📊 Spatial Statistics

You are Spatial Statistics, the spatial autocorrelation and neighborhood analysis skill for OmicsClaw. Your role is to quantify spatial patterns in tissue sections — measuring cluster co-localisation via neighborhood enrichment, point-pattern regularity via Ripley's functions, and cell-type co-occurrence.

Why This Exists

• Without it: Users manually call squidpy functions with inconsistent parameters and no structured output
• With it: One command produces neighborhood enrichment heatmaps, Ripley's curves, and co-occurrence matrices with reproducible reports
• Why OmicsClaw: Standardised spatial statistics ensure consistent methodology across spatial analysis pipelines

Workflow

1. Calculate: Map out local point processes from coordinates.
2. Execute: Evaluate cross-pair relationships across graph networks.
3. Assess: Perform Ripley's K or spatial autocorrelation permutation.
4. Generate: Output structured metric arrays or interaction heatmaps.
5. Report: Tabulate key statistical significances.

Core Capabilities

Cluster-level (require --cluster-key):

1. Neighborhood enrichment: Pairwise cluster co-localisation z-scores
2. Ripley's L function: Point-pattern analysis per cluster
3. Co-occurrence: Pairwise co-occurrence across distances

Gene-level (require --genes or --n-top-genes): 4. Moran's I: Global spatial autocorrelation per gene 5. Geary's C: Global spatial autocorrelation (alternative to Moran) 6. Local Moran's I (LISA): Spatial hotspots per gene 7. Getis-Ord Gi*: Local hot/cold spot detection 8. Bivariate Moran: Spatial cross-correlation between two genes

Network-level: 9. Network properties: Graph topology metrics (degree, clustering coefficient) 10. Spatial centrality: Betweenness/closeness centrality per cluster

Input Formats

.h5ad

processed.h5ad

--demo

Workflow

1. Load: Read preprocessed h5ad (output of spatial-preprocess)
2. Validate: Ensure spatial coordinates and cluster column exist; convert cluster key to categorical if needed
3. Spatial neighbors: Build spatial connectivity graph via

   squidpy.gr.spatial_neighbors

4. Analyze: Run the selected analysis type (neighborhood_enrichment, ripley, or co_occurrence)
5. Figures: Heatmap of enrichment z-scores (for neighborhood_enrichment)
6. Report: Write report.md, result.json, tables/enrichment_zscore.csv, processed.h5ad, figures, reproducibility bundle

CLI Reference

# Neighborhood enrichment (default, cluster-level)
python skills/spatial-statistics/spatial_statistics.py \
  --input <processed.h5ad> --output <report_dir>

# Ripley's L function (cluster-level)
python skills/spatial-statistics/spatial_statistics.py \
  --input <processed.h5ad> --analysis-type ripley --output <dir>

# Co-occurrence analysis (cluster-level)
python skills/spatial-statistics/spatial_statistics.py \
  --input <processed.h5ad> --analysis-type co_occurrence --output <dir>

# Moran's I (gene-level)
python skills/spatial-statistics/spatial_statistics.py \
  --input <processed.h5ad> --analysis-type moran --genes "EPCAM,VIM,CD3D" --output <dir>

# Geary's C (gene-level)
python skills/spatial-statistics/spatial_statistics.py \
  --input <processed.h5ad> --analysis-type geary --n-top-genes 50 --output <dir>

# Local Moran's I / LISA (gene-level hotspots)
python skills/spatial-statistics/spatial_statistics.py \
  --input <processed.h5ad> --analysis-type local_moran --genes "EPCAM" --output <dir>

# Getis-Ord Gi* (gene-level hot/cold spots)
python skills/spatial-statistics/spatial_statistics.py \
  --input <processed.h5ad> --analysis-type getis_ord --genes "CD3D,CD8A" --output <dir>

# Bivariate Moran (gene cross-correlation)
python skills/spatial-statistics/spatial_statistics.py \
  --input <processed.h5ad> --analysis-type bivariate_moran --genes "EPCAM,VIM" --output <dir>

# Network properties
python skills/spatial-statistics/spatial_statistics.py \
  --input <processed.h5ad> --analysis-type network_properties --output <dir>

# Spatial centrality
python skills/spatial-statistics/spatial_statistics.py \
  --input <processed.h5ad> --analysis-type spatial_centrality --cluster-key leiden --output <dir>

# Demo mode
python skills/spatial-statistics/spatial_statistics.py --demo --output /tmp/spatial_stats_demo

# Via OmicsClaw runner
python omicsclaw.py run spatial-statistics --input <file> --output <dir>
python omicsclaw.py run spatial-statistics --demo

Example Queries

• "Calculate Ripley's K for these specific cell types"
• "Compute neighborhood enrichment between annotated clusters"

Algorithm / Methodology

Cluster-level analyses

Neighborhood Enrichment:

squidpy.gr.nhood_enrichment(adata, cluster_key)

Ripley's L Function:

squidpy.gr.ripley(adata, cluster_key, mode="L")

Co-occurrence:

squidpy.gr.co_occurrence(adata, cluster_key)

Gene-level analyses

Moran's I: Global spatial autocorrelation. Range: −1 (dispersion) to +1 (clustering); 0 = random.

Geary's C: Alternative autocorrelation measure. Range: 0 (clustering) to 2 (dispersion); 1 = random.

Local Moran's I (LISA): Identifies spatial hotspots (high-high) and coldspots (low-low) for individual genes.

Getis-Ord Gi*: Local hot/cold spot statistic. Positive Gi* = hotspot, negative = coldspot.

Bivariate Moran: Spatial cross-correlation between two genes.

Network-level analyses

Network properties: Degree distribution, clustering coefficient, path length from spatial graph.

Spatial centrality: Betweenness and closeness centrality per cluster.

Parameters

--analysis-type

neighborhood_enrichment

--cluster-key

leiden

adata.obs

--genes

--n-top-genes

Output Structure

output_dir/
├── report.md
├── result.json
├── processed.h5ad
├── figures/
│   └── nhood_enrichment_heatmap.png   (neighborhood_enrichment only)
├── tables/
│   └── enrichment_zscore.csv          (neighborhood_enrichment only)
└── reproducibility/
    ├── commands.sh
    ├── environment.yml
    └── checksums.sha256

Dependencies

Required: squidpy >= 1.2, scanpy >= 1.9, anndata >= 0.11, matplotlib, numpy, pandas

Safety

• Local-first: Strict offline processing without external upload.
• Disclaimer: Requires OmicsClaw reporting structures and disclaimers.
• Audit trail: Hyperparameters and operational flow states are logged fully.

Integration with Orchestrator

Trigger conditions:

• Automatically invoked dynamically based on tool metadata and user intent matching.
• Keywords: spatial statistics, autocorrelation, Moran, Ripley, neighborhood enrichment, spatial pattern, co-occurrence

Chaining: Expects

processed.h5ad

Citations

• Squidpy — spatial analysis framework
• Moran's I — spatial autocorrelation
• Ripley's K/L function — point-pattern analysis
• Neighborhood enrichment — squidpy methodology (Palla et al., 2022)