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

Max

imum

Jul

y Te

mpe

ratu

re (C

)

10

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25

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Current202020502080

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/