Linkage Disequilibrium 101: What LD Measures and When It Matters

TL;DR — The 30-second answer

Linkage disequilibrium (LD) describes non-random associations between alleles at different loci. In linkage equilibrium vs disequilibrium, allele combinations occur as expected or depart from expectation. In linkage disequilibrium analysis, we quantify this with r² vs D'. Use r² to judge how well one variant predicts another. Use D' to infer historical recombination. LD powers GWAS tagging, imputation, and quality control. It also reveals population structure and past demography.

Before You Dive In

This guide explains linkage disequilibrium (LD) in plain language and shows how it shapes GWAS, QC, and fine-mapping decisions. You'll learn the difference between linkage equilibrium vs disequilibrium, when to use r² vs D', and the practical steps to design, compute, visualise, and interpret LD for research-use projects. By the end, you can apply linkage disequilibrium analysis directly to tag SNP selection, clumping/pruning, imputation, and reporting.

What Is LD, Really?

LD exists when alleles at two positions co-occur more or less often than chance. Imagine two biallelic SNPs: A/a and B/b. If chromosomes carrying A are more likely to carry B than b, the locus pair shows positive LD. If A tends to pair with b, LD is negative. When observed haplotype counts match the product of single-locus frequencies, the pair is in linkage equilibrium.

A tiny toy example helps. Suppose in 1,000 chromosomes we see:

• AB: 360
• Ab: 140
• aB: 140
• ab: 360

Allele frequencies are A=0.5 and B=0.5. Under equilibrium, each haplotype should be 0.25 (250 counts). We see an excess of AB and ab. That is LD.

LD is not only about physical proximity. Recombination breaks LD over time, but drift, bottlenecks, selection, and admixture can also create or maintain LD among distant sites. Genotyping error can mimic LD. Good LD work always starts with sound quality control.

Why LD Matters in Modern Studies

LD is a workhorse behind many common analyses.

• GWAS tagging and power. We rarely genotype every causal variant. Instead, we type tag SNPs that capture signals through LD. Strong r² between a tag and a causal allele preserves power while reducing assay cost.
• Imputation. Reference panels leverage LD to infer missing genotypes. Better LD models, especially across ancestries, improve accuracy.
• Population structure and demography. Admixture, founder effects, and expansions leave LD signatures. LD-aware analyses complement PCA and f-statistics.
• Quality control. LD clumping and pruning remove redundant markers. This stabilises association tests and prevents inflation from correlated predictors.
• Fine-mapping. LD patterns define credible sets and guide experimental validation.

Bottom line: LD, used well, saves cost, boosts power, and prevents misleading results.

r² vs D': What Each Measure Captures

Two related metrics answer different questions.

• r² (squared correlation).
  • Question: How well does one variant predict another?
  • Use cases: tag SNP selection, GWAS power, imputation quality.
  • Properties: bounded by allele frequencies; penalises mismatched MAFs; intuitive for variance explained.
• D' (standardised disequilibrium).
  • Question: Has recombination likely occurred between the sites?
  • Use cases: recombination mapping, historical events, haplotype block discovery.
  • Properties: can be high even when alleles are rare; sensitive to sampling noise at low MAF.

At-a-glance guide

Practical tip. For GWAS and pruning, use r² thresholds. For block boundaries or hotspot detection, consider D' with MAF filters and confidence bounds.

Forces That Shape LD

Several processes change LD over space and time.

Marginal effects for the interactions of LD (r2) estimated from pool-seq. (Lucek K. & Willi Y. (2021) PLOS Genetics)

• Recombination. Crossovers break down LD. Hotspots create sharp LD decay over short distances.
• Genetic drift. In small populations, random sampling can create strong LD among nearby or even distant sites.
• Demography. Bottlenecks increase LD genome-wide; expansions reduce it. Admixture introduces long-range LD between ancestry-informative markers.
• Selection. Selective sweeps hitchhike linked variants, raising LD around the target. Balancing selection can maintain distinctive long-range patterns.
• Mutation rate and gene conversion. New variants begin in complete LD with their background haplotypes. Gene conversion can erode LD locally.
• Genotyping error and batch effects. Systematic errors create spurious non-random associations. QC is essential.

Understanding these forces helps you design analyses and interpret exceptions, such as the extended LD around the MHC region.

LD Decay and Haplotype Blocks

LD typically decays with physical distance. In many species, r² drops sharply over a few kilobases, then approaches a low background level. The exact curve depends on recombination rate, effective population size, and demography.

Patterns of LD for Orthologous Genomic Segments of Approximately 5 Mb in Rat, Human, and Mouse. (Guryev V. et al. (2006) PLOS Genetics)

Haplotype blocks are segments where recombination has been historically limited, yielding clusters of variants in high LD. Within blocks, a small set of tag SNPs can capture most variation. Between blocks, recombination has been frequent.

Why this matters:

• Array design. Place tags that span blocks efficiently.
• Imputation. Better results when target and reference share block structures.
• Fine-mapping. Blocks guide which variants form credible sets and deserve functional follow-up.

Effect of MAF on the nature of LD and its decay in the mini core collection. (Otyama P.I. et al. (2019) BMC Genomics)

Study Design Basics for LD Analyses

Good study design avoids headaches later. Plan these items early.

Cohort size and balance

• Aim for enough samples to stabilise LD estimates, especially for rare alleles.
• Balance ancestries or stratify analyses. Mixed ancestries inflate long-range LD.

Marker density and coverage

• Dense markers improve LD estimates and imputation.
• For targeted panels, ensure even spacing and block coverage.

Allele frequency filters

• Set minimum MAF thresholds before computing D'.
• Calibrate r² thresholds by MAF bin if possible.

Hardy–Weinberg equilibrium and call quality

• Remove markers with extreme HWE deviations after accounting for structure.
• Filter by depth, call rate, and batch tags.

Relatedness and duplicates

• Identify cryptic relatives. Either exclude or model them.
• Remove duplicates and problematic samples early.

Phasing choices

• Many LD calculations do not require phasing.
• Phasing improves haplotype resolution and D' reliability when needed.

Documentation

• Record thresholds, software versions, and command flags.
• Pre-register your LD thresholds for transparency.

Tools & Pipelines You'll Actually Use

Purpose. A practical, decision-first path from raw genotypes to LD-driven outputs—no commands required.

Inputs. VCF/PLINK files, sample metadata (ancestry, batches, relatedness), reference build.

Workflow.

1. Pre-QC: call rate, allele harmonisation, depth/MAF/HWE filters, batch flags.
2. Structure control: assign/confirm ancestry; compute PCs; decide stratify vs include PCs.
3. Frequency screens: set MAF cut-offs (higher for stable D', flexible for r² tagging).
4. Compute LD: sliding windows per chromosome/region; produce r² (and D' if needed).
5. Decide: pruning (independent set), clumping (lead signals), block calling (fine-mapping).
6. Report: thresholds, versions, and rationale.

Key parameters. Window 200–1,000 kb; r² = 0.1–0.2 (pruning), ≥0.8 (strong tagging); apply MAF filters for D'; analyse per-ancestry; exclude long-range LD regions (e.g., MHC); phasing optional for r², helpful for D'.

Outputs. Pruned/clumped variant lists, block BEDs, LD matrices; LD heatmaps, decay curves, locus figures; a 1–2 page summary explaining choices and next steps.

Tool selection guide (when to use what)

Interpreting LD for GWAS and Fine-Mapping

Interpretation ties statistics to decisions.

Clumping vs pruning

• Pruning uses sliding windows and r² thresholds to keep quasi-independent markers. Useful for PCA and PRS inputs.
• Clumping groups association hits by LD around index SNPs. Useful to summarise GWAS results without double-counting the same signal.

Credible sets and conditional tests

• Create locus windows. Use LD to group variants.
• Fit conditional models to check if secondary signals remain after accounting for the lead variant.
• Combine with functional priors to refine credible sets.

Trans-ethnic fine-mapping

• Different LD patterns across ancestries help break apart correlated variants.
• Harmonise QC and imputation first. Then meta-analyse with ancestry-aware methods.

Reporting

• Always report reference panel and window sizes.
• Include LD thresholds, population labels, and software versions.
• Show LocusZoom-style plots with r² colouring to guide readers.

Quality Control & Common Pitfalls

A short checklist prevents most LD headaches.

• Ancestry mixture unmodelled. Stratify by ancestry or include PCs. Do not compute LD on heterogenous samples without care.
• Rare-variant traps. D' inflates when counts are low. Use MAF filters and report confidence.
• Long-range LD regions. Exclude or handle with special rules (e.g., MHC) during clumping.
• Batch effects. LD can reflect lab artefacts. Audit by plate, centre, and run date.
• Window misuse. Very narrow windows miss relevant pairs; very wide windows waste time. Tune by genome and species.
• Over-pruning. Aggressive thresholds remove informative markers. Pilot different r² cut-offs and inspect PCA stability.

Mini Case Study: Tagging to Cut Costs Without Losing Power

A research team planned a GWAS for a quantitative trait. They began with a dense pilot panel and linkage disequilibrium analysis across 500,000 common variants. Using r² ≥ 0.8 within 250 kb windows, they selected tag SNPs that captured most local correlation. The final array had ~35% fewer markers than the draft list. In power simulations based on the pilot LD matrices, >95% of associations detectable by the dense panel were still detectable. This reduced lab costs and data storage, while maintaining statistical performance. The team then applied stricter pruning for PRS construction and looser clumping for discovery analyses. The combination delivered robust signals and efficient follow-up.

The lesson is simple. Calibrate r² thresholds to your trait architecture and sample size. Test choices on a pilot before you scale.

Quick Glossary

• Linkage disequilibrium (LD): Non-random association of alleles at different loci.
• Linkage equilibrium: Allele combinations occur at expected frequencies from single-locus rates.
• r²: Squared correlation between alleles; best for predictability and tagging.
• D': Standardised disequilibrium; best for recombination and block boundaries.
• Haplotype block: Region with limited recombination and high internal LD.
• Tag SNP: Marker chosen to capture nearby variation using LD.
• Clumping: Grouping association hits by LD around lead variants.
• Pruning: Removing correlated markers to keep near-independent sets.
• Imputation: Inferring missing genotypes using LD patterns from references.
• Recombination hotspot: Narrow region with high recombination rate.
• Long-range LD: Extended correlation spanning large distances or special regions.
• MAF: Minor allele frequency; informs LD stability and metric choice.
• Phasing: Assigning alleles to parental chromosomes; improves haplotype inference.

FAQs the Internet Actually Asks

What is LD in simple terms?

It is a measure of how often certain allele pairs appear together more or less than chance.

When should I use r² vs D'?

Use r² for tagging and power. Use D' to infer recombination or define blocks, with MAF filters.

What is "high LD"?

For tagging, many groups call r² ≥ 0.8 high. Always state thresholds and context.

How do I compute LD from a VCF?

Filter for quality and MAF. Then run PLINK --r2 in windows. Inspect matrices and plots.

Why does LD differ across ancestries?

Demography and recombination histories differ. Populations with larger effective size often show faster LD decay.

Does phasing affect LD estimates?

Phasing improves haplotypes and D' accuracy. Many r² calculations work on unphased genotypes.

How large should my sample be?

Larger samples stabilise LD, especially for low-frequency alleles. Power calculations should guide final numbers.

Can I compare LD across species or panels?

Yes, with care. Match MAF bins, sample sizes, filters, and window settings.

What regions need special handling?

The MHC and known long-range LD regions. Check species-specific lists before clumping or pruning.

Ready to Apply LD in Your Project?

You do not need to guess your thresholds alone. We help teams design LD-aware GWAS and fine-mapping plans, set transparent QC, and deliver clear, citable reports. Discuss your cohort, array or WGS plan, and the downstream analyses you want to enable. We align LD steps with your trait models, ancestry makeup, and regulatory reporting needs for research.

Start your project: Linkage Disequilibrium Analysis Service

Note: Services are for research use only. We do not provide clinical or personal testing.

Related reading:

• Practical Guide: Designing an LD Study (MAF, r² Thresholds, Sample Size)
• Running LD the Right Way: PLINK Workflow, Parameters, and LD Pruning
• LD Decay and Haplotype Blocks: Interpreting Curves for Marker Strategy