GPTomics/bio-population-genetics-selection-statistics

Version Compatibility

Reference examples tested with: STAR 2.7.11+, matplotlib 3.8+, numpy 1.26+, scipy 1.12+

Before using code patterns, verify installed versions match. If versions differ:

• Python: pip show <package> then help(module.function) to check signatures
• CLI: <tool> --version then <tool> --help to confirm flags

If code throws ImportError, AttributeError, or TypeError, introspect the installed package and adapt the example to match the actual API rather than retrying.

Selection Statistics

"Scan my population data for signs of natural selection" -> Calculate selection statistics (Fst, Tajima's D, iHS, XP-EHH) to detect selective sweeps and departures from neutrality.

• Python: allel.moving_hudson_fst(), allel.ihs(), allel.xpehh() (scikit-allel)
• CLI: vcftools --weir-fst-pop for pairwise Fst

Detect natural selection signatures using diversity statistics and extended haplotype homozygosity.

Fst - Population Differentiation

scikit-allel

import allel
import numpy as np

callset = allel.read_vcf('data.vcf.gz')
gt = allel.GenotypeArray(callset['calldata/GT'])
pos = callset['variants/POS']

subpops = {'pop1': [0, 1, 2, 3, 4], 'pop2': [5, 6, 7, 8, 9]}
ac_subpops = gt.count_alleles_subpops(subpops)

num, den = allel.hudson_fst(ac_subpops['pop1'], ac_subpops['pop2'])
fst_per_snp = num / den
# ratio-of-averages (preferred over mean of per-SNP ratios)
fst_mean = np.nansum(num) / np.nansum(den)
print(f'Mean Fst: {fst_mean:.4f}')

Windowed Fst

fst_windowed, windows, n_snps = allel.windowed_hudson_fst(
    pos, ac_subpops['pop1'], ac_subpops['pop2'],
    size=100000, step=50000)

import matplotlib.pyplot as plt
plt.figure(figsize=(14, 4))
plt.plot(windows[:, 0], fst_windowed)
plt.xlabel('Position')
plt.ylabel('Fst')
plt.savefig('fst_windows.png')

vcftools

# Calculate Fst between populations
vcftools --vcf data.vcf --weir-fst-pop pop1.txt --weir-fst-pop pop2.txt --out fst_result

# With window
vcftools --vcf data.vcf --weir-fst-pop pop1.txt --weir-fst-pop pop2.txt \
         --fst-window-size 100000 --fst-window-step 50000 --out fst_windowed

Choosing an Fst Estimator

| Estimator | Method | Best for | |-----------|--------|----------| | Weir & Cockerham (1984) | vcftools --weir-fst-pop | Unequal sample sizes; corrects for sample size bias | | Hudson (Bhatia et al. 2013) | allel.hudson_fst() | Very unequal sample sizes; robust two-population estimator | | Nei's Gst | allel.average_nei_fst() | Avoid when sample sizes are unequal; biased downward with small samples |

When sample sizes between populations are known and unequal, prefer Weir & Cockerham or Hudson over Nei's Gst. Hudson's estimator is especially robust when one population is much larger than the other (Bhatia et al. 2013).

For genome-wide mean Fst, always compute as ratio-of-averages (sum(numerators) / sum(denominators)), not the arithmetic mean of per-SNP Fst values. Per-SNP ratios are noisy at low-diversity loci and inflate the average.

Fst estimator methodology evolves; before selecting an estimator, verify current best practices by checking the latest scikit-allel and vcftools documentation for any updated or newly recommended approaches.

When Population Labels Are Unknown

When samples lack predefined population assignments, population structure must be inferred before computing Fst:

1. Run PCA (allel.pca() or PLINK --pca) to identify clusters visually
2. Use an assignment method (ADMIXTURE, sklearn.cluster.KMeans on PC space) to assign population labels
3. Compute Fst between inferred groups

For continuous population structure (isolation-by-distance, clines), per-population Fst may not be meaningful. Consider instead:

• Pairwise individual-level relatedness or kinship matrices
• Spatial autocorrelation of allele frequencies
• Landscape genomics approaches (see ecological-genomics/landscape-genomics)

Tajima's D - Departures from Neutrality

scikit-allel

import allel
import numpy as np

callset = allel.read_vcf('data.vcf.gz')
gt = allel.GenotypeArray(callset['calldata/GT'])
pos = callset['variants/POS']
ac = gt.count_alleles()

D, windows, counts = allel.windowed_tajima_d(pos, ac, size=100000, step=50000)

plt.figure(figsize=(14, 4))
plt.plot(windows[:, 0], D)
plt.axhline(y=0, color='r', linestyle='--')
plt.xlabel('Position')
plt.ylabel("Tajima's D")
plt.savefig('tajima_d.png')

Interpretation

| D Value | Interpretation | |---------|---------------| | D < -2 | Recent selective sweep or population expansion | | D ≈ 0 | Neutral evolution | | D > 2 | Balancing selection or population bottleneck |

vcftools

vcftools --vcf data.vcf --TajimaD 100000 --out tajima
# Output: tajima.Tajima.D (CHROM, BIN_START, N_SNPS, TajimaD)

iHS - Integrated Haplotype Score

Detects ongoing selective sweeps.

import allel
import numpy as np

callset = allel.read_vcf('data.vcf.gz')
gt = allel.GenotypeArray(callset['calldata/GT'])
pos = callset['variants/POS']
h = gt.to_haplotypes()
ac = h.count_alleles()
flt = (ac[:, 0] > 1) & (ac[:, 1] > 1)
h_flt = h.compress(flt, axis=0)
pos_flt = pos[flt]
ac_flt = ac.compress(flt, axis=0)

ihs = allel.ihs(h_flt, pos_flt, include_edges=True)
ihs_std = allel.standardize_by_allele_count(ihs, ac_flt[:, 1])

significant_ihs = np.abs(ihs_std[0]) > 2
print(f'Significant iHS hits: {significant_ihs.sum()}')

Plot iHS

import matplotlib.pyplot as plt

plt.figure(figsize=(14, 4))
plt.scatter(pos_flt, ihs_std[0], s=1)
plt.axhline(y=2, color='r', linestyle='--')
plt.axhline(y=-2, color='r', linestyle='--')
plt.xlabel('Position')
plt.ylabel('Standardized iHS')
plt.savefig('ihs.png')

XP-EHH - Cross-Population Extended Haplotype Homozygosity

Detects completed sweeps by comparing populations.

import allel
import numpy as np

h = gt.to_haplotypes()
h_pop1 = h.take(pop1_hap_idx, axis=1)
h_pop2 = h.take(pop2_hap_idx, axis=1)

xpehh = allel.xpehh(h_pop1, h_pop2, pos, include_edges=True)

significant = np.abs(xpehh) > 2
print(f'Significant XP-EHH hits: {significant.sum()}')

NSL - Number of Segregating Sites by Length

Alternative to iHS, less sensitive to recombination rate variation.

nsl = allel.nsl(h_flt)
nsl_std = allel.standardize_by_allele_count(nsl, ac_flt[:, 1])

Garud's H Statistics

Detect soft sweeps.

h1, h12, h123, h2_h1 = allel.garud_h(h)

h12_windowed = allel.moving_garud_h(h, size=100)

Composite Selection Score

Combine multiple statistics:

import numpy as np
from scipy import stats

def composite_score(fst, tajD, ihs_abs):
    fst_rank = stats.rankdata(fst) / len(fst)
    tajD_rank = stats.rankdata(-tajD) / len(tajD)  # Low Tajima's D
    ihs_rank = stats.rankdata(ihs_abs) / len(ihs_abs)
    return (fst_rank + tajD_rank + ihs_rank) / 3

css = composite_score(fst_per_snp, tajD_values, np.abs(ihs_values))

Complete Selection Scan

Goal: Scan a genomic region for signatures of natural selection using multiple complementary statistics.

Approach: Filter to segregating biallelic variants, compute windowed Tajima's D for neutrality departures and windowed nucleotide diversity for reduced variation, then visualize both statistics along the chromosome.

import allel
import numpy as np
import matplotlib.pyplot as plt

callset = allel.read_vcf('data.vcf.gz')
gt = allel.GenotypeArray(callset['calldata/GT'])
pos = callset['variants/POS']
ac = gt.count_alleles()

flt = ac.is_segregating() & (ac.max_allele() == 1)
gt = gt.compress(flt, axis=0)
pos = pos[flt]
ac = ac.compress(flt, axis=0)

window_size = 100000
window_step = 50000

tajD, tajD_windows, _ = allel.windowed_tajima_d(pos, ac, size=window_size, step=window_step)

pi, pi_windows, _, _ = allel.windowed_diversity(pos, ac, size=window_size, step=window_step)

fig, axes = plt.subplots(2, 1, figsize=(14, 8), sharex=True)

axes[0].plot(tajD_windows[:, 0], tajD)
axes[0].axhline(0, color='r', linestyle='--')
axes[0].set_ylabel("Tajima's D")

axes[1].plot(pi_windows[:, 0], pi)
axes[1].set_ylabel('Pi')
axes[1].set_xlabel('Position')

plt.tight_layout()
plt.savefig('selection_scan.png', dpi=150)

Related Skills

• scikit-allel-analysis - Data loading and basic statistics
• population-structure - Population assignment for Fst
• linkage-disequilibrium - EHH depends on LD patterns
• ecological-genomics/landscape-genomics - Genotype-environment association for non-model organisms