Linkage Disequilibrium
Calculate LD statistics, prune correlated variants, and identify haplotype blocks.
PLINK LD Calculations
Pairwise r²
bash
# All pairs within window plink2 --bfile data --r2 --ld-window-kb 1000 --ld-window-r2 0.2 --out ld_results # With SNP names in output plink2 --bfile data --r2 inter-chr --ld-window-r2 0 --out all_pairs # Squared correlation matrix plink2 --bfile data --r2-phased square --out ld_matrix
Output Format
code
# ld_results.ld contains: CHR_A BP_A SNP_A CHR_B BP_B SNP_B R2
PLINK 1.9 Options
bash
# r² with D' statistics plink --bfile data --r2 dprime --ld-window-kb 500 --out ld_with_dprime # Inter-chromosome LD plink --bfile data --r2 inter-chr --ld-snp-list target_snps.txt --out target_ld
LD Pruning
Standard Pruning
bash
# Calculate pruning list plink2 --bfile data --indep-pairwise 50 10 0.1 --out prune # Output files: # prune.prune.in - Variants to keep # prune.prune.out - Variants to remove # Extract pruned set plink2 --bfile data --extract prune.prune.in --make-bed --out data_pruned
Pruning Parameters
| Parameter | Description | Common Values |
|---|---|---|
| Window (50) | Variants per window | 50-200 |
| Step (10) | Variants to shift | 5-50 |
| r² threshold (0.1) | Max LD allowed | 0.1-0.5 |
Use Cases
bash
# Strict pruning for PCA/Admixture plink2 --bfile data --indep-pairwise 50 10 0.1 --out strict_prune # Moderate pruning for polygenic scores plink2 --bfile data --indep-pairwise 200 50 0.5 --out moderate_prune # Region-based pruning plink2 --bfile data --indep-pairwise 50 10 0.2 --chr 6 --from-mb 25 --to-mb 35 --out mhc_prune
scikit-allel LD
Pairwise r²
python
import allel
import numpy as np
callset = allel.read_vcf('data.vcf.gz')
gt = allel.GenotypeArray(callset['calldata/GT'])
pos = callset['variants/POS']
gn = gt.to_n_alt()
r2 = allel.rogers_huff_r(gn[:100]) ** 2
LD Decay
python
import allel
import numpy as np
import matplotlib.pyplot as plt
gn = gt.to_n_alt()
r2, dist = [], []
n_variants = min(1000, gn.shape[0])
for i in range(n_variants):
for j in range(i + 1, min(i + 100, n_variants)):
r = allel.rogers_huff_r(gn[[i, j]])[0, 1] ** 2
d = pos[j] - pos[i]
r2.append(r)
dist.append(d)
r2 = np.array(r2)
dist = np.array(dist)
bins = np.arange(0, 100001, 1000)
bin_means = []
for i in range(len(bins) - 1):
mask = (dist >= bins[i]) & (dist < bins[i + 1])
if mask.sum() > 0:
bin_means.append(np.mean(r2[mask]))
else:
bin_means.append(np.nan)
plt.figure(figsize=(10, 6))
plt.plot(bins[:-1] / 1000, bin_means)
plt.xlabel('Distance (kb)')
plt.ylabel('Mean r²')
plt.title('LD Decay')
plt.savefig('ld_decay.png')
Haplotype Blocks
PLINK
bash
# Identify haplotype blocks (Gabriel et al.) plink --bfile data --blocks no-pheno-req --out blocks # Output: blocks.blocks (block boundaries) # Output: blocks.blocks.det (block details)
Block Statistics
python
import pandas as pd
blocks = pd.read_csv('blocks.blocks.det', sep='\s+')
print(f'Number of blocks: {len(blocks)}')
print(f'Mean block size: {blocks["KB"].mean():.1f} kb')
print(f'Mean SNPs per block: {blocks["NSNPS"].mean():.1f}')
LD Matrix Visualization
python
import allel
import numpy as np
import matplotlib.pyplot as plt
gn = gt.to_n_alt()[:200]
r = allel.rogers_huff_r(gn)
r2_matrix = r ** 2
plt.figure(figsize=(10, 10))
plt.imshow(r2_matrix, cmap='hot', vmin=0, vmax=1)
plt.colorbar(label='r²')
plt.xlabel('Variant index')
plt.ylabel('Variant index')
plt.title('LD Matrix')
plt.savefig('ld_matrix.png', dpi=150)
LD-based Clumping (GWAS)
bash
# Clump GWAS results by LD
plink --bfile data \
--clump gwas_results.txt \
--clump-p1 5e-8 \
--clump-p2 1e-5 \
--clump-r2 0.1 \
--clump-kb 250 \
--out clumped
# Output: clumped.clumped (independent signals)
Clump Parameters
| Parameter | Description |
|---|---|
| --clump-p1 | Index SNP p-value threshold |
| --clump-p2 | Clumped SNP p-value threshold |
| --clump-r2 | LD threshold for clumping |
| --clump-kb | Physical distance threshold |
vcftools LD
bash
# Pairwise LD for region vcftools --vcf data.vcf --geno-r2 --ld-window-bp 100000 --out ld_results # Output: ld_results.geno.ld # Haplotype-based r² vcftools --vcf data.vcf --hap-r2 --ld-window-bp 100000 --out hap_ld
Complete Workflow
bash
# 1. Calculate genome-wide LD plink2 --bfile data --r2 --ld-window-kb 500 --ld-window-r2 0.2 --out ld_genome # 2. Generate pruned set for PCA plink2 --bfile data --indep-pairwise 50 10 0.1 --out prune plink2 --bfile data --extract prune.prune.in --make-bed --out pruned # 3. Identify haplotype blocks plink --bfile data --blocks no-pheno-req --out blocks # 4. Visualize LD for specific region plink --bfile data --r2 dprime --chr 6 --from-mb 28 --to-mb 34 --out mhc_ld
Related Skills
- •plink-basics - File format handling
- •population-structure - Use pruned data for PCA
- •association-testing - LD clumping for GWAS
- •selection-statistics - LD affects EHH statistics