## 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 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, LOD values are displayed in full mode. 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

Genotypes from HapMap Phase II release 19 were used with Haploview to infer phasing and calculate LD values for all SNP pairs within 250 kb. As the children in the trios are not independent samples, Haploview uses only the parents from those populations. The YRI and CEU tracks each use 60 unrelated individuals (parents from the trios), the CHB and JPT tracks use 45 unrelated individuals each.

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. Haplotype phase is inferred using a standard EM algorithm with a partition-ligation approach for blocks with greater than 10 markers.

## 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)
  - CHB: Han Chinese in Beijing (45 unrelated individuals)
  - JPT: Japanese in Tokyo (45 unrelated individuals)

## Credits

This track was created by Daryl Thomas at UCSC using data from the International HapMap Project, following the display style from Haploview.

## References

### HapMap Project

The International HapMap Consortium. A haplotype map of the human genome. Nature 437, 1299-1320 (2005).

The International HapMap Consortium. The International HapMap Project. Nature 426, 789-96 (2003).

### HapMap Data Coordination Center

Thorisson, G.A., Smith, A.V., Krishnan, L. and Stein, L.D. The International HapMap Project Web site. Genome Res 15, 1591-3 (2005).

### Haploview

Barrett, J.C., Fry, B., Maller, J. and Daly, M.J. Haploview: analysis and visualization of LD and haplotype maps. Bioinformatics 21(2), 263-5 (2005).

### General references on Linkage Disequilibrium

Lewontin, R.C. On measures of gametic disequilibrium. Genetics 120, 849-52 (1988).

Hill, W. G. and Robertson, A. The effect of linkage on limits to artificial selection. Genet. Res., 8:269-294 (1966).