Bio Population Genetics Population Structure

Population Structure

Analyze genetic ancestry and population stratification using PCA and ADMIXTURE.

Principal Component Analysis (PCA)

PLINK 2.0 PCA

# Basic PCA (10 PCs)
plink2 --bfile data --pca 10 --out pca_results

# More PCs
plink2 --bfile data --pca 20 --out pca_results

# Approximate PCA (faster for large datasets)
plink2 --bfile data --pca 10 approx --out pca_results

# Output variant loadings
plink2 --bfile data --pca 10 var-wts --out pca_results

Output Files

Variance Explained

import numpy as np

eigenvalues = np.loadtxt('pca_results.eigenval')
variance_explained = eigenvalues / eigenvalues.sum() * 100
cumulative = np.cumsum(variance_explained)

for i, (ve, cum) in enumerate(zip(variance_explained, cumulative), 1):
    print(f'PC{i}: {ve:.2f}% (cumulative: {cum:.2f}%)')

PCA Visualization

import pandas as pd
import matplotlib.pyplot as plt

eigenvec = pd.read_csv('pca_results.eigenvec', sep='\s+', header=None)
eigenvec.columns = ['FID', 'IID'] + [f'PC{i}' for i in range(1, len(eigenvec.columns) - 1)]

pop_info = pd.read_csv('population_labels.txt', sep='\t')  # FID, IID, Population
eigenvec = eigenvec.merge(pop_info, on=['FID', 'IID'])

plt.figure(figsize=(10, 8))
for pop in eigenvec['Population'].unique():
    subset = eigenvec[eigenvec['Population'] == pop]
    plt.scatter(subset['PC1'], subset['PC2'], label=pop, s=20, alpha=0.7)

plt.xlabel('PC1')
plt.ylabel('PC2')
plt.legend()
plt.savefig('pca_plot.png', dpi=150)

LD Pruning (Before Admixture)

ADMIXTURE requires LD-pruned SNPs:

# Calculate LD and identify pruned set
plink2 --bfile data --indep-pairwise 50 10 0.1 --out prune

# Extract pruned variants
plink2 --bfile data --extract prune.prune.in --make-bed --out data_pruned

Pruning Parameters

ADMIXTURE Analysis

Basic Usage

# Run ADMIXTURE for K=3 clusters
admixture data_pruned.bed 3

# With cross-validation
admixture --cv data_pruned.bed 3

# Multithreaded
admixture -j4 data_pruned.bed 3

Output Files

Testing Multiple K Values

# Run for K=2 through K=10
for K in $(seq 2 10); do
    admixture --cv -j4 data_pruned.bed $K 2>&1 | tee log${K}.out
done

# Extract CV errors
grep -h "CV" log*.out | awk '{print NR+1, $4}' > cv_errors.txt

Choose Optimal K

import matplotlib.pyplot as plt

cv_errors = []
with open('cv_errors.txt') as f:
    for line in f:
        k, cv = line.strip().split()
        cv_errors.append((int(k), float(cv)))

ks, cvs = zip(*cv_errors)
plt.figure(figsize=(8, 5))
plt.plot(ks, cvs, 'o-')
plt.xlabel('K')
plt.ylabel('Cross-validation error')
plt.title('Admixture CV Error')
plt.savefig('admixture_cv.png', dpi=150)

optimal_k = ks[cvs.index(min(cvs))]
print(f'Optimal K: {optimal_k}')

Visualize Admixture

import pandas as pd
import matplotlib.pyplot as plt
import numpy as np

K = 3
Q = pd.read_csv(f'data_pruned.{K}.Q', sep='\s+', header=None)
fam = pd.read_csv('data_pruned.fam', sep='\s+', header=None)
Q.columns = [f'Cluster{i}' for i in range(1, K + 1)]
Q['IID'] = fam[1].values

pop_info = pd.read_csv('population_labels.txt', sep='\t')
Q = Q.merge(pop_info, on='IID')
Q = Q.sort_values('Population')

colors = plt.cm.Set1(range(K))
fig, ax = plt.subplots(figsize=(14, 4))

bottom = np.zeros(len(Q))
for i in range(K):
    ax.bar(range(len(Q)), Q[f'Cluster{i+1}'], bottom=bottom, color=colors[i], width=1)
    bottom += Q[f'Cluster{i+1}'].values

ax.set_xlim(0, len(Q))
ax.set_ylim(0, 1)
ax.set_ylabel('Ancestry proportion')
plt.savefig('admixture_barplot.png', dpi=150, bbox_inches='tight')

MDS (Alternative to PCA)

# PLINK 1.9 MDS
plink --bfile data --cluster --mds-plot 10 --out mds_results

# Output: mds_results.mds (sample coordinates)

Kinship/Relatedness

PLINK 2.0 KING-robust

# Calculate kinship matrix
plink2 --bfile data --make-king-table --out kinship

# Output: kinship.kin0 (pairs with kinship > 0.0442)

Identify Related Individuals

import pandas as pd

kin = pd.read_csv('kinship.kin0', sep='\t')
related = kin[kin['KINSHIP'] > 0.0884]  # First-degree relatives
print(f'Related pairs (1st degree): {len(related)}')

related = kin[kin['KINSHIP'] > 0.0442]  # Second-degree
print(f'Related pairs (2nd degree): {len(related)}')

Remove Related Individuals

# Create list to remove (keep one per pair)
plink2 --bfile data --king-cutoff 0.0884 --out unrelated

# Filter to unrelated
plink2 --bfile data --keep unrelated.king.cutoff.in.id --make-bed --out unrelated

Complete Workflow

# 1. QC filtering
plink2 --bfile raw --maf 0.01 --geno 0.05 --hwe 1e-6 --make-bed --out qc

# 2. LD pruning
plink2 --bfile qc --indep-pairwise 50 10 0.1 --out prune
plink2 --bfile qc --extract prune.prune.in --make-bed --out pruned

# 3. PCA
plink2 --bfile pruned --pca 20 --out pca

# 4. Admixture (multiple K)
for K in 2 3 4 5 6; do
    admixture --cv -j4 pruned.bed $K 2>&1 | tee log${K}.out
done

Related Skills

• plink-basics - Data preparation and QC
• linkage-disequilibrium - LD pruning details
• association-testing - Use PCs as covariates