## Description

Linkage disequilibrium (LD) is the association of alleles on chromosomes. It measures the difference between the observed allele frequency for a two-locus allele combination as compared to its expected frequency, which is the product of the two single allele frequencies. When LD is low, the two loci tend to be inherited in a nearly random manner.

This track shows three different measures of linkage disequilibrium — D', r2, and LOD (log odds) — between pairs of SNPs as genotyped by the HapMap consortium. LD is useful for understanding the associations between genetic variants throughout the genome, and can be helpful in selecting SNPs for genotyping.

By default, the display in full mode shows LOD values. Each diagonal represents a different SNP with each diamond representing a pairwise comparison between two SNPs. Shades are used to indicate linkage disequilibrium between the pair of SNPs, with darker shades indicating stronger LD. For the LOD values, additional colors are used in some cases:

- White diamonds indicate pairwise D' values less than 1 with no statistically significant evidence of LD (LOD < 2).
- Light blue diamonds indicate high D' values (>0.99) with low statistical significance (LOD < 2).
- Light pink diamonds are drawn when the statistical significance is high (LOD >= 2) but the D' value is low (less than 0.5).

## Methods

Phased genotypes from HapMap Phase II release 22 were used with Haploview to calculate LD values for all SNP pairs within 250 kb. The YRI and CEU tracks each use 30 parents+child trios (90 individuals) and the combined JPT+CHB track uses 90 unrelated individuals.

Haploview uses a two marker EM (ignoring missing data) to estimate the maximum-likelihood values of the four gamete frequencies, from which the D', LOD, and r2 calculations derive.

## Display Conventions and Configuration

- Display Mode
  - Full mode shows the pairwise LD values in a Haploview-style mountain plot.
  - Dense mode shows the pairwise LD values in a single line for each population, where the intensity at each position is the average of all of the LD values between the SNP at that position and all other SNPs within 250 kb.
- LD Values: measures of linkage disequilibrium
  - r2 displays the raw r2 value, or the square of the correlation coefficient for a given marker pair. SNPs that have not been separated by recombination have r2 = 1; in this case, these two markers are said to be redundant for genotyping, but may have different functional effects. Lower r2 values show a lower degree of LD, indicating that some recombination has occurred in this population. See Hill and Robertson (1966) for details.
  - D' displays the raw D' value, which is the normalized covariance for a given marker pair. A D' value of 1 (complete LD) indicates that two SNPs have not been separated by recombination, while lower values indicate evidence of recombination in the history of the sample. Only D' values near 1 are a reliable measure of LD; lower values are difficult to interpret as the magnitude of D' depends strongly on sample size. See Lewontin (1988) for more details.
  - LOD displays the log odds score for linkage disequilibrium between a given marker pair, and is shown by default.
- Track Geometry
  - Trim to triangle shows the standard mountain plot (default); turning this option off will show LD values with SNPs outside the window.
  - Inverting makes it easier to visually compare two adjacent populations.
- Colors
  - LD Values can be drawn in a variety of colors, with red as default. The intensity of the color is proportional to the strength of the LD measure chosen above.
  - Outlines can be drawn in contrasting colors or turned off. Outlines are automatically suppressed when the window is larger than 100,000 bp.
- Population Selection
  The HapMap populations can be individually displayed or hidden.
  - YRI: Yoruba people in Ibadan, Nigeria (30 parent-and-adult-child trios)
  - CEU: European samples from the Centre d'Etude du Polymorphisme Humain (CEPH) (30 trios)
  - JPT+CHB: Combination of Japanese in Tokyo (45 unrelated individuals) and Han Chinese in Beijing (45 unrelated individuals)

## Credits

This track was created at UCSC using data from the International HapMap Project and LD scores were computed using the Haploview program. The genome browser track display was created by Daryl Thomas following the display style from Haploview.

## References

### HapMap Project

The International HapMap Consortium. A second generation human haplotype map of over 3.1 million SNPs. Nature. 2007 Oct 18;449(7164):851-61.

The International HapMap Consortium. A haplotype map of the human genome. Nature. 2005 Oct 27;437(7063):1299-320.

The International HapMap Consortium. The International HapMap Project. Nature. 2003 Dec 18;426(6968):789-96.

### HapMap Data Coordination Center

Thorisson GA, Smith AV, Krishnan L, Stein LD. The International HapMap Project Web site. Genome Res. 2005 Nov;15(11):1592-3.

### Haploview

Barrett JC, Fry B, Maller J, Daly MJ. Haploview: analysis and visualization of LD and haplotype maps. Bioinformatics. 2005 Jan 15;21(2):263-5. Epub 2004 Aug 5.

### General references on Linkage Disequilibrium

Lewontin, RC. On measures of gametic disequilibrium. Genetics. 1988 Nov;120(3):849-52.

Hill WG, Robertson A. The effect of linkage on limits to artificial selection. Genet Res. 1966 Dec;8(3):269-94.