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