1. Have some donuts

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. 0 2 4 km
Somalia
Mcfayden
Nature 1950

4. 0 2 4 km
Somalia
Mcfayden
Nature 1950

5. 0 200 400 m
Somalia
Mcfayden
Nature 1950

6. Australia
Dunkerley & Brown
Arid Environments 1995
0 500 1000 m

7. Mali
Couteron & Kokou
Plant Ecology 1997
0 2 4 km

8. Mexico
Cornet & Delhoume
Diversity and Pattern In
Plant Communities 1988
0 500 1000 m

9. Mexico
Cornet & Delhoume
Diversity and Pattern In
Plant Communities 1988
0 500 1000 m

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. study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
Conceptual model

12. study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
established plant
Conceptual model

13. study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
established plant
Conceptual model

14. study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
established plant
vegetated patch
Conceptual model

15. study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
established plant
area of facilitation
Conceptual model

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. study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
Conceptual model

18. study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
Conceptual model

19. study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
Conceptual model

20. study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
Conceptual model

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. Mexico
Cornet & Delhoume
Diversity and Pattern In
Plant Communities 1988
0 500 1000 m

23. Mexico
Cornet & Delhoume
Diversity and Pattern In
Plant Communities 1988
0 500 1000 m

24. study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
Conceptual model
What determines
consistency?

25. study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
Consistency

26. study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
Consistency

27. study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
Consistency

28. study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
Consistency

29. study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
Consistency

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. study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
Shape/Orientation

32. study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
Shape/Orientation

33. study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
Shape/Orientation

34. study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
Shape/Orientation

35. study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
Shape/Orientation

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. study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
Formal models
formulation
• cellular automata
• equation-based

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. 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. 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. 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. Central New Mexico
34°11’34”N 106°32’08”W
0 100 200 m

43. North Western New
Mexico
34°47’44”N 106°15’56”W
0 150 300 m

44. Central Arizona
35°23’26”N 111°36’20”W
0 250 500 m

45. Central Arizona
35°24’32”N 111°35’29”W
0 100 200 m

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. 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. study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
Study sites
• piñon-juniper woodland
• 5 sites

49. Piñon-juniper woodland

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. study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
Sites

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. 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. study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
Mapping vegetation
Input:
1m color aerial
orthoimagery

55. study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
Mapping vegetation
Input:
1m color aerial
orthoimagery

60. study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
Quantifying vegetation shape
landscape metrics

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. study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
Quantifying vegetation shape

63. study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
Quantifying vegetation shape

64. study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
Quantifying vegetation shape

65. 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

66. 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

67. 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

68. 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

69. 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

70. 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

76. 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)

77. 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

78. 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

80. 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

81. 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

82. 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

84. 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

85. study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
Statistical correlation
water
WI, RSP
shape
MSI
density
CA?

86. 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

87. 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

88. 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

89. 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

90. 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

91. 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

92. 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

93. 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

94. 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

95. study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
water
WI, RSP
shape
MSI
density
CA
Expected relationships

96. 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

97. 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

98. 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

99. 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

100. 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?

101. 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.