Application of the Getis-Ord Gi* statistic (Hot Spot Analysis) to seafloor organisms

Transcription

1 Application of the Getis-Ord Gi* statistic (Hot Spot Analysis) to seafloor organisms Diana Watters Research Fisheries Biologist Habitat Ecology Team Santa Cruz, CA Southwest Fisheries Science Center Fisheries Ecology Division

2 Hot Spot Analysis: Vandalism, Lincoln Nebraska Rockfish density, central California 2

3 Acknowledgements: Mary Yoklavich, Habitat Ecology Team Chief Scientist, SWFSC Barry Nickel, Center for Integrated Spatial Research, UC Santa Cruz Lauren Scott, Esri product engineer 3

4 Overview of Talk: Getis-Ord Gi* statistic Hot Spot Analysis Tool How I applied Hot Spot Analysis Tool 4

5 Getis Ord Gi* statistic How Hot Spot Analysis (Getis-Ord Gi*) works Getis, A. and J.K. Ord The Analysis of Spatial Association by Use of Distance Statistics. Geographical Analysis 24(3) Located in: Spatial Statistics Tools, Mapping Clusters, Local statistic, calculated for each feature (point, line, polygon) within context of neighbors determines whether local pattern (feature & its neighbors) is statistically significant from global pattern (all features) Null hypothesis: Hot Spot Analysis There is Complete Spatial Randomness of the Values associated with features 5

6 Hot Spot Analysis (Getis Ord Gi*): What is a z-score? What is a p-value? Outputs: Z score (standard deviations), p value (probability) Hot spot: statistically significant cluster of features w high values Cold spot: statistically significant cluster of features w low values Hot spot Cold spot Hot spot Cold spot 6

7 Hot Spot Analysis (Getis Ord Gi*): Inputs: Feature: at least 30 objects, projected, with value field Hot Spot Analysis (Getis-Ord Gi*) 7

8 Hot Spot Analysis (Getis Ord Gi*): Inputs: Conceptualization of Spatial Relationships Esri recommends Fixed Distance Band (read about others) consistent scale of analysis across each/every feature must provide adequate neighbors & appropriate scale Alternative: Spatial Weights Matrix Fixed Distance Band AND a minimum number of neighbors (expands distance band where needed) Modeling spatial relationships 8

9 Hot Spot Analysis (Getis Ord Gi*): Inputs: False Discovery Rate Correction (optional) What is a z-score? What is a p-value? Estimates # of false positives for each CI, adjusts critical p-value Multiple Testing at 95% CI, 5% could be falsely significant Spatial Dependency features near each other share neighbors, can artificially inflate statistical significance 9

10 How I Applied Hot Spot Analysis: Purpose: Spatially compare abundance of corals/sponges with rockfishes Gorgonian & Lophelia corals Vase sponge Rosy rockfish Cowcod How I chose a distance band that: a) provides adequate neighbors; and b) appropriate scale for analysis There is no perfect distance band (keep this in mind) 10

11 Choosing a distance band: Modeling spatial relationships Look at features: Points (n=1,284 transects) Rocky habitats Depths meters 11

12 Choosing a distance band: Modeling spatial relationships Look at values: Create Graphs Wizard Densities (# per100m 2 ) of corals/sponges, small & large rockfishes For skewed data, minimum of 8 neighbors recommended for reliable z scores 12

13 Choosing a distance band: Calculate Distance Band from Neighbor Count Calculate Distance Band from Neighbor Count Tool: What distance band provides 8 neighbors for each point? 5,400m 13

14 Choosing a distance band: Incremental Spatial Autocorrelation Incremental Spatial Autocorrelation Tool: Peak spatial clustering distance (m) 14

15 Choosing a distance band: Incremental Spatial Autocorrelation Tool: Corals/sponges = 1,715 m Incremental Spatial Autocorrelation Small rockfishes = 1,892 m Large rockfishes = 1,449 m These distances may not provide an adequate # of neighbors, or the best scale for Hot Spot Analysis 15

16 Choosing a distance band: Near (Analysis) Nearest Neighbor Distances (meters): Look for extreme outliers, Near Tool 19 points have nearest-neighbor distances > 3 s.d. (yellow points) range = 430-1,271 mean=88.6 s.d.=113 3 s.d.=428 16

17 Choosing a distance band: Neighborhood Analysis: Evaluate # of neighbors with increasing distance bands Buffer, Spatial Join Tools Buffer, Spatial Join (Analysis) Number of neighbors, all transects (n=1,284) Distance band (m) # with 8 % # with 6 % 1,000 1, , ,500 1, , ,000 1, , ,500 1, , ,000* 1, , * 9 transects with <8 neighbors, & 7 transects with 5 neighbors. All are located near each other (red circles). 17

18 Choosing a distance band: Neighborhood Analysis without Outliers (>3 s.d. from nearest neighbor): No real advantage to excluding outliers Number of neighbors, without outliers (n=1,265) Distance band (m) # with 8 % # with 6 % 2,000 1, , ,000* 1, , *this distance leaves more transects (10) with <8 neighbors, from 2 different areas. 4 transects have only 3 neighbors. 18

19 Choosing a distance band: 5,400m distance band, 8 neighbor minimum Spatial Weights Matrix 3000m distance band, 6 neighbor minimum 19

20 Hot Spot Analysis: 5,400m distance band, 8 neighbor minimum Spatial Weights Matrix 3000m distance band, 6 neighbor minimum Coral & Sponge Hot Spot Analysis Gi_Bin!( Cold Spot - 99% Confidence!( Cold Spot - 95% Confidence!( Cold Spot - 90% Confidence!( Not Significant!( Hot Spot - 90% Confidence!( Hot Spot - 95% Confidence!( Hot Spot - 99% Confidence Coral & Sponge Density number per 100m

21 Hot Spot Analysis: 5,400m distance band, 8 neighbor minimum Spatial Weights Matrix 3000m distance band, 6 neighbor minimum Small Rockfish Hot Spot Analysis Gi_Bin!( Cold Spot - 99% Confidence!( Cold Spot - 95% Confidence!( Cold Spot - 90% Confidence!( Not Significant!( Hot Spot - 90% Confidence!( Hot Spot - 95% Confidence!( Hot Spot - 99% Confidence Small Rockfish Density number per 100m

22 Hot Spot Analysis Reminders: Examine your data carefully There is no perfect distance band (but do your best to find it) Evaluate results 22