1. Dose-Response Calculator for ArcGIS Steven E. Hanser, Cameron L. Aldridge, Matthias Leu, and Scott E. Nielsen

2. 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

3. Why is this helpful?  Visualization tool  Populations  Thresholds Russell et al. 1982

4. Dose-response curves in ecology  Species-habitat relationships  Multivariate models  Explanatory tool Aldridge et al. 2008

5. 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

6. How does this apply to GIS?  Spatially explicit models Prob low = 1 / (1 + (exp(-(-3.56 + 2.57 * ABIGSAGE 1km - 0.07 * TRI 270 + 0.002 * ELEV - 1.75 * WELL 1km - 2.44 * MjRD 1km - 2.12 * POWER 500 + 0.04 * Tmin + 0.25 * RIP 1km + 0.99 * MIX 3km )))) Hanser et al. in press Greater sage-grouse

7. How does this apply to GIS?  Spatially explicit models  Large array of analysis techniques –Linear models –Multivariate statistics Mahalanobis distance –MAXENT Phillips 2005

8. 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

9. Dose-Response Calculator  Python script tool  ArcToolbox interface Dose Raster Response Raster Calculator Integer Zone Raster Zonal Statistics Tabular or Graph Output Multiplier

10. Dose-Response Calculator Greater sage-grouse Dose Raster Response Raster Calculator Integer Zone Raster Zonal Statistics Tabular or Graph Output Multiplier

11. Sagebrush within 1 km radius Dose-Response Calculator Dose Raster Response Raster Calculator Integer Zone Raster Zonal Statistics Tabular or Graph Output Multiplier

12. Sagebrush within 1 km radius Dose-Response Calculator Dose Raster Response Raster Calculator Integer Zone Raster Zonal Statistics Tabular or Graph Output Multiplier

13. Sagebrush within 1 km radius Dose-Response Calculator Dose Raster Response Raster Calculator Integer Zone Raster Zonal Statistics Tabular or Graph Output Multiplier

14. Sagebrush within 1 km radius Dose-Response Calculator Dose Raster Response Raster Calculator Integer Zone Raster Zonal Statistics Tabular or Graph Output Multiplier

15. Raster Calculator Dose-Response Calculator  Raster Calculator –int (dose * multiplier) –Convert the dose raster into zones Dose Raster Response Raster Calculator Integer Zone Raster Zonal Statistics Tabular or Graph Output Multiplier Zonal Statistics Dose Raster Integer Zone Raster Response Raster

16. Dose-Response Calculator  Integer conversion 1 = original values 100 = 0-1 to 0-100% 0.001 = meters to km Dose Raster Response Raster Calculator Integer Zone Raster Zonal Statistics Tabular or Graph Output Multiplier

17. Dose-Response Calculator  MakeGraph .grf file Dose Raster Response Raster Calculator Integer Zone Raster Zonal Statistics Tabular or Graph Output Multiplier

18. Dose-Response Calculator Output  Tabular output  Graph output

19. Linear model example Prob low = 1 / (1 + (exp(-(-3.56 + 2.57 * ABIGSAGE 1km - 0.07 * TRI 270 + 0.002 * ELEV - 1.75 * WELL 1km - 2.44 * MjRD 1km - 2.12 * POWER 500 + 0.04 * Tmin + 0.25 * RIP 1km + 0.99 * MIX 3km )))) Hanser et al. in press Greater sage-grouse Sagebrush within 1 km radius

20. Linear model example Hanser et al. in press

21. 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)

22. Complex relationships Aldridge et al. in press

23. Simple comparisons

24. Summary  Facilitates comparisons between 2 raster datasets  Incorporates variation into the dose-response curve  Simple pair wise comparisons  Complex linear or multivariate models

25. Summary  ArcToolbox interface  Easy to use analysis tool  Tabular and graphic output  Range of applications

26. Dose-response Calculator for ArcGIS  http://pubs.usgs.gov/ds/631/