Linkage Disequilibrium vs Linkage: Flowchart, GWAS & HLA

Linkage disequilibrium (LD) is the nonrandom association of alleles at two or more loci in a population: two alleles sit on the same haplotype more often (or less often) than their separate frequencies predict. Linkage is a different idea, the physical closeness of loci that makes them co-segregate within families, measured by the recombination fraction (θ) and the LOD score. LD is quantified as D (observed minus expected haplotype frequency), D′ (D scaled to its maximum) and r² (the correlation between two sites), and recombination erodes it every generation. It is why a GWAS hit is often a tag SNP standing in for a nearby causal variant, and why HLA alleles travel as haplotypes.

Linkage vs linkage disequilibrium

The step-by-step flowchart

In one line: pedigree → linkage (LOD). Population → observed vs expected haplotypes → measure (D′, r²) → explain (distance, history) → use (tag SNPs, HLA) → confirm (sequence the region, rule out stratification).

Step 1: Families or a population?

• Within a pedigree, a marker and a disease passing together through meioses is linkage. The evidence for it is summarized by the LOD score: the log10 of the odds that the data reflect linkage at a given θ rather than independent assortment (θ = 0.5). Classically, a LOD of 3 or more supports linkage (a LOD of 3 means odds of 1,000:1 in favor); some sources set the bar at 3.3, and a LOD below −2 argues against linkage.
• Across unrelated people, an allele that is more common in cases than in controls, or two alleles found together more often than chance, is association, and the usual genetic explanation is LD.
• Distance units: 1 centimorgan (cM) is a 1% chance of recombination between two markers per meiosis, roughly 1 million base pairs in the human genome.

Step 2: Compare observed with expected

If alleles A and B were independent (linkage equilibrium), the AB haplotype would occur at pA × pB. Any difference is LD:

$D = p_{AB} - p_A p_B$

Worked example. Allele A has a frequency of 0.6 and allele B 0.5, so AB is expected at 0.30. It is observed at 0.45, so D = 0.45 − 0.30 = +0.15: A and B travel together more often than chance.

Step 3: Measure how strong it is

Finishing the example: for a positive D, the maximum possible value is the smaller of pA·pb (0.6 × 0.5) and pa·pB (0.4 × 0.5), which is 0.20, so D′ = 0.15 ÷ 0.20 = 0.75; and r² = 0.15² ÷ (0.6 × 0.4 × 0.5 × 0.5) = 0.375. The two measures disagree because r² is also sensitive to how different the allele frequencies are.

Step 4: Ask why the alleles travel together

• Close physical distance (little recombination) is the usual reason, so LD generally falls with distance, but not smoothly: the genome is a patchwork of haplotype blocks separated by recombination hotspots.
• A young mutation starts in complete LD with the haplotype it arose on, and recombination has had few generations to break it up.
• Founder effects, bottlenecks and genetic drift in small populations leave a few haplotypes very common.
• Selection: a favored allele drags nearby variants along (hitchhiking), and when both loci are held polymorphic by balancing selection, LD can persist indefinitely.
• Admixture and population structure can create LD even between unlinked loci, which is why GWAS adjust for ancestry.

Step 5: Ask what the LD means

• A GWAS hit may only be tagging along. A GWAS scans markers across the genome in unrelated people with and without a disease (a case-control design). The associated variant may not cause the disease itself but sit in LD with the variant that does, so follow-up sequencing and fine mapping are needed to find the actual change.
• Tag SNPs are chosen because they capture (high r²) the variation at nearby sites, so an array can survey the genome without typing every variant. A hit at a tag SNP is an indirect association.
• Rule out population stratification. If cases and controls differ in ancestry, any allele whose frequency differs between ancestries looks "associated" (confounding). Studies match ancestry or adjust for it with principal components.
• Effect sizes are odds ratios, because the design is case-control (relative risk vs odds ratio).

Step 6: Remember what erodes it

Every meiosis gives recombination a chance to break up a haplotype. After t generations:

$D_t = D_0 (1 - \theta)^t$

For unlinked loci (θ = 0.5), LD halves every generation; for tightly linked loci (θ near 0), it can persist for many generations.

HLA: the classic LD region

• The HLA (MHC) genes sit on the short arm of chromosome 6 and are extremely polymorphic (more than 11,000 named HLA-B alleles alone). Their alleles are usually inherited together in blocks called HLA haplotypes, with strong LD across the region. The MHC class II region provided some of the first evidence of haplotype blocks and recombination hotspots.
• Associations are not destiny. HLA-B27 is strongly associated with ankylosing spondylitis and reactive arthritis, yet only about 1-5% of HLA-B27 carriers develop ankylosing spondylitis (see the ankylosing spondylitis memory palace).
• Type 1 diabetes risk is tied to HLA haplotypes: particular combinations of HLA-DRB1, HLA-DQA1 and HLA-DQB1 alleles inherited together. The two highest-risk haplotypes are named for their DR allele: the DR3 haplotype carries the DQ2 alleles and the DR4 haplotype carries the DQ8 alleles, and people with one of each (DR3/DR4) have the highest risk. That is why classic exam tables list DR3/DR4 while Merck lists DQ2/DQ8: the DR and DQ alleles travel on the same haplotypes. Only about 5% of people with the risk variants develop the disease.
• The full set of pairings is in the HLA associations question.

How USMLE tests it (and the traps)

• Family vs population. A LOD score or a pedigree means linkage; an association in unrelated cases and controls means LD.
• "Associated" is not "causal." An intronic or intergenic GWAS hit with no function of its own is usually a tag in LD with the causal variant.
• LD is not Hardy-Weinberg. Hardy-Weinberg equilibrium describes genotype frequencies at one locus; LD describes allele combinations across two loci.
• Distance helps but does not decide. Close loci usually show more LD, but blocks, hotspots and population history matter, and loci on different chromosomes can show LD after admixture.
• Linkage without LD. A marker can co-segregate with a disease in every family yet show no population association, because different families carry the disease allele on different marker alleles.

Practice question

Investigators compare 8,000 unrelated adults with an autoimmune disease and 8,000 unrelated controls. Cases and controls are matched for ancestry, and ancestry principal components are included in the analysis. An intronic SNP, rs-A, is strongly associated with the disease. Laboratory studies show that rs-A does not alter splicing or expression of any nearby gene. Sequencing of the region finds a missense variant 6 kb away that impairs the function of the encoded protein. In the study population, the rs-A risk allele and the missense variant are almost always found on the same haplotype (r² = 0.96). Which of the following best explains the association between rs-A and the disease?

A. Genetic linkage of rs-A to the disease locus, shown by a LOD score above 3 B. Linkage disequilibrium between rs-A and a causal variant C. Population stratification D. A direct regulatory effect of rs-A on a nearby gene E. Deviation from Hardy-Weinberg equilibrium at rs-A

Answer: B. rs-A has no function of its own, but its risk allele sits on the same haplotype as a damaging missense variant far more often than chance (r² = 0.96). Typing rs-A is almost the same as typing the causal variant, so the association is indirect, through LD. This is why GWAS hits need fine mapping before anyone calls them causal.

• A: a LOD score comes from family (pedigree) data, which this study of unrelated people did not collect. Linkage describes co-segregation within families; association across a population reflects LD.
• C: stratification creates false associations when cases and controls differ in ancestry. Ancestry matching and principal-component adjustment were used to exclude it.
• D: the laboratory studies found no effect of rs-A on splicing or expression, and a far better causal candidate sits on the same haplotype.
• E: Hardy-Weinberg equilibrium concerns genotype frequencies at a single locus. A deviation (often a sign of genotyping error) would not explain why one SNP tracks another.

Key takeaways

• LD = nonrandom association of alleles at different loci in a population; linkage = co-segregation of nearby loci within families.
• Linkage is measured with θ and the LOD score (3 or more supports linkage; below −2 argues against); LD is measured with D, D′ and r².
• D = pAB − pA·pB. D′ = 1 means at least one haplotype is missing; r² = 1 means two SNPs are perfect proxies.
• LD comes from close distance plus population history (new mutations, founder effects, drift, selection, admixture) and decays with recombination: $D_t = D_0(1 - \theta)^t$.
• A GWAS hit is often a tag SNP in LD with the causal variant; association is not causation, and stratification must be excluded.
• HLA alleles travel as haplotypes, which is why HLA-disease associations are markers of risk, not diagnoses.

Sources

• Linkage disequilibrium: understanding the evolutionary past and mapping the medical future — Nature Reviews Genetics (Slatkin, 2008)
• Chapter 11: Genome-Wide Association Studies — PLOS Computational Biology (Bush and Moore, 2012)
• Genome-Wide Association Studies Fact Sheet — National Human Genome Research Institute (2020)
• LOD score — NCI Dictionary of Genetics Terms, National Cancer Institute
• Genetic maps, markers, linkage analysis and LOD scores — NHGRI Current Topics in Genome Analysis handout (Ostrander, 2005)
• Centimorgan (cM) — Talking Glossary of Genomic and Genetic Terms, NHGRI
• Human Leukocyte Antigen (HLA) System — Merck Manual Professional Edition (2026)
• HLA allele statistics — IPD-IMGT/HLA Database, EMBL-EBI (2026)
• HLA-B gene — MedlinePlus Genetics, National Library of Medicine (2022)
• HLA-DRB1 gene — MedlinePlus Genetics, National Library of Medicine (2026)
• HLA DR-DQ haplotypes and genotypes and type 1 diabetes risk — Diabetes (Erlich et al., 2008)
• Type 1 diabetes — MedlinePlus Genetics, National Library of Medicine (2013)