Dose-Response Calculator for ArcGIS
Steven E. Hanser, Cameron L. Aldridge, Matthias Leu, and Scott E. Nielsen
What is a dose-response curve?
A graph
Dosage rates on the X-axis
Response of interest on the Y-axis
Russell et al. 1982
Why is this helpful?
Visualization tool
Populations
Thresholds
Russell et al. 1982
Dose-response curves in ecology
Species-habitat relationships
Multivariate models
Explanatory toolAldridge et al. 2008
Converting an equation to a dose- response curve
Aldridge et al. 2008
• Apply the range of values for variable of interest
• Hold all other variables at their mean or median
Persistence = -0.186 * Pop1950 - 0.038 * crop% + 0.019 * km_edge - 0.058 * sev1950 + 0.049 * sb%_30
• Apply the range of values for variable of interest
• Hold all other variables at their mean or median
Persistence = -0.186 * Pop1950 + 0.7124
How does this apply to GIS?
Spatially explicit models
Problow = 1 / (1 + (exp(-(-3.56 + 2.57 * ABIGSAGE1km - 0.07 * TRI270 + 0.002 * ELEV - 1.75 * WELL1km - 2.44 * MjRD1km - 2.12 * POWER500 + 0.04 * Tmin + 0.25 * RIP1km + 0.99 * MIX3km))))
Hanser et al. in press
Greater sage-grouse
How does this apply to GIS?
Spatially explicit models
Large array of analysis techniques– Linear models– Multivariate statistics
• Mahalanobis distance– MAXENT
Phillips 2005
How do we incorporate variation?
Overcome the need to use mean values for variables in the model
Provide dose-response curves with confidence intervals
Provide data that can inform conservation and management actions
Dose-Response Calculator
Python script tool
ArcToolbox interface
DoseRaster
ResponseRaster
RasterCalculator
Integer ZoneRaster
Zonal Statistics
Tabular orGraph Output
Multiplier
Dose-Response CalculatorGreater sage-grouse
DoseRaster
ResponseRaster
RasterCalculator
Integer ZoneRaster
Zonal Statistics
Tabular orGraph Output
Multiplier
Sagebrush within 1 km radius
Dose-Response Calculator
DoseRaster
ResponseRaster
RasterCalculator
Integer ZoneRaster
Zonal Statistics
Tabular orGraph Output
Multiplier
Sagebrush within 1 km radius
Dose-Response Calculator
DoseRaster
ResponseRaster
RasterCalculator
Integer ZoneRaster
Zonal Statistics
Tabular orGraph Output
Multiplier
Sagebrush within 1 km radius
Dose-Response Calculator
DoseRaster
ResponseRaster
RasterCalculator
Integer ZoneRaster
Zonal Statistics
Tabular orGraph Output
Multiplier
Sagebrush within 1 km radius
Dose-Response Calculator
DoseRaster
ResponseRaster
RasterCalculator
Integer ZoneRaster
Zonal Statistics
Tabular orGraph Output
Multiplier
RasterCalculator
Dose-Response Calculator Raster Calculator
– int (dose * multiplier)
– Convert the dose raster into zones
DoseRaster
ResponseRaster
RasterCalculator
Integer ZoneRaster
Zonal Statistics
Tabular orGraph Output
Multiplier
Zonal Statistics
Dose Raster Integer Zone Raster Response Raster
Dose-Response Calculator Integer conversion
1 = original values
100 = 0-1 to 0-100%
0.001 = meters to km DoseRaster
ResponseRaster
RasterCalculator
Integer ZoneRaster
Zonal Statistics
Tabular orGraph Output
Multiplier
Dose-Response Calculator
MakeGraph
.grf file
DoseRaster
ResponseRaster
RasterCalculator
Integer ZoneRaster
Zonal Statistics
Tabular orGraph Output
Multiplier
Dose-Response Calculator Output
Tabular output
Graph output
Linear model example
Problow = 1 / (1 + (exp(-(-3.56 + 2.57 * ABIGSAGE1km - 0.07 * TRI270 + 0.002 * ELEV - 1.75 * WELL1km - 2.44 * MjRD1km - 2.12 * POWER500 + 0.04 * Tmin + 0.25 * RIP1km + 0.99 * MIX3km))))
Hanser et al. in press
Greater sage-grouse Sagebrush within 1 km radius
Linear model example
Hanser et al. in press
Complex relationships
Aldridge et al. in press
Sage sparrow Sagebrush within 18 km radius
Density = 1 / (1 + (exp(-(15.90 + -9.46 * ALLSAGE18km - 54.46 * NDVI18km + 48.79 * NDVI18km 2 - 86.06 * MIX5km + 1.22 * RIP1km + 0.055 * CONTAG3km + 9.18 * SALT1km - 0.08 * TRI5km + 1.52 * RDdens18km + 4.68 * WELL250 - 1.49 * GRASS3km)))) * exp(1.29 - 2.32 * ALLSAGE18km + 2.51 * NDVI18km - 11.45 * NDVI18km 2 - 19.58 * MIX5km - 3.63 * RIP1km - 0.0008 * CONTAG3km - 0.97 * SALT1km - 0.01 * TRI5km - 0.31 * RDdens18km + 1.70 * WELL250 - 0.27 * GRASS3km + 2.09)
Complex relationships
Aldridge et al. in press
Simple comparisons
Elevation (m)
0 1000 2000 3000 4000
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Summary
Facilitates comparisons between 2 raster datasets
Incorporates variation into the dose-response curve
Simple pair wise comparisons
Complex linear or multivariate models
Summary
ArcToolbox interface
Easy to use analysis tool
Tabular and graphic output
Range of applications
Dose-response Calculator for ArcGIS http://pubs.usgs.gov/ds/631/