].

==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

: <math>
\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}
</math>

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).

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

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

=== Equilibrium ===
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:
<br />
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%.<ref>Brooker R, Widmaier E, Graham L, and Stiling P. ''Biology'' (2011): p. 492</ref>

For a [[gene]] that exists in two alleles, the Hardy–Weinberg equation states that '''(''p''<sup>2</sup>)&nbsp;+&nbsp;(2''pq'')&nbsp;+&nbsp;(''q''<sup>2</sup>)&nbsp;=&nbsp;1'''.
If we apply this equation to our flower color gene, then

:<math>f(\mathbf{AA}) = p^2</math> (genotype frequency of homozygotes)
:<math>f(\mathbf{Aa}) = 2pq</math> (genotype frequency of heterozygotes)
:<math>f(\mathbf{aa}) = q^2</math> (genotype frequency of homozygotes)

If '''p'''=0.7 and '''q'''=0.3, then
<br />
:<math>f(\mathbf{AA}) = p^2</math> = (0.7)<sup>2</sup> = 0.49
:<math>f(\mathbf{Aa}) = 2pq</math> = 2×(0.7)×(0.3) = 0.42
:<math>f(\mathbf{aa}) = q^2</math> = (0.3)<sup>2</sup> = 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%.<ref>Brooker R, Widmaier E, Graham L, and Stiling P. ''Biology'' (2011): p. 493</ref>

==References==
{{Reflist}}

==Notes==
* {{Cite book |vauthors=Brooker R, Widmaier E, Graham L, Stiling P |title=Biology |edition=2nd |year=2011 |isbn=978-0-07-353221-9 |publisher=McGraw-Hill |location=New York}}

{{Population genetics}}

{{DEFAULTSORT:Genotype Frequency}}
[[Category:Genetics concepts]]
[[Category:Population genetics]]