Bio Spatial Transcriptomics Spatial Statistics

Version Compatibility

Reference examples tested with: numpy 1.26+, pandas 2.2+, scanpy 1.10+, scipy 1.12+, squidpy 1.3+

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

• Python: pip show <package> then help(module.function) to check signatures

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

Spatial Statistics

Compute spatial statistics and identify spatially variable features.

Required Imports

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

Compute Spatial Autocorrelation (Moran's I)

Goal: Identify genes whose expression is spatially autocorrelated across tissue.

Approach: Build a spatial neighbor graph, then compute Moran's I statistic per gene to measure clustering of similar values.

"Find spatially variable genes" -> Compute Moran's I autocorrelation on the spatial neighbor graph to rank genes by spatial patterning.

# 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

# 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

# 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

Goal: Determine whether cell types co-localize or segregate in tissue space.

Approach: Compute pairwise co-occurrence probabilities at multiple distance intervals using Squidpy.

# 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

co_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

Goal: Test whether cell type clusters are enriched or depleted in each other's spatial neighborhoods.

Approach: Run permutation-based neighborhood enrichment test, yielding z-scores for each cluster pair.

# 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

enrichment = 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

# 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

# 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

# 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

from 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)

Goal: Identify local hotspots and coldspots of gene expression in tissue space.

Approach: Compute Local Indicators of Spatial Association (LISA) using PySAL, which assigns each spot to a cluster-outlier quadrant (HH, HL, LH, LL).

from 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

Goal: Efficiently compute spatial autocorrelation for a large set of genes.

Approach: Subset to highly variable genes before running Moran's I to reduce computation time.

# 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