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2014-01-25T19:11:34Z

24.55.35.201: /* Alcohol content */ Typo? FG should be close to 1, not 0 in wine-making

The '''fixation index''' ('''FST''') is a measure of [[population differentiation]] due to [[genetic structure]]. It is frequently estimated from [[Polymorphism (biology)|genetic polymorphism]] data, such as [[single-nucleotide polymorphism]]s (SNP) or [[Microsatellite (genetics)|microsatellite]]s. Developed as a special case of [[Sewall Wright|Wright's]] [[F-statistics]], it is one of the most commonly used statistics in [[population genetics]].

==Definition==
Two of the most commonly used definitions for FST are based on the variance of [[Allele frequency|allele frequencies]] between populations, and on the probability of [[Identity by descent]].

If <math>\bar{p}</math> is the average frequency of an allele in the total population, <math>\sigma^2_S</math> is the variance in the frequency of alleles in different subpopulations, and <math>\sigma^2_T</math> is the variance of allele frequencies in the total population, FST is defined as <ref>{{Cite journal
| pmid = 19687804
| issn = 1471-0056
| volume = 10
| issue = 9
| pages = 639–650
| last = Holsinger
| first = Kent E.
| coauthors = Bruce S. Weir
| title = Genetics in geographically structured populations: defining, estimating and interpreting FST
| journal = Nat Rev Genet
| year = 2009
| doi = 10.1038/nrg2611
}}</ref>

: <math> F_{ST} = \frac{\sigma^2_S}{\sigma^2_T} = \frac{\sigma^2_S}{\bar{p}(1-\bar{p})}</math>

This definition, which is due to Wright, illustrates that FST measures the amount of genetic variance that can be explained by population structure.

Alternatively,<ref name="Durrett2008">{{cite book|author=Richard Durrett|title=Probability Models for DNA Sequence Evolution|url=http://books.google.com/books?id=o4_bMHy7jFoC|accessdate=25 October 2012|date=12 August 2008|publisher=Springer|isbn=978-0-387-78168-6}}</ref>

: <math> F_{ST} = \frac{f_0-\bar{f}}{1-\bar{f}}</math>

where <math>f_0</math> is the probability of identity by descent of two individuals from the same subpopulation, and <math>\bar{f}</math> is the probability that two individuals from the total population are identical by descent. Using this definition, FST can be interpreted as measuring how much closer two individuals from the same subpopulation are, compared to the total population. If the [[mutation rate]] is small, this interpretation can be made more explicit by linking the probability of identity by descent to [[coalescent theory|coalescent times]]: Let T0 and T denote the average time to coalescence for individuals from the same subpopulation and the total population, respectively. Then,

: <math> F_{ST} \approx 1-\frac{T_0}{T}</math>

This formulation has the advantage that the expected time to coalescence can easily be estimated from genetic data, which led to the development of various estimators for FST.

==Estimation==
In practice, none of the quantities used for the definitions can be easily measured. As a consequence, various estimators have been proposed. A particularly simple estimator applicable to DNA sequence data is:<ref name="Hudson1992">{{Cite journal | last1 = Hudson | first1 = RR. | last2 = Slatkin | first2 = M. | last3 = Maddison | first3 = WP. | title = Estimation of Levels of Gene Flow from DNA Sequence Data | journal = Genetics | volume = 132 | issue = 2 | pages = 583–9 |date=Oct 1992 | doi = | pmid = 1427045 | pmc = 1205159 }}</ref>

: <math> F_{ST} = \frac{ \pi_\text{Between} - \pi_\text{Within} } { \pi_\text{Between} } </math>

where <math> \pi_\text{Between} </math> and <math> \pi_\text{Within} </math> represent the [[Nucleotide diversity|average number of pairwise differences]] between two individuals sampled from different sub-populations (<math> \pi_\text{Between} </math>) or from the same sub-population (<math> \pi_\text{Within}</math>). The average pairwise difference within a population can be calculated as the sum of the pairwise differences divided by the number of pairs. However, this estimator is biased when sample sizes are small or if they vary between populations. Therefore, more elaborate methods are used to compute FST in practice. Two of the most widely used procedures are the estimator by Weir & Cockerham (1984),<ref name="WeirCockerham1984">{{cite journal|last1=Weir|first1=B. S.|last2=Cockerham|first2=C. Clark|title=Estimating F-Statistics for the Analysis of Population Structure|journal=Evolution|volume=38|issue=6|year=1984|pages=1358|issn=00143820|doi=10.2307/2408641}}</ref> or performing an [[Analysis of molecular variance]]. A list of implementations is available at the end of this article.

==Interpretation==
This comparison of genetic variability within and between populations is frequently used in applied [[population genetics]]. The values range from 0 to 1. A zero value implies complete [[Panmixia|panmixis]]; that is, that the two populations are interbreeding freely. A value of one implies that all genetic variation is explained by the population structure, and that the two populations do not share any genetic diversity.

For idealized models such as Wright's finite island model, FST can be used to estimate migration rates. Under that model, the migration rate is

: <math>\hat{M}\approx\frac{1}{2}\left (\frac{1}{F_{ST}} -1 \right ) </math>.

The interpretation of FST can be difficult when the data analyzed are highly polymorphic. In this case, the probability of identity by descent is very low and FST can have an arbitrarily low upper bound, which might lead to misinterpretation of the data. Also, strictly speaking FST is not a genetic distance, as it does not satisfy the [[triangle inequality]]. As a consequence new tools for measuring genetic differentiation continue being developed.

==FST in humans==

The [[International HapMap Project]] estimated FST for three human populations using SNP data. Across the [[autosome]]s, FST was estimated to be 0.12. The significance of this FST value in humans is contentious. As an FST of zero indicates no divergence between populations, whereas an FST of one indicates complete isolation of populations, [[Anthropologists]] often cite Lewontin's 1972 work which came to a similar value and interpreted this number as meaning there was little biological differences between human races.<ref>{{Cite journal
| volume = 6
| issue = 38
| pages = 381–398
| last = Lewontin | first = Richard C. | authorlink = Richard Lewontin
| title = The apportionment of human diversity
| journal = Evolutionary biology
| year = 1972
}}</ref> On the other hand, while an FST value of 0.12 is lower than that found between populations of many other species, [[Henry Harpending]] argued that this value implies on a world scale a "kinship between two individuals of the same human population is equivalent to kinship between grandparent and grandchild or between half siblings".<ref>{{Cite journal
| doi = 10.1023/A:1020815420693
| volume = 24
| issue = 2
| pages = 141–147
| last = Harpending | first = Henry
| title = Kinship and Population Subdivision
| journal = [[Population & Environment]]
| date = 2002-11-01
| jstor = 27503827
| url = http://www.humanbiologicaldiversity.com/articles/Harpending,%20Henry.%20%22Kinship%20and%20Population%20Subdivision.%22%20Population%20and%20Environment%2024,%20no.%202%20(2002).pdf
}}</ref>

===Autosomal genetic distances based on SNPs===

{| class="wikitable" style="text-align:center; width:80%;"
|+ Intercontinental autosomal genetic distances based on SNPs<ref name="nelis">{{Cite journal
| doi = 10.1371/journal.pone.0005472
| volume = 4
| issue = 5
| pmc = 2675054
| pages = e5472
| last = Nelis
| pmid = 19424496
| first = Mari
| coauthors = et al
| title = Genetic Structure of Europeans: A View from the North–East
| journal = PLoS ONE
| date = 2009-05-08
| bibcode=2009PLoSO...4.5472N
| editor1-last = Fleischer
| editor1-first = Robert C.
}}, [http://www.plosone.org/article/fetchSingleRepresentation.action?uri=info:doi/10.1371/journal.pone.0005472.s003 see table]</ref>
|-
! scope=col |
! scope=col |Europe (CEU)
! scope=col |Sub-Saharan Africa (Yoruba)
! scope=col |East-Asia (Japanese)
|-
! scope=row |Sub-Saharan Africa (Yoruba)
|0.153
|
|
|-
! scope=row |East-Asia (Japanese)
|0.111
|0.190
|
|-
! scope=row |East-Asia (Chinese)
|0.110
|0.192
|0.007
|-
|}

{| class="wikitable" style="text-align:center; width:80%;"
|+ Intra-European/mediterranean autosomal genetic distances based on SNPs<ref name="nelis"/><ref>{{Cite journal
| doi = 10.2119/molmed.2009.00094
| issn = 1076-1551
| volume = 15
| issue = 11-12
| pages = 371–383
| last = Tian
| journal = Molecular Medicine
| first = Chao
| coauthors = et al.
| title = European Population Genetic Substructure: Further Definition of Ancestry Informative Markers for Distinguishing among Diverse European Ethnic Groups
| date = November 2009
| pmid=19707526
| pmc=2730349
}}, [http://www.ncbi.nlm.nih.gov/pmc/articles/PMC2730349/table/t1-09_94_tian/ see table]</ref>
|-
! scope=col |
! scope=col | Italians
! scope=col | Palestinians
! scope=col | Swedish
! scope=col | Finns
! scope=col | Spanish
! scope=col | Germans
! scope=col | Russians
! scope=col | French
! scope=col | Greeks
|-
! scope=row | Palestinians
|0.0064
|
|
|
|
|
|
|
|
|-
! scope=row |Swedish
|0.0064-0.0090
|0.0191
|
|
|
|
|
|
|
|-
! scope=row |Finns
|0.0130-0.0230
|
|0.0050-0.0110
|
|
|
|
|
|
|-
! scope=row |Spanish
|0.0010-0.0050
|0.0101
|0.0040-0055
|0.0110-0.0170
|
|
|
|
|
|-
! scope=row |Germans
|0.0029-0.0080
|0.0136
|0.0007-0.0010
|0.0060-0.0130
|0.0015-0.0030
|
|
|
|
|-
! scope=row |Russians
|0.0088-0.0120
|0.0202
|0.0030-0.0036
|0.0060-0.0120
|0.0070-0.0079
|0.0030-0.0037
|
|
|
|-
! scope=row |French
|0.0030-0.0050
|
|0.0020
|0.0080-0.0150
|0.0010
|0.0010
|0.0050
|
|
|-
! scope=row |Greeks
|0.0000
|0.0057
|0.0084
|
|0.0035
|0.0039
|0.0108
|
|
|-
|}

==Programs for calculating FST==

* [[Arlequin]]
* [[FSTAT (software)|Fstat]]
* [http://people.bu.edu/ngcrawfo/smogd/ SMOGD]<ref>{{cite doi|10.1111/j.1755-0998.2009.02801.x}}</ref>
* [http://cran.r-project.org/web/packages/diveRsity/index.html diveRsity]
* [http://i122server.vu-wien.ac.at/MSA/info.html/MSA_info.html Microsatellite Analyzer (MSA)]
* [http://vcftools.sourceforge.net/index.html VCFtools]

==Modules for calculating FST==
* [[#External_links|BioPerl]]
* [http://cran.r-project.org/web/packages/hierfstat/index.html hierfstat (R package)]

==References==
<references/>

===Further reading===
{{refbegin}}
* Evolution and the Genetics of Populations Volume 2: the Theory of Gene Frequencies, pg 294–295, S. Wright, Univ. of Chicago Press, Chicago, 1969
* A haplotype map of the human genome, The International HapMap Consortium, Nature 2005
{{refend}}

==External links==
* [http://www.bioperl.org/wiki/HOWTO:PopGen#Population_Statistics_using_Bio::PopGen::PopStats BioPerl - Bio::PopGen::PopStats]

{{Population genetics}}

{{DEFAULTSORT:Fixation Index}}
[[Category:Population genetics]]

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Gravity (alcoholic beverage)