Strictness analysis

Genetic distance refers to the genetic divergence between species or between 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. 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.

Biological foundation

Each gene in an organisms genome exists at a specific location, called the locus for that gene. Viable variations (called alleles) at these 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.

Measures of genetic distance

Genetic distance works by examining the 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. As a result, there are several measures used to indicate genetic distance. The most commonly used are Nei's genetic distance, Cavalli-Sforza and Edwards measure, Reynolds, Weir and Cockerham's genetic distance, listed below.

In all the formulae in this section, we suppose that $X$ and $Y$ are two populations for which $L$ loci have been sampled and let $X_{u}$ represent the $u$^th allele at the $l$^th locus.

Nei's standard genetic distance

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.

${\begin{aligned}D_{a}=-\ln {\frac {\sum \limits _{l}\sum \limits _{u}X_{u}Y_{u}}{\sqrt {(\sum \limits _{l}\sum \limits _{u}X_{u}^{2})(\sum \limits _{l}\sum \limits _{u}Y_{u}^{2})}}}\end{aligned}}$

This distance can also be expressed in terms of the arithmetic mean probabilities of identity. Let $j_{X}$ be the probability the two members of population $X$ having the same allele at a particular locus and $j_{XY}$ the probability of a member of $X$ and a member of $Y$ having the same allele. $J_{X}$, $J_{Y}$ and $J_{XY}$ are the arithmetic mean of $j_{X}$, $j_{Y}$ and $j_{XY}$ over all loci. These can be written

${\begin{aligned}J_{X}=\sum \limits _{l}\sum \limits _{u}{\frac {{X_{u}}^{2}}{r}}\end{aligned}}$

${\begin{aligned}J_{Y}=\sum \limits _{l}\sum \limits _{u}{\frac {{Y_{u}}^{2}}{r}}\end{aligned}}$

${\begin{aligned}J_{XY}=\sum \limits _{l}\sum \limits _{u}{\frac {X_{u}Y_{u}}{r}}\end{aligned}}$

Nei's standard distance can then be written

${\begin{aligned}D_{a}=-\ln {\frac {J_{XY}}{\sqrt {J_{X}J_{Y}}}}\end{aligned}}$

Cavalli-Sforza chord measure

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.

${\begin{aligned}D_{CH}={\frac {2}{\pi }}{\sqrt {2(L-\sum \limits _{l}\sum \limits _{u}{\sqrt {X_{u}Y_{u})}}}}\end{aligned}}$

Some authors drop the factor of ${\frac {2}{\pi }}$. This simplifies the formula at the cost of losing the property that the scale is one unit per gene substitution.

Reynolds, Weir, and Cockerham's genetic distance

In 1983, this measure was published by John Reynolds, B.S. Weir and C. Clark Cockerham. This measure assumes that genetic differences arise due to genetic drift only. It estimates the coancestry coefficient $\Theta$ which provides a measure of the genetic distance by:

${\begin{aligned}\Theta _{w}={\sqrt {\frac {\sum \limits _{l}\sum \limits _{u}(X_{u}-Y_{u})^{2}}{2\sum \limits _{l}(1-\sum \limits _{u}X_{u}Y_{u})}}}\end{aligned}}$

Other measures of genetic distance

Many other measures of genetic distance have been proposed with varying success.

Nei's distance 1983

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.

${\begin{aligned}D_{A}=1-\sum \limits _{u}{\sqrt {X_{u}Y_{u}}}\end{aligned}}$

Euclidean distance

Mining Engineer (Excluding Oil ) Truman from Alma, loves to spend time knotting, largest property developers in singapore developers in singapore and stamp collecting. Recently had a family visit to Urnes Stave Church.

${\begin{aligned}D_{EU}={\sqrt {\sum \limits _{u}(X_{u}-Y_{u})^{2}}}\end{aligned}}$

Goldstein distance 1995

It was specifically devoloped for microsatellite markers and is based on the stepwise-mutation model (SMM). $\mu _{X}$ and $\mu _{Y}$ are the means of the allele frequencies in population X and Y.

${\begin{aligned}(\delta \mu )^{2}=(\mu _{X}-\mu _{Y})^{2}\end{aligned}}$

Nei's minimum genetic distance 1973

This measure assumes that genetic differences arise due to mutation and genetic drift.

${\begin{aligned}D_{m}={\frac {(J_{X}+J_{Y})}{2}}-J_{XY}\end{aligned}}$

Roger's distance 1972

${\begin{aligned}D_{R}={\frac {1}{r}}{\sqrt {\frac {\sum \limits _{u}(X_{u}-Y_{u})^{2}}{2}}}\end{aligned}}$

Fixation index

Mining Engineer (Excluding Oil ) Truman from Alma, loves to spend time knotting, largest property developers in singapore developers in singapore and stamp collecting. Recently had a family visit to Urnes Stave Church. 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.

Software

• PHYLIP uses GENDIST
  • Nei's standard genetic distance 1972
  • Cavalli-Sforza and Edwards 1967
  • Reynolds, Weir, and Cockerham's 1983
• TFPGA
  • Nei's standard genetic distance (original and unbiased)
  • Nei's minimum genetic distance (original and unbiased)
  • Wright's (1978) modification of Roger's (1972) distance
  • Reynolds, Weir, and Cockerham's 1983
• GDA
• POPGENE
  • Nei's standard genetic distance (original and unbiased) and identity measures
• DISPAN
  • Nei's standard genetic distance 1972
  • Nei's genetic distance between populations 1983

See also

• Human genetic variation
• Human genetic clustering
• Phylogenetics
• Allele frequency

External links

• The Estimation of Genetic Distance and Population Substructure from Microsatellite allele frequency data., Brent W. Murray (May 1996), McMaster University website on genetic distance
• 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
• Britten RJ. Divergence between samples of chimpanzee and human DNA sequences is 5%, counting indels. PNAS; 2002:13633