Linkage disequilibrium

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Linkage disequilibrium is a term used in the study of population genetics for the non-random association of alleles at two or more loci, not necessarily on the same chromosome. It is not the same as linkage, which describes the association of two or more loci on a chromosome with limited recombination between them. Linkage disequilibrium describes a situation in which some combinations of alleles or genetic markers occur more or less frequently in a population than would be expected from a random formation of haplotypes from alleles based on their frequencies. Non-random associations between genes at different loci are measured by the degree of linkage disequilibrium (D).

Linkage disequilibrium is generally caused by selection in the form of epistatic fitness interactions between genes, genetic linkage and the rate of recombination, random drift or non-random mating and population structure. For example, some organisms may show linkage disequilibrium (such as bacteria) because they reproduce asexually and there is no recombination(r=0) to break down the linkage disequilibrium: D'=(1-r)D.

The International HapMap Project enables the study of LD in human populations online. The Ensembl project integrates HapMap data and such from dbSNP in general with other genetic information.

Contents 1 Linkage disequilibrium measure, δ 2 Linkage disequilibrium measure, D 3 Analysis Software 4 See also 5 References 6 Further reading

[edit] Linkage disequilibrium measure, δ

Formally, if we define pairwise LD, we consider indicator variables on alleles at two loci, say I₁,I₂. We define the LD parameter δ as:

Here p₁,p₂ denote the marginal allele frequencies at the two loci and h₁₂ denotes the haplotype frequency in the joint distribution of both alleles. Various derivatives of this parameter have been developed. In the genetic literature the wording "two alleles are in LD" usually means to imply . Contrariwise, linkage equilibrium, denotes the case δ = 0.

[edit] Linkage disequilibrium measure, D

If inspecting the two loci A and B with two alleles each, a two-locus, two-allele model, the following table shall denote the frequencies of each combination:

Haplotype	Frequency
A1B1	x11
A1B2	x12
A2B1	x21
A2B2	x22

From there one can determine the frequency of each of the alleles:

Allele	Frequency
A1	p1 = x11 + x12
A2	p2 = x21 + x22
B1	q1 = x11 + x21
B2	q2 = x12 + x22

if the two loci and the alleles are independent from each other, then one can express the observation A1B1 as "A1 must be found and B1 must be found". The table above lists the frequencies for A₁,p₁, and B₁,q₁, hence the frequency of A₁B₁, x₁₁, equals according to the rules of elementary statistics x₁₁ = p₁ * q₁.

A deviation of the observed frequencies from the expected is referred to as the linkage disequilibrium parameter, introduced by Robbins (1918)^[1] and named by Lewontin and Kojima (1960)^[2] and commonly denoted by a capital D as defined by D = x₁₁ − p₁q₁. It is vividly presented in the following table.

	A1	A2	Total
B1	x11 = p1q1 + D	x21 = p2q1 − D	q1
B2	x12 = p1q2 − D	x22 = p2q2 + D	q2
Total	p1	p2	1

When extending these formula for diploid cells rather than investigating the gametes/haplotypes directly, the laid out principle prevails, the recombination rate between the two loci A and B must be taken into account, though, which is commonly denoted by the letter c.

D is nice to calculate with but has the disadvantage of depending on the frequency of the alleles inspected. This is evident since frequencies are between 0 and 1. There can be no D observed if any locus has an allele frequency 0 or 1 and is maximal when frequencies are at 0.5. Lewontin (1964) suggested normalising D by dividing it with the theoretical maximum for the observed allele frequencies. Thus .

Another value is the correlation coefficient as also laid out in the initial paragraphs of this page, denoted as . This however is not adjusted to the loci having different allele frequencies. If it was, r, the square root of r² if given the sign of D would be equivalent to D' ^[3]

[edit] Analysis Software

• Haploview
• PyPop
• HelixTree

[edit] See also

• Hardy-Weinberg principle
• Genetic linkage
• Co-adaptation

[edit] References

1. ^ Robbins, R.B. (1918). "Some applications of mathematics to breeding problems III". Genetics 3: 375-389. 
2. ^ R.C. Lewontin and K. Kojima (1960). "The evolutionary dynamics of complex polymorphisms.". Evolution 14: 458-472. 
3. ^ P.W. Hedrick and S. Kumar (2001). "Mutation and linkage disequilibrium in human mtDNA". Eur. J. Hum. Genet. 9: 969-972. 

[edit] Further reading

• Hedrick, Philip W. (2005). Genetics of Populations, 3rd, Sudbury, Boston, Toronto, London, Singapure: Jones and Bartlett Publishers. ISBN 0763747726. 

Topics in population genetics v • d • e
Key concepts: Hardy-Weinberg law | genetic linkage | linkage disequilibrium | Fisher's fundamental theorem | neutral theory
Selection: natural | sexual | artificial | ecological
Effects of selection on genomic variation: genetic hitchhiking | background selection
Genetic drift: small population size | population bottleneck | founder effect | coalescence
Founders: R.A. Fisher | J. B. S. Haldane | Sewall Wright
Related topics: evolution | microevolution | evolutionary game theory | fitness landscape | genetic genealogy
List of evolutionary biology topics