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Genetic variation in [[population]]s 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 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 et al.|title=Genomic profiling: the critical importance of genotype frequency|url=http://www.phgfoundation.org/news/3740/|publisher=PHG Foundation}}</ref> or even a birth defect.<ref>{{cite web|last=Shields et al.|title=Neural Tube Defects: an Evaluation of Genetic Risk|url=http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1377828/pdf/10090889.pdf}}</ref> 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 | |||
: <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 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: | |||
<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> | |||
<br /> | |||
For a [[gene]] that exists in two alleles, the Hardy-Weinberg equation states that '''(''p''<sup>2</sub>) + (2''pq'') + (''q''<sup>2</sup>) = 1''' | |||
<br /> | |||
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> | |||
[[File:De Finetti diagram.svg|thumb|right|A de Finetti diagram. The curved line is the expected [[Hardy-Weinberg principle|Hardy-Weinberg frequency]] as a function of ''p''.]] | |||
Genotype frequencies may be represented by a [[De Finetti diagram]]. | |||
==References== | |||
{{Reflist}} | |||
==Notes== | |||
* {{Cite book |author=Brooker R, Widmaier E, Graham L, and Stiling P |title=Biology |edition=2nd |year=2011 |isbn=978-0-07-353221-9 |publisher=McGraw-Hill |location=New York}} | |||
{{DEFAULTSORT:Genotype Frequency}} | |||
[[Category:Population genetics]] | |||
Latest revision as of 12:33, 7 March 2013
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 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
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 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
- (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]
Genotype frequencies may be represented by a De Finetti diagram.
References
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Notes
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- ↑ 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
- ↑ Template:Cite web
- ↑ Template:Cite web
- ↑ 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