1. GIS & Environmental Protection Richard Church University of California, Santa Barbara April 2008 Case studies of the San Joaquin Kit Fox and the California Spotted Owl

2. : Real Example: modeling the spatial requirements of the San Joaquin Kit Fox, an Endangered species. Objective: sustain a population of Kit Fox in a planning region of 2 counties

3. Protecting the SJKF 1

4. The SJKF has been listed as endangered for the last 20 years. The SJKF: Questions? Is their habitat threatened? How much desired habitat area is needed? Where should land be protected for sustaining the SJKF?

5. The requirements of the SJKF were determined by a panel of experts. The panel described a “model” for mapping habitat suitability for the SJKF as well as the needs of a demographic unit i.e. a mated pair of kit fox. How much habitat is needed ? Each mated pair needs 4 square miles of the best habitat or an Equivalently larger area of lower quality habitat Land use data is given as a raster (grid cells) that are 4 ha in size (200m.), so approximately 256 cells of the highest quality habitat are required for a mated pair. Their goal was to protect enough habitat for 6-20 mated pairs

6. Where have the Kit Fox been sighted?

7. Habitat suitability can be based upon a land use/cover map

8. Expert Panel Approach

9. …add in neighborhood effects

10. Final suitability values grid: “A combined map of intrinsic & neighborhood values”

11. Habitat planning and the SJKF From the work described in the previous slides, we know what is potential kit fox habitat. The questions is: Which areas should we set aside in order to protect and enhance kit fox populations?

12. The kit fox does not adhere to parcel boundaries, isn’t concerned with ownership, and is probably oblivious to the boundaries of watersheds. Just how would the Kit fox view the landscape?  The panel of experts stated that a mated pair of kit fox requires the equivalent of 256 cells of high quality habitat or 256x6= 1536 habitat quality points.  Any feasible patch must be relatively compact and contain 1536 habitat quality points  One approach is to develop a process to generate possible kit fox territories or patches…….,

13. Patch Generation Model Given a habitat suitability map A patch “size equivalent” which is a size and quality value large enough to support a mated pair of Kit Fox The Patch model: starts with a seed cell, and iteratively adds perimeter cells At each iteration it adds a percentage of the top-valued perimeter cells to the patch (typically 10-20%), until the patch has the desired size and contains a minimum amount of habitat quality points The value of adding a cell to the patch is calculated as the suitability score plus a weight times the number of edges that the cell shares with the patch

14. 1) Start with seed cell; expand out to a 3x3, 5x5, or some other size 2) Along the perimeter. add the top x% of the cells (in terms of habitat value and connectivity measure) 3) Continue building process until the patch meets minimum required elements of size habitat value points, etc. Repeat process for many seed cells, and Generate hundreds if not thousands of patches

15. Example Perimeter

16. Cells taken from perimeter as an iteration of patch growth Valued equally for addition to the patch. Teeth appearance created due to random ordering of perimeter cells. Valued more than the other 2 cells because of connectivity (habitat value also = 6, plus shares 2 edges with existing patch).

17. cell’s value = kit fox habitat value + delta*# sides shared with cells that have already been chosen for the patch Seed cell Poor habitat Open grassland (high value) Poor habitat

18. California Spotted Owl

20. Iteration 1 Spotted owl example of Patch growing

21. Iteration 30

22. Iteration 60

23. Iteration 90

24. Iteration 116 – FINISHED (7251 points) Has enough size and quality to support the owl nest site

25. Iteration 1 An example with greater emphasis on compactness

26. Iteration 30

27. Iteration 60

28. Iteration 90

29. Iteration 120

30. Iteration 150

31. Iteration 165 – FINISHED (6036 points) User-defined parameters can generate alternative PAC definitions.

32. : The Environmental Landscape: Habitat values map with 2 sample patches Kit Fox patches must have 4 sq. miles of “best” habitat or a larger area that is equivalent. (Must reach 1536 value points)

33. Patches: represent feasible, biologically defensible areas for kit fox protection. Figure to right depicts 350 patches Can be used as the basic decision making unit on the landscape for the kit fox

34. What we’ve done so far Created a map of habitat suitability Generated a large number of potential planning units based upon the needs of the kit fox Next, we need to develop a process of patch selection

35. Now, step 4 Step 1: Generated an understanding from a biological perspective of what is important for the targeted species Step 2: Created a map of habitat suitability Step 3: Generated a large number of potential planning units defined based upon the needs of the kit fox Step 4: We need to develop a process of patch selection in order to design a reserve of desired size

36. Minimize total cost and maximize total biological benefit among all patches selected: s.t. MinMax 1) If patch j is selected, then no patch defined as having excessive overlap with j can be chosen: or R = {patch pairs (j,k) | patch j and patch k have excessive overlap (jk)} = {patches k | k is defined as having excessive overlap with patch j} for each j for each (j,k) in set R 2) Select p-patches: OHPAS model

37. L to 17 Locating 17 Patches from OHPAS

38. But what if we desired some level of connectivity between Chosen patches. We can add this to the earlier problem by adding an objective: and constraints……

39. Adding an objective to encourage connectivity Locating 6 patches Results from OHPASc

40. Adding an objective to encourage connectivity Results from OHPASc Locating 12 patches

41. Summary of approach Step 1: Develop an understanding from a biological perspective of what is important for the targeted species Step 2: Created a map of habitat suitability Step 3: Generated a large number of potential planning units defined based upon the needs of the kit fox Step 4: develop an optimization model to select the best units for the reserve.

42. fini

43. We are now applying the PGP to the California Spotted Owl Not listed as endangered, but is considered at risk and represents a focal species The USFS has to develop a protection plan for the entire Sierra Nevada Range The record of decision states that fuel treatment “SPATS” and owl “PACs” must be allocated.

44. Patches as Owl PACs The patch, using the nest location as the seed cell, represents a protected activity center (PACS) around the nest Each “PAC” patch must be at least 300 acres The quality of the “PAC” patch should be as high as possible

45. The USFS has delineated PACS in a number of ranger districts In the Kings Canyon area of the Sierra National Forest, there are 30 currently active nest sites The USFS staff has already determined PACS for those nests We can compare those PACS with the one determined by the PGP process

46. FS PAC in gray (4237 points)

47. Comparing PGP Patches vs. the owl PACs of the USFS staff

48. Questions?

49. This slide is intentionally left blank. The following slides are included to address questions or point out features of a DSS

50. SOM: Optimal Habitat Patch Selection (OHPAS) 0-1 integer-linear programming model Each generated patch j is a possible planning unit, meets standards for support of some demographic unit We would like to think that “biology has been used to define the planning unit Think of this model as attempt to create a reserve plan by the selection of well-defined but overlapping set of puzzle pieces

51. Requires a formal mathematical model Some general purpose optimization software is available Specialized algorithms can be developed Limits on size of problem that can be solved How can such a model be solved? Optimal (guarantee on goodness) or heuristic (no guarantee) Subsitution/swapping Tabu search Simulated annealing GRASP with path re-linking Variable neighborhood search Genetic algorithm Multi-agent based, e.g. ant colony Heuristic concentration Lagrangean relaxation

52. Reserve Design for threatened biological elements Richard Church University of California, Santa Barbara April 2008 Case studies of the San Joaquin Kit Fox and the California Spotted Owl