Extended Formula Derivation

The Getis-Ord Gi* statistic, introduced by Getis and Ord (1992) and refined by Ord and Getis (1995), is a local indicator of spatial association (LISA). It evaluates whether the sum of an attribute value within a defined neighborhood is significantly different from the sum expected under spatial randomness.

Equivalent forms:

• Numerator: Observed local sum minus expected local sum
• Denominator: Standard error of the local sum under the null hypothesis of complete spatial randomness
• Output: A standardized z-score directly comparable across spatial units

Moran's I (global autocorrelation):

I = (n / ∑∑w_ij) × [ ∑∑w_ij(x_i−x̄)(x_j−x̄) / ∑(x_i−x̄)² ]

Assumptions

• Spatial units are properly delineated and exhaustive (no gaps, no overlaps)
• Sampling effort is approximately equal across units (or normalized as a rate)
• Conflict reporting is comparable across units (no bias in detection/reporting)
• Spatial weights (queen, rook, or distance-based) correctly reflect ecological adjacency
• Sufficient sample size (n ≥ 30 spatial units) for asymptotic normality of Gi*

Limitations

• Modifiable Areal Unit Problem (MAUP): Results can change with different grid sizes or aggregation schemes
• Edge effects: Units near the study area boundary have fewer neighbors, potentially biasing local statistics
• Reporting bias: Areas with higher human density or active monitoring may show artificial hotspots
• Temporal aggregation: Pooling multiple years can mask seasonal or annual hotspot shifts
• Causation: Hotspots indicate where conflict clusters, not why — covariate analyses are needed for mechanism

Decision Checklist

• ✓ You have geographically referenced wildlife conflict incident counts (livestock losses, vehicle collisions, crop damage, attacks)
• ✓ You want to identify statistically significant clusters, not just visual concentrations
• ✓ You need to prioritize mitigation resources (fencing, deterrents, ranger patrols, compensation payouts)
• ✓ Your study has at least 30 spatial units with conflict count data
• ✓ You want publication-ready output for ecology, wildlife management, or conservation journals
• ✗ Do NOT use if you have only point coordinates without spatial unit aggregation (use KDE separately)
• ✗ Do NOT use if sampling/reporting effort varies drastically across units (standardize first)
• ✗ Do NOT use if your n < 30 spatial units (consider exact permutation tests instead)

Real-World Examples (USA)

1. Wolf-Livestock Depredation — Rocky Mountain West: Identifying hotspots of confirmed wolf depredation on cattle and sheep across Montana, Idaho, and Wyoming to target proactive non-lethal deterrents.
2. Black Bear-Human Conflict — Great Smoky Mountains: Mapping bear-incident clusters in gateway communities to focus bear-resistant trash infrastructure and visitor education.
3. Mountain Lion Encounters — California Wildland-Urban Interface: Pinpointing puma encounter hotspots in Los Angeles and Bay Area suburbs for collared monitoring and outreach.
4. Deer-Vehicle Collisions — Pennsylvania DOT corridors: Identifying collision hotspots along state highways to prioritize wildlife crossing structures, signage, and seasonal speed limits.
5. Coyote-Pet Conflict — Chicago Metro: Detecting urban coyote conflict clusters to guide neighborhood-level hazing training and pet-owner advisories.
6. Alligator-Human Encounters — Florida: Mapping nuisance alligator complaints across Lake Okeechobee watershed for trapper deployment.

Sampling Design Guidance

• Minimum 30 spatial units for reliable Gi* z-scores; ≥ 100 units preferred for Moran's I
• Grid cells of 1–5 km² typically balance resolution and sample adequacy for terrestrial mammals
• Use at least 3–5 years of pooled data unless investigating temporal hotspot shifts
• Normalize by area, road length, or human density if these confound raw counts
• Apply FDR correction (Benjamini-Hochberg) when testing many local Gi* statistics

Related Metrics — Decision Tree

Need to detect hotspots?         → Getis-Ord Gi* (this tool)
Need to detect spatial outliers? → Local Moran's I (LISA)
Need a smooth density surface?   → Kernel Density Estimation
Need to test global clustering?  → Global Moran's I or Geary's C
Have point data only?            → Ripley's K-function or nearest neighbor
Need risk/probability surface?   → MaxEnt, GLM, or Bayesian hierarchical model

1. Enter Your Data: Choose Paste/Type (default), Upload CSV/Excel, or Column Entry mode. Example: 52, 48, 55, 61, 47, 8, 12, 15, ...
2. Choose a Sample Dataset: Pick one of five USA-based wildlife conflict datasets to test the tool.
3. Configure Analysis: Enter Study Area (e.g., "Yellowstone NP"), Species (e.g., "Gray Wolf"), Conflict Type (e.g., "Livestock Depredation"), and significance threshold (default α = 0.05).
4. Click Run Hotspot Analysis: The tool computes Getis-Ord Gi* z-scores, Moran's I, and classifies each unit as Hotspot, Coldspot, or Not Significant.
5. Read the Summary Cards: Green = hotspots detected (priority mitigation sites); Amber = mixed pattern; Red = no significant clustering.
6. Examine the Results Table: See total incidents, mean, SD, Moran's I, z-score range, and hotspot/coldspot counts.
7. Review All Four Charts: Conflict intensity, z-score distribution, classification breakdown, and density curve — each tells part of the story.
8. Read the Detailed Interpretation: 5 paragraphs explaining what the values mean for your site, in plain English.
9. Copy a Reporting Example: Pick the format that matches your audience — journal, thesis, policy brief, abstract, or LTER monitoring report.
10. Export: Download a .txt report or full PDF for submission, sharing, or printing.