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name: bio-spatial-transcriptomics-spatial-statistics description: Compute spatial statistics for spatial transcriptomics data using Squidpy. Calculate Moran's I, Geary's C, spatial autocorrelation, co-occurrence analysis, and neighborhood enrichment. Use when computing spatial autocorrelation or co-occurrence statistics. tool_type: python primary_tool: squidpy

Spatial Statistics

Compute spatial statistics and identify spatially variable features.

Required Imports

Copyimport squidpy as sq
import scanpy as sc
import pandas as pd
import numpy as np

Compute Spatial Autocorrelation (Moran's I)

Copy# Requires spatial neighbors
sq.gr.spatial_neighbors(adata, coord_type='generic', n_neighs=6)

# Compute Moran's I for all genes (can be slow)
sq.gr.spatial_autocorr(adata, mode='moran')

# Or for specific genes
sq.gr.spatial_autocorr(adata, mode='moran', genes=['GENE1', 'GENE2', 'GENE3'])

# Results stored in adata.uns['moranI']
moran_results = adata.uns['moranI']
print(moran_results.head(20))

Interpret Moran's I

Copy# Moran's I ranges from -1 to 1
# I > 0: positive spatial autocorrelation (similar values cluster)
# I = 0: random spatial distribution
# I < 0: negative spatial autocorrelation (dissimilar values cluster)

# Get significantly spatially variable genes
svg = moran_results[moran_results['pval_norm'] < 0.05].sort_values('I', ascending=False)
print(f'Found {len(svg)} spatially variable genes (p < 0.05)')
print('\nTop 10 spatially variable genes:')
print(svg.head(10)[['I', 'pval_norm']])

Compute Geary's C

Copy# Alternative spatial autocorrelation measure
sq.gr.spatial_autocorr(adata, mode='geary')

# Results in adata.uns['gearyC']
geary_results = adata.uns['gearyC']
# C < 1: positive spatial autocorrelation
# C = 1: random
# C > 1: negative spatial autocorrelation

Co-occurrence Analysis

Copy# Analyze co-localization of cell types/clusters
# First, ensure you have cluster labels
sc.pp.neighbors(adata)
sc.tl.leiden(adata)

# Compute co-occurrence
sq.gr.co_occurrence(adata, cluster_key='leiden')

# Results in adata.uns['leiden_co_occurrence']
# Visualize co-occurrence
sq.pl.co_occurrence(adata, cluster_key='leiden')

Interpret Co-occurrence

Copyco_occ = adata.uns['leiden_co_occurrence']
occ_matrix = co_occ['occ']  # Occurrence matrix
interval = co_occ['interval']  # Distance intervals

# occ_matrix[i, j, k] = occurrence of cluster j around cluster i at distance interval k
print(f'Occurrence matrix shape: {occ_matrix.shape}')
print(f'Distance intervals: {interval}')

Neighborhood Enrichment

Copy# Test if clusters are enriched in each other's neighborhoods
sq.gr.nhood_enrichment(adata, cluster_key='leiden')

# Results in adata.uns['leiden_nhood_enrichment']
# zscore > 0: clusters co-localize more than expected
# zscore < 0: clusters avoid each other

# Visualize
sq.pl.nhood_enrichment(adata, cluster_key='leiden')

Extract Enrichment Z-scores

Copyenrichment = adata.uns['leiden_nhood_enrichment']
zscore = enrichment['zscore']
clusters = adata.obs['leiden'].cat.categories

# Convert to DataFrame
zscore_df = pd.DataFrame(zscore, index=clusters, columns=clusters)
print('Neighborhood enrichment z-scores:')
print(zscore_df)

Ripley's Statistics

Copy# Ripley's K/L function for point pattern analysis (single-cell resolution data)
sq.gr.ripley(adata, cluster_key='leiden', mode='L')

# Results in adata.uns['leiden_ripley']
sq.pl.ripley(adata, cluster_key='leiden')

Centrality Scores

Copy# Compute centrality of each cell type
sq.gr.centrality_scores(adata, cluster_key='leiden')

# Results in adata.uns['leiden_centrality_scores']
centrality = adata.uns['leiden_centrality_scores']
print(centrality)

Interaction Matrix

Copy# Build interaction matrix between clusters
sq.gr.interaction_matrix(adata, cluster_key='leiden')

# Results in adata.uns['leiden_interactions']
interactions = adata.uns['leiden_interactions']
print(interactions)

Custom Spatial Statistic

Copyfrom scipy.stats import pearsonr

def spatial_correlation(adata, gene1, gene2):
    '''Compute spatial correlation between two genes'''
    expr1 = adata[:, gene1].X.toarray().flatten()
    expr2 = adata[:, gene2].X.toarray().flatten()
    r, p = pearsonr(expr1, expr2)
    return r, p

r, p = spatial_correlation(adata, 'GENE1', 'GENE2')
print(f'Spatial correlation: r={r:.3f}, p={p:.2e}')

Local Moran's I (LISA)

Copyfrom esda.moran import Moran_Local
from libpysal.weights import KNN

# Build weights matrix
coords = adata.obsm['spatial']
w = KNN.from_array(coords, k=6)
w.transform = 'r'

# Compute local Moran's I for a gene
gene_expr = adata[:, 'GENE1'].X.toarray().flatten()
lisa = Moran_Local(gene_expr, w)

# Add to adata
adata.obs['GENE1_lisa'] = lisa.Is
adata.obs['GENE1_lisa_q'] = lisa.q  # Quadrant (HH, HL, LH, LL)

Batch Spatial Statistics

Copy# Compute Moran's I for top variable genes only
hvg = adata.var_names[adata.var['highly_variable']][:500]
sq.gr.spatial_autocorr(adata, mode='moran', genes=hvg)

results = adata.uns['moranI']
significant = results[results['pval_norm'] < 0.01]
print(f'{len(significant)} genes with significant spatial autocorrelation')

Related Skills

• spatial-neighbors - Build spatial graphs (prerequisite)
• spatial-domains - Identify spatial domains
• spatial-visualization - Visualize spatial statistics