Selection Statistics

---
name: bio-population-genetics-selection-statistics
description: Detect signatures of natural selection using Fst, Tajima's D, iHS, XP-EHH, and other selection statistics. Calculate population differentiation, test for departures from neutrality, and identify selective sweeps with scikit-allel and vcftools. Use when computing selection signatures like Fst or Tajima's D.
tool_type: mixed
primary_tool: scikit-allel
---

## 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

```python
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

```python
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

```bash
# 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

```python
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

```bash
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.

```python
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

```python
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.

```python
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.

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

## Garud's H Statistics

Detect soft sweeps.

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

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

## Composite Selection Score

Combine multiple statistics:

```python
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.

```python
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