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| '''Genetic distance''' refers to the [[genetics|genetic]] divergence between [[species]] or between [[population#genetics|populations]] within a species. Smaller genetic distances indicate that the populations have more similar genes. This indicates that they are closely related i.e. that they have a recent [[common ancestor]] or recent interbreeding has taken place. Genetic distance is useful in reconstructing the history of populations. For example, evidence from genetic distance suggests that humans arrived in America about 30 000 years ago.<ref>{{cite book|last=Piazza|first=L. Luca Cavalli-Sforza, Paolo Menozzi, Alberto|title=The history and geography of human genes|year=1994|publisher=Princeton University Press|location=Princeton, N.J.|isbn=0-691-08750-4|page=95|edition=Abridged paperback ed.}}</ref> Genetic distance is also used in conservation, where the genetic distance between breeds of domesticated animals are measured in order to determine which breeds must be protected to maintain [[biodiversity]].<ref>Ruane, J. (1999). A critical review of the value of genetic distance studies in conservation of animal genetic resources. Journal of Animal Breeding and Genetics, 116(5), 317-323.
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| </ref>
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| ==Biological foundation==
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| Each [[gene]] in an [[organisms]] [[genome]] exists at a specific location, called the [[locus (genetics)|locus]] for that gene. Viable variations (called [[alleles]]) at these [[locus (genetics)|loci]] cause variety within [[species]] (eg. hair colour, eye colour). Most alleles do not have an observable impact on the organism. Within a population new alleles caused by mutation quickly die out or spread throughout the population. However when a population is split into two smaller populations (by either geography or [[speciation]]), mutations occurring after the split will be present in only one of the two groups. Random fluctuations in the prevalence of other alleles (due to the essentially random process of reproduction) also produce differences between isolated populations. This process is known as [[genetic drift]]. By examining the difference between [[allele frequencies]] between the populations, genetic distance can estimate how long ago the two populations were together.
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| ==Measures of genetic distance==
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| Genetic distance works by examining the [[statistical frequency|frequency]] with which particular alleles are found in the populations or species. Two populations with the same frequencies for all alleles are considered genetically identical. There is less consensus on how to measure differing populations, and a large number of different distance metrics are used. The principle difficulty is how best to combine the information detected for large numbers of alleles.<ref name=Cavalli-Bodmer>{{cite book
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| |author = L.L Cavalli-Sforza, W.F. Bodmer
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| |title=The Genetics of Human Populations
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| |year=1971
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| |publisher=W.H. Freeman and Company
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| |isbn=0-7167-0681-4}}
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| </ref>
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| As a result, there are several measures used to indicate genetic distance.<ref name="Population Genetics IV">[http://www.uwyo.edu/dbmcd/molmark/lect06/lect6.html Population Genetics IV: Genetic distances -- biological vs. geometric approaches.]</ref> The most commonly used are Nei's genetic distance, Cavalli-Sforza and Edwards measure, Reynolds, Weir and Cockerham's genetic distance,<ref>{{cite web|last1=McEachern|first1=MaryBrooke|last2=Savage|first2=W.|last3=Hooper|first3=S.|last4=Kanthaswamy|first4=S.|title=Measures of Genetic Distance|url=http://genome-lab.ucdavis.edu/Links/Pop_Genet_ECL290/Week-4/Measures_of_Genetic_Distance.ppt|accessdate=21 October 2013}}</ref> listed below.
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| In all the formulae in this section, we suppose that <math>X</math> and <math>Y</math> are two populations for which <math>L</math> loci have been sampled and let <math>X_{u}</math> represent the <math>u</math><sup>th</sup> allele at the <math>l</math><sup>th</sup> locus.
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| ===Nei's standard genetic distance===
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| In 1972, [[Masatoshi Nei]] published what came to be known as Nei's standard genetic distance. This distance has the nice property that, if the rate of genetic change does not vary between loci then Nei's standard genetic distance is the number of changes per locus. This measure assumes that genetic differences arise due to [[mutation]] and [[genetic drift]].<ref>[[Masatoshi Nei|Nei, M.]] (1972) Genetic distance between populations. ''Am. Nat.'' 106:283-292.</ref>
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| :<math>\begin{align}
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| D_{a}=-\ln\frac{\sum \limits_l \sum \limits_{u} X_{u} Y_{u}}{\sqrt{(\sum \limits_{l} \sum \limits_{u} X_{u}^2)(\sum \limits_{l} \sum \limits_{u} Y_{u}^2)}}
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| \end{align}
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| </math>
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| This distance can also be expressed in terms of the arithmetic mean probabilities of identity. Let <math>j_X</math> be the probability the two members of population <math>X</math> having the same allele at a particular locus and <math>j_{XY}</math> the probability of a member of <math>X</math> and a member of <math>Y</math> having the same allele. <math>J_X</math>, <math>J_Y</math> and <math>J_{XY}</math> are the [[arithmetic mean]] of <math>j_X</math>, <math>j_Y</math> and <math>j_{XY}</math> over all loci. These can be written<ref name="NeiGenDis">
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| {{cite web
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| |last=Nei
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| |first=Masatochi
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| |title=Measures of Genetic Distance
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| |url=http://nsgl.gso.uri.edu/washu/washub87001/washub87001_part6.pdf
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| |accessdate=22 October 2013}}</ref>
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| :<math>\begin{align}
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| J_X=\sum \limits_{l} \sum \limits_{u} \frac{{X_u}^2}{r}
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| \end{align}
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| </math>
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| :<math>\begin{align}
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| J_Y=\sum \limits_{l} \sum \limits_{u} \frac{{Y_u}^2}{r}
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| \end{align}
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| </math>
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| :<math>\begin{align}
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| J_{XY}=\sum \limits_{l} \sum \limits_{u} \frac{X_uY_u}{r}
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| \end{align}
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| </math>
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| Nei's standard distance can then be written
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| :<math>\begin{align}
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| D_{a}=-\ln{\frac{J_{XY}}{\sqrt{J_XJ_Y}}}
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| \end{align}</math><ref name="Population Genetics IV"/>
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| ===Cavalli-Sforza chord measure===
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| In 1967 [[Luigi Luca Cavalli-Sforza]] and [[A. W. F. Edwards]] published this measure. It assumes that genetic differences arise due to [[genetic drift]] only. One major advantage of the Cavalli-Sforza is that the populations are represented in a high dimensional [[Euclidean space]], the scale of which is one unit per gene substitution. This makes the distance a [[Euclidean distance]] and gives the distance an intuitive biological foundation.<ref name="Cavalli-Sforza">
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| {{cite journal
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| |author=L.L. Cavalli-Sforza, A.W.F. Edwards
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| |title=Phylogenetic Analysis -Models and Estimation Procedures
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| |journal=The American Journal of Human Genetics
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| |volume=19
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| |issue= 3 Part I (May)
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| |year=1967
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| }}
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| </ref>
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| :<math>\begin{align}
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| D_{CH} = \frac{2}{\pi} \sqrt{2(L-\sum \limits_{l}\sum \limits_u \sqrt{X_{u}Y_{u})}}
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| \end{align}</math>
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| Some authors drop the factor of <math>\frac{2}{\pi}</math>. This simplifies the formula at the cost of losing the property that the scale is one unit per gene substitution.
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| ===Reynolds, Weir, and Cockerham's genetic distance===
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| In 1983, this measure was published by John Reynolds, B.S. Weir and C. Clark Cockerham.
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| This measure assumes that genetic differences arise due to [[genetic drift]] only. It estimates the [[Malecot's method of coancestry|coancestry coefficient]] <math>\Theta</math> which provides a measure of the genetic distance by:<ref name="Reynold,Weir,Cockerham">
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| {{cite journal
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| |author=John Reynolds, B.S. Weir, C. Clark Cockerham
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| |title=Estimation of the coancestry coefficient: Basis for a short-term genetic distance
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| |journal=Genetics
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| |volume=105
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| |pages=767–779
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| |date=November 1983}}
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| </ref>
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| :<math>\begin{align}
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| \Theta_w=\sqrt{\frac{\sum \limits_{l} \sum \limits_{u} (X_u-Y_u)^2}{2\sum \limits_{l} (1-\sum \limits_{u}X_uY_u)}}
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| \end{align}
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| </math>
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| ===Other measures of genetic distance===
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| Many other measures of genetic distance have been proposed with varying success.
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| ====Nei's distance 1983====
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| This distance assumes that genetic differences arise due to [[mutation]] and [[genetic drift]], but this distance measure is known to give more reliable population trees than other distances particularly for microsatellite DNA data.<ref name="Genetic distances and reconstruction of phylogenetic trees from microsatellite DNA">Takezaki, N. and [[Masatoshi Nei|Nei, M.]] (1996) Genetic distances and reconstruction of phylogenetic trees from microsatellite DNA. ''Genetics'' 144:389-399.</ref>
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| :<math>\begin{align} | |
| D_{A}=1-\sum \limits_{u} \sqrt{X_uY_u}
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| \end{align}
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| </math> <ref name="Genetic distances and reconstruction of phylogenetic trees from microsatellite DNA"/>
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| ====Euclidean distance====
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| {{Main|Euclidean distance}}
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| :<math>\begin{align} | |
| D_{EU}=\sqrt{\sum \limits_{u}(X_u-Y_u)^2}
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| \end{align}
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| </math> <ref name="Population Genetics IV"/>
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| ====Goldstein distance 1995====
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| It was specifically devoloped for microsatellite markers and is based on the stepwise-mutation model (SMM). <math> \mu_X </math> and <math> \mu_Y </math> are the means of the allele frequencies in population X and Y.<ref name="An Empirical Exploration of the dmu2 Genetic Distance for 213 Human Microsatellite Markers">
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| {{cite journal
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| |author1=Gillian Cooper
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| |author2=William Amos
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| |author3=Richard Bellamy
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| |author4=Mahveen Ruby Siddiqui
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| |author5=Angela Frodsham
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| |author6=Adrian V. S. Hill
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| |author7=David C. Rubinsztein
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| |title=An Empirical Exploration of the <math>(\delta\mu)^2</math> Genetic Distance for 213 Human Microsatellite Markers
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| |journal=The American Journal of Human Genetics
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| |volume=65
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| |pages=1125–1133
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| |year=1999}}
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| </ref>
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| :<math>\begin{align}
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| (\delta\mu)^2=(\mu_X-\mu_Y)^2
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| \end{align}
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| </math> <ref name="An Empirical Exploration of the dmu2 Genetic Distance for 213 Human Microsatellite Markers"/>
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| ====Nei's minimum genetic distance 1973====
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| This measure assumes that genetic differences arise due to [[mutation]] and [[genetic drift]].
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| :<math>\begin{align}
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| D_{m}=\frac{(J_X+J_Y)}{2}-J_{XY}
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| \end{align}
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| </math> <ref name="Sampling vaiances of heterozygosity and genetic distance">
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| {{cite journal
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| |author=Masatoshi Nei, A.K. Roychoudhury
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| |title=Sampling vaiances of heterozygosity and genetic distance
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| |journal=Genetics
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| |volume=76
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| |pages=379–390
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| |date=February 1974}}
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| </ref>
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| ====Roger's distance 1972====
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| :<math>\begin{align}
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| D_{R}=\frac{1}{r}\sqrt\frac{\sum \limits_{u} (X_u-Y_u)^2}{2}
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| \end{align}
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| </math> <ref name="Genetic Distances and Reconstruction of Phylogenetic Trees From Microsatellite DNA">
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| {{cite journal
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| |author1=Naoko Takezaki
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| |author2=Masatoshi Nei
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| |title=Genetic Distances and Reconstruction of Phylogenetic Trees From Microsatellite DNA
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| |journal=Genetics
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| |volume=144
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| |pages=389–399
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| |date=Septemher 1996}}
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| </ref>
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| ====Fixation index====
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| {{main|Fixation index}}
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| A commonly used measure of genetic distance is the [[fixation index]] which varies between 0 and 1. A value of 0 indicates that two populations are genetically identical whereas a value of 1 indicates that two populations are different species.
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| ==Software==
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| *[[PHYLIP]] uses [http://evolution.genetics.washington.edu/phylip/doc/gendist.html GENDIST]
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| **Nei's standard genetic distance 1972
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| **Cavalli-Sforza and Edwards 1967
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| **Reynolds, Weir, and Cockerham's 1983
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| *[http://tomato.biol.trinity.edu/programs/index.php/TFPGA TFPGA]
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| **Nei's standard genetic distance (original and unbiased)
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| **Nei's minimum genetic distance (original and unbiased)
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| **Wright's (1978) modification of Roger's (1972) distance
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| **Reynolds, Weir, and Cockerham's 1983
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| *[http://tomato.biol.trinity.edu/programs/index.php/Genetic_Data_Analysis GDA]
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| *[http://tomato.biol.trinity.edu/programs/index.php/POPGENE POPGENE]
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| **Nei's standard genetic distance (original and unbiased) and identity measures
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| *[http://www.personal.psu.edu/nxm2/dispan2.htm DISPAN]
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| **Nei's standard genetic distance 1972
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| **Nei's genetic distance between populations 1983
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| ==See also==
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| * [[Human genetic variation]]
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| * [[Human genetic clustering]]
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| * [[Phylogenetics]]
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| * [[Allele frequency]]
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| == References ==
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| <references/>
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| ==External links==
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| *[http://helix.biology.mcmaster.ca/brent/node7.html ''The Estimation of Genetic Distance and Population Substructure from Microsatellite allele frequency data.'', Brent W. Murray (May 1996), McMaster University website on genetic distance]
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| *[http://nitro.biosci.arizona.edu/ftDNA/Distance.html Computing distance by stepwise genetic distance model, web pages of Bruce Walsh at the Department of Ecology and Evolutionary Biology at the University of Arizona]
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| *[http://www.pnas.org/cgi/content/full/99/21/13633 Britten RJ. Divergence between samples of chimpanzee and human DNA sequences is 5%, counting indels. PNAS; 2002:13633]
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| <br>
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| {{DEFAULTSORT:Genetic Distance}}
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| [[Category:Phylogenetics]]
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