Editing F-statistics (section)

== Fixation index ==
{{main|Fixation index}}

A reformulation of the definition of <math>F</math> would be the ratio of the average number of differences between pairs of chromosomes sampled within diploid individuals with the average number obtained when sampling chromosomes randomly from the population (excluding the grouping per individual).
One can modify this definition and consider a grouping per sub-population instead of per individual. Population geneticists have used that idea to measure the degree of structure in a population.

Unfortunately, there is a large number of definitions for [[Fixation index|<math>F_{ST}</math>]], causing some confusion in the scientific literature. A common definition is the following:

: <math> F_{ST} = \frac{\operatorname{var}(\mathbf{p})}{p\,(1 - p)} \!</math>

where the variance of <math>\mathbf{p}</math> is computed across sub-populations and  <math>p\,(1 - p)</math> is the expected frequency of heterozygotes.

=== Fixation index in human populations ===

It is well established that the genetic diversity among human populations is low,<ref>{{cite journal |doi=10.1038/nrg2611 |title=Genetics in geographically structured populations: Defining, estimating and interpreting FST |year=2009 |last1=Holsinger |first1=Kent E. |last2=Weir |first2=Bruce S. |journal=Nature Reviews Genetics |volume=10 |issue=9 |pages=639–50 |pmid=19687804|pmc=4687486 }}</ref> although the distribution of the genetic diversity was only roughly estimated. Early studies argued that 85–90% of the genetic variation is found within individuals residing in the same populations within continents (intra-continental populations) and only an additional 10–15% is found between populations of different continents (continental populations).<ref>{{cite book |author=Lewontin |chapter=The Apportionment of Human Diversity |title=Evolutionary Biology |volume=6 |pages=381–98 |year=1972 |doi=10.1007/978-1-4684-9063-3_14 |isbn=978-1-4684-9065-7}}</ref><ref>{{cite journal |first1=Anne M. |last1=Bowcock |first2=Judith R. |last2=Kidd |first3=Joanna L. |last3=Mountain |first4=Joan M. |last4=Herbert |first5=Luciano |last5=Carotenuto |first6=Kenneth K. |last6=Kidd |first7=Luca |last7=Cavalli-Sforza |bibcode=1991PNAS...88..839B |doi=10.1073/pnas.88.3.839 |jstor=2356081 |title=Drift, admixture, and selection in human evolution: A study with DNA polymorphisms |year=1991 |journal=Proceedings of the National Academy of Sciences |volume=88 |issue=3 |pages=839–43 |pmid=1992475 |pmc=50909|doi-access=free }}</ref><ref>{{cite journal |pmid=9114021 |year=1997 |last1=Barbujani |first1=Guido |last2=Magagni |first2=Arianna |last3=Minch |first3=Eric |last4=Cavalli-Sforza |first4=L. Luca |title=An apportionment of human DNA diversity |volume=94 |issue=9 |pages=4516–9 |pmc=20754 |journal=Proceedings of the National Academy of Sciences of the United States of America |doi=10.1073/pnas.94.9.4516 |jstor=42042 |bibcode=1997PNAS...94.4516B|doi-access=free }}</ref><ref>{{cite journal |doi=10.1086/302825 |title=The Distribution of Human Genetic Diversity: A Comparison of Mitochondrial, Autosomal, and Y-Chromosome Data |year=2000 |last1=Jorde |first1=L.B. |last2=Watkins |first2=W.S. |last3=Bamshad |first3=M.J. |last4=Dixon |first4=M.E. |last5=Ricker |first5=C.E. |last6=Seielstad |first6=M.T. |last7=Batzer |first7=M.A. |journal=The American Journal of Human Genetics |volume=66 |issue=3 |pages=979–88 |pmid=10712212 |pmc=1288178}}</ref><ref>{{cite journal |doi=10.1038/ng1435 |title=Genetic variation, classification and 'race' |year=2004 |last1=Jorde |first1=Lynn B |last2=Wooding |first2=Stephen P |journal=Nature Genetics |volume=36 |issue=11s |pages=S28-33 |pmid=15508000|doi-access=free }}</ref> Later studies based on hundreds of thousands [[single-nucleotide polymorphism]] (SNPs) suggested that the genetic diversity between continental populations is even smaller and accounts for 3 to 7%<ref>{{cite journal |doi=10.1007/s10038-006-0041-1 |title=Similarity of the allele frequency and linkage disequilibrium pattern of single nucleotide polymorphisms in drug-related gene loci between Thai and northern East Asian populations: Implications for tagging SNP selection in Thais |year=2006 |last1=Mahasirimongkol |first1=Surakameth |last2=Chantratita |first2=Wasun |last3=Promso |first3=Somying |last4=Pasomsab |first4=Ekawat |last5=Jinawath |first5=Natini |last6=Jongjaroenprasert |first6=Wallaya |last7=Lulitanond |first7=Viraphong |last8=Krittayapoositpot |first8=Phanida |last9=Tongsima |first9=Sissades |display-authors= 4 |journal=Journal of Human Genetics |volume=51 |issue=10 |pages=896–904 |pmid=16957813|doi-access=free }}</ref><ref>{{cite journal |doi=10.1186/1471-2156-9-54 |title=Population substructure in Finland and Sweden revealed by the use of spatial coordinates and a small number of unlinked autosomal SNPs |year=2008 |last1=Hannelius |first1=Ulf |last2=Salmela |first2=Elina |last3=Lappalainen |first3=Tuuli |last4=Guillot |first4=Gilles |last5=Lindgren |first5=Cecilia M |last6=Von Döbeln |first6=Ulrika |last7=Lahermo |first7=Päivi |last8=Kere |first8=Juha |journal=BMC Genetics |volume=9 |pages=54 |pmid=18713460 |pmc=2527025 |doi-access=free }}</ref><ref>{{cite journal |doi=10.1016/j.cub.2008.07.049 |title=Correlation between Genetic and Geographic Structure in Europe |year=2008 |last1=Lao |first1=Oscar |last2=Lu |first2=Timothy T. |last3=Nothnagel |first3=Michael |last4=Junge |first4=Olaf |last5=Freitag-Wolf |first5=Sandra |last6=Caliebe |first6=Amke |last7=Balascakova |first7=Miroslava |last8=Bertranpetit |first8=Jaume |last9=Bindoff |first9=Laurence A. |display-authors= 4 |journal=Current Biology |volume=18 |issue=16 |pages=1241–8 |pmid=18691889|doi-access=free |bibcode=2008CBio...18.1241L }}</ref><ref>{{cite journal |doi=10.1016/j.ajhg.2009.04.015 |title=Genome-wide Insights into the Patterns and Determinants of Fine-Scale Population Structure in Humans |year=2009 |last1=Biswas |first1=Shameek |last2=Scheinfeldt |first2=Laura B. |last3=Akey |first3=Joshua M. |journal=The American Journal of Human Genetics |volume=84 |issue=5 |pages=641–650 |pmid=19442770 |pmc=2681007}}</ref><ref>{{cite journal |doi=10.1371/journal.pone.0005472 |title=Genetic Structure of Europeans: A View from the North–East |year=2009 |editor1-last=Fleischer |editor1-first=Robert C |last1=Nelis |first1=Mari |last2=Esko |first2=Tõnu |last3=Mägi |first3=Reedik |last4=Zimprich |first4=Fritz |last5=Zimprich |first5=Alexander |last6=Toncheva |first6=Draga |last7=Karachanak |first7=Sena |last8=Piskácková |first8=Tereza |last9=Balašcák |first9=Ivan |display-authors= 4 |journal=PLOS ONE |volume=4 |issue=5 |pages=e5472 |pmid=19424496 |pmc=2675054|bibcode = 2009PLoSO...4.5472N |doi-access=free }}</ref><ref>{{cite journal |doi=10.1038/nature08365 |title=Reconstructing Indian population history |year=2009 |last1=Reich |first1=David |last2=Thangaraj |first2=Kumarasamy |last3=Patterson |first3=Nick |last4=Price |first4=Alkes L. |last5=Singh |first5=Lalji |display-authors= 4 |journal=Nature |volume=461 |issue=7263 |pages=489–94 |pmid=19779445 |pmc=2842210|bibcode = 2009Natur.461..489R }}</ref> A later study based on three million SNPs found that 12% of the genetic variation is found between continental populations and only 1% within them.<ref>{{cite journal |year=2012 |last1=Elhaik |first1=E |title=Empirical Distributions of FST from Large-Scale Human Polymorphism Data |volume=7 |issue=11 |pages=e49837 |pmc=3504095 |journal=PLOS ONE |doi=10.1371/journal.pone.0049837 |pmid=23185452|bibcode=2012PLoSO...749837E |doi-access=free }}</ref> Most of these studies have used the [[Fixation index|''F''<sub>''ST''</sub>]] statistics <ref>{{cite journal |first1=Sewall |last1=Wright |year=1965 |title=The Interpretation of Population Structure by F-Statistics with Special Regard to Systems of Mating |journal=Evolution |volume=19 |issue=3 |pages=395–420 |jstor=2406450 |doi=10.2307/2406450}}</ref> or closely related statistics.<ref>{{cite journal |doi=10.1080/00071669108417396 |title=Long-term goose breeding for egg production and crammed liver weight |year=1991 |last1=Shalev |first1=B. A. |last2=Dvorin |first2=A. |last3=Herman |first3=R. |last4=Katz |first4=Z. |last5=Bornstein |first5=S. |journal=British Poultry Science |volume=32 |issue=4 |pages=703–9 |pmid=1933444}}</ref><ref>{{cite journal |pmid=1644282 |year=1992 |last1=Excoffier |first1=L |last2=Smouse |first2=PE |last3=Quattro |first3=JM |title=Analysis of molecular variance inferred from metric distances among DNA haplotypes: Application to human mitochondrial DNA restriction data |volume=131 |issue=2 |pages=479–91 |pmc=1205020 |journal=Genetics|doi=10.1093/genetics/131.2.479 }}</ref>