Linkage disequilibrium

In population genetics, linkage disequilibrium is 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 polymorphisms at different loci are measured by the degree of linkage disequilibrium (LD).

Linkage disequilibrium is generally caused by genetic linkage and the rate of recombination; rate of mutation; random drift or non-random mating; and population structure. For example, some organisms (such as bacteria) may show linkage disequilibrium because they reproduce asexually and there is no recombination to break down the linkage disequilibrium.

Linkage disequilibrium measure, "D"

If we look at haplotypes for two loci A and B with two alleles each—a two-locus, two-allele model—the following table denotes the frequencies of each combination:

In the genetic literature the phrase "two alleles are in LD" usually means that $D\; e\; 0$. Contrariwise, "linkage equilibrium" denotes the case $D\; =\; 0$.

The following table illustrates the relationship between the haplotype frequencies and allele frequencies and D.

so thatwhere $D$ at the $n$-th generation is designated as $D\_n$. Thus we haveIf $n\; o\; infty$, then $(1-c)^n\; o\; 0$ so that $D\_n$ converges to zero.

If at some time we observe linkage disequilibrium, it will disappear in future due to recombination. However, the smaller the distance between the two loci, the smaller will be the rate of convergence of $D$ to zero.

Resources

A comparison of different measures of LD is provided by Devlin & Risch [cite journal|author=Devlin B., Risch N. |title=A Comparison of Linkage Disequilibrium Measures for Fine-Scale Mapping|journal=Genomics|year=1995|volume=29|pages=311–322|url=http://www.sciencedirect.com/science?_ob=MImg&_imagekey=B6WG1-45S9156-30-1&_cdi=6809&_user=128590&_orig=browse&_coverDate=09%2F30%2F1995&_sk=999709997&view=c&wchp=dGLbVtb-zSkzk&md5=71c2158ad4c51ae80b12a68c68814f78&ie=/sdarticle.pdf |doi=10.1006/geno.1995.9003]

The International HapMap Project enables the study of LD in human populations [http://www.hapmap.org/cgi-perl/gbrowse/hapmap/ online] . The Ensembl project integrates HapMap data and such from dbSNP in general with other genetic information.

Analysis software

* Haploview
* [http://www.affymetrix.com/support/developer/tools/devnettools.affx LdCompare] [cite journal|author=Hao K., Di X., Cawley S.|title=LdCompare: rapid computation of single- and multiple-marker r2 and genetic coverage|journal=Bioinformatics|year=2007|volume=23|pages=252–254|url=http://bioinformatics.oxfordjournals.org/cgi/reprint/23/2/252|doi=10.1093/bioinformatics/btl574|pmid=17148510] — open-source software for calculating LD.
* [http://www.pypop.org/ PyPop]
* [http://www.goldenhelix.com/SNP_Variation/HelixTree/linkage_disequilibrium_analysis.html HelixTree] - commercial software with interactive LD plot.

References

ee also

*Haploview
*Hardy-Weinberg principle
*Genetic linkage
*Co-adaptation
*Genealogical DNA test
*Tag SNP

Further reading

*cite book| first=Philip W.| last=Hedrick| title=Genetics of Populations| year=2005 | edition=3rd| id=ISBN 0763747726| location=Sudbury, Boston, Toronto, London, Singapore | publisher=Jones and Bartlett Publishers

* [http://www.nslij-genetics.org/ld/ Bibliography: Linkage Disequilibrium Analysis] : a bibliography of more than one thousand articles on Linkage disequilibrium published since 1918.