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  1. 1. Have some donuts
  2. 2. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 Self patterning of piñon-juniper woodlands in the American southwest. Hugh Stimson
  3. 3. 0 2 4 km Somalia Mcfayden Nature 1950
  4. 4. 0 2 4 km Somalia Mcfayden Nature 1950
  5. 5. 0 200 400 m Somalia Mcfayden Nature 1950
  6. 6. Australia Dunkerley & Brown Arid Environments 1995 0 500 1000 m
  7. 7. Mali Couteron & Kokou Plant Ecology 1997 0 2 4 km
  8. 8. Mexico Cornet & Delhoume Diversity and Pattern In Plant Communities 1988 0 500 1000 m
  9. 9. Mexico Cornet & Delhoume Diversity and Pattern In Plant Communities 1988 0 500 1000 m
  10. 10. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 Self patterning vegetation world-wide Description and conceptual models: • Somalia 1950 • Niger 1970 • Mexico 1988 • Australia 1995 • West African savanna 1997 • others Dynamic modeling: 1995 on.
  11. 11. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 Conceptual model
  12. 12. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 established plant Conceptual model
  13. 13. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 established plant Conceptual model
  14. 14. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 established plant vegetated patch Conceptual model
  15. 15. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 established plant area of facilitation Conceptual model
  16. 16. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 established plant area of facilitation • water retention • soil organic content • temperate microclimate • soil structure Conceptual model
  17. 17. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 Conceptual model
  18. 18. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 Conceptual model
  19. 19. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 Conceptual model
  20. 20. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 Conceptual model
  21. 21. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 What determines consistency? What determines shape & orientation? Conceptual model
  22. 22. Mexico Cornet & Delhoume Diversity and Pattern In Plant Communities 1988 0 500 1000 m
  23. 23. Mexico Cornet & Delhoume Diversity and Pattern In Plant Communities 1988 0 500 1000 m
  24. 24. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 Conceptual model What determines consistency?
  25. 25. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 Consistency
  26. 26. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 Consistency
  27. 27. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 Consistency
  28. 28. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 Consistency
  29. 29. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 Consistency
  30. 30. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 Conceptual model What determines consistency? What determines shape & orientation?
  31. 31. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 Shape/Orientation
  32. 32. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 Shape/Orientation
  33. 33. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 Shape/Orientation
  34. 34. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 Shape/Orientation
  35. 35. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 Shape/Orientation
  36. 36. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 Formal models motivation • testing plausibility of conceptual model • exploring dynamic outcomes
  37. 37. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 Formal models formulation • cellular automata • equation-based
  38. 38. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 Formal models outcomes from Reitkerk et al Science 2004 p. 1928 modified from Thiery Ecology 1994
  39. 39. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 Formal models outcomes from Reitkerk et al Science 2004 p. 1929
  40. 40. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 Formal models self-patterned semi-arid systems are theorized to • be more efficient at retaining precipitation • undergo “catastrophic shifts” under a threshold • not re-establish unless returned to above that threshold
  41. 41. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 In America "The patterns proved very difficult to recognize in the field, so that air photographs are essential for their study.“ Mcfayden Nature 1950 p. 121
  42. 42. Central New Mexico 34°11’34”N 106°32’08”W 0 100 200 m
  43. 43. North Western New Mexico 34°47’44”N 106°15’56”W 0 150 300 m
  44. 44. Central Arizona 35°23’26”N 111°36’20”W 0 250 500 m
  45. 45. Central Arizona 35°24’32”N 111°35’29”W 0 100 200 m
  46. 46. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 Question: Is the subtle patterning observable at some semi-arid locations attributable to resource-limited self patterning?
  47. 47. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 Question: Is the subtle patterning observable at some semi-arid locations attributable to water-limited self organization? Approach: Test the spatial correlation of pattern with surface water conditions.
  48. 48. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 Study sites • piñon-juniper woodland • 5 sites
  49. 49. Piñon-juniper woodland
  50. 50. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 Sites 3 in northern Arizona 2 in northern New Mexico
  51. 51. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 Sites
  52. 52. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 Sites Arizona: New Mexico: 1 1150 25% 1960 to 2230 2 2030 16% 1680 to 1880 3 2500 27% 1940 to 2260 site size (ha) canopy cover elevation (m) 4 250 52% 1900 to 2000 5 450 27% 1890 to 1990
  53. 53. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 Measurement • Mapping vegetation • Quantifying vegetation shape Estimation • Modeling surface water hydrology
  54. 54. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 Mapping vegetation Input: 1m color aerial orthoimagery
  55. 55. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 Mapping vegetation Input: 1m color aerial orthoimagery
  56. 56. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 Quantifying vegetation shape landscape metrics
  57. 57. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 Quantifying vegetation shape landscape metrics • Shape Index p = perimeter of a patch a = area of a patch
  58. 58. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 Quantifying vegetation shape
  59. 59. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 Quantifying vegetation shape
  60. 60. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 Quantifying vegetation shape
  61. 61. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 Quantifying vegetation shape landscape metrics • Shape Index p = perimeter of a patch a = area of a patch
  62. 62. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 Quantifying vegetation shape landscape metrics • Mean Shape Index (MSI) pij = perimeter of patch ij aij = area of a patch ij
  63. 63. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 Quantifying vegetation shape landscape metrics also tried: • Area Weighted Mean Shape Index • Mean Patch Fractal Dimesion • Area Weighted Mean Patch Fractal Dimension
  64. 64. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 Quantifying vegetation shape landscape metrics • Class Area (CA) aij = area of a patch ij
  65. 65. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 Quantifying vegetation shape landscape metrics • Mean Shape Index (MSI) pattern • Class Area (CA) density
  66. 66. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 Modeling surface water hydrology Input: • digital elevation model • 1/3rd arc-second National Elevation Dataset
  67. 67. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 Modeling surface water hydrology • Relative Stream Power (RSP) • Wetness Index (WI)
  68. 68. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 Modeling surface water hydrology • Relative Stream Power (RSP) As = accumulation surface S = slope
  69. 69. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 Modeling surface water hydrology • Relative Stream Power (RSP) RSP accumulation surface slope
  70. 70. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 Modeling surface water hydrology • Relative Stream Power (RSP)  highest when accumulation is high and slope is high  estimates the erosive force of flowing water
  71. 71. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 Modeling surface water hydrology • Wetness Index (WI) As = accumulation surface S = slope
  72. 72. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 Modeling surface water hydrology • Wetness Index (WI) accumulation surface slope W I
  73. 73. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 Modeling surface water hydrology • Wetness Index (WI)  highest when accumulation is high and slope is low  estimates amount of ground water
  74. 74. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 Statistical correlation water WI, RSP shape MSI density CA?
  75. 75. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 Spatial lag model regression • accounts for spatial autocorrelation • accounts for interactivity
  76. 76. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 water WI, RSP shape MSI density CA Expected under self-patterning
  77. 77. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 water WI, RSP shape MSI density CA Expected under self-patterning
  78. 78. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 water WI, RSP shape MSI density CA Expected under self-patterning
  79. 79. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 water WI, RSP shape MSI density CA Expected under self-patterning
  80. 80. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 water WI, RSP shape MSI density CA Expected under self-patterning
  81. 81. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 water WI, RSP shape MSI density CA Expected in any case
  82. 82. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 water WI, RSP shape MSI density CA Expected in any case
  83. 83. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 water WI, RSP shape MSI density CA Expected in any case
  84. 84. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 water WI, RSP shape MSI density CA Expected relationships
  85. 85. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 water WI, RSP shape MSI density CA Measured relationships – Arizona sites WI: 0.67 (-) RSP: 0.67 WI: none RSP: 0.67 0.89 0.80
  86. 86. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 Measured relationships – Arizona sites water WI, RSP shape MSI density CA WI: 0.67 (-) RSP: 0.67 WI: none RSP: 0.67 0.89 0.80   ? ? Interpretation • some relationships consistent with hypothesis • some relationships ecologically unlikely (although not inconsistent with hypothesis) • surface water not the only (or strongest) driver of vegetation shape
  87. 87. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 water WI, RSP shape MSI density CA Measured relationships – New Mexico sites WI: 0.60 (+) RSP: 0.60 WI: 0.78 (+) RSP: 0.78 0.84 0.71
  88. 88. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 Measured relationships – New Mexico sites water WI, RSP shape MSI density CA WI: 0.60 (+) RSP: 0.60 WI: 0.78 (+) RSP: 0.78 0.84 0.71   ? Interpretation • one relationship consistent with hypothesis • one relationship inconsistent with hypothesis • expected ecological relationship present
  89. 89. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 Questions • If self patterning happens in Arizona, why not in New Mexico? • How could there be no relationship between ground water and vegetation density in Arizona? • Why is there a relationship between stream power and density? • How much vegetation structure is really due to self- patterning, and how much due to density?
  90. 90. study sitesbackground measurement statistical conclusions Hugh Stimson – SNRE University of Michigan – 15 Dec 2008 Conclusions Even if all the relationships had been consistent with the hypothesis, it wouldn’t have proven that self-patterning is happening. • BUT given the underlying ecological mechanisms, the results relationships suggest it may well occur in Arizona sites. • If self-patterning is occurring, water may be a driver both as a limited resource and as a physical force. • This is a start.

Editor's Notes

  • For decades people have recognized that some vegetation in explicitly
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