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Have some donuts
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
0 2 4 km
Somalia Mcfayden
Nature 1950
0 2 4 km
Somalia Mcfayden
Nature 1950
0 200 400 m
Somalia Mcfayden
Nature 1950
Australia Dunkerley & Brown
Arid Environments 1995 0 500 1000 m
MaliCouteron & Kokou Plant Ecology 1997 0 2 4 km
MexicoCornet & Delhoume
Diversity and Pattern In Plant Communities
1988 0 500 1000 m
MexicoCornet & Delhoume
Diversity and Pattern In Plant Communities
1988 0 500 1000 m
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.
study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
Conceptual model
study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
established plant
Conceptual model
study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
established plant
Conceptual model
study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
established plant
vegetated patch
Conceptual model
study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
established plant
area of facilitation
Conceptual model
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
study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
Conceptual model
study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
Conceptual model
study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
Conceptual model
study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
Conceptual model
study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
What determines consistency?
What determines shape & orientation?
Conceptual model
MexicoCornet & Delhoume
Diversity and Pattern In Plant Communities
1988 0 500 1000 m
MexicoCornet & Delhoume
Diversity and Pattern In Plant Communities
1988 0 500 1000 m
study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
Conceptual model
What determines consistency?
study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
Consistency
study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
Consistency
study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
Consistency
study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
Consistency
study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
Consistency
study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
Conceptual model
What determines consistency?
What determines shape & orientation?
study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
Shape/Orientation
study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
Shape/Orientation
study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
Shape/Orientation
study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
Shape/Orientation
study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
Shape/Orientation
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
study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
Formal models
formulation
• cellular automata• equation-based
study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
Formal models
outcomes
from Reitkerk et al Science 2004 p. 1928modified from Thiery Ecology 1994
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
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
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.“
McfaydenNature 1950 p. 121
Central New Mexico34°11’34”N 106°32’08”W 0 100 200 m
North Western New Mexico
34°47’44”N 106°15’56”W
0 150 300 m
Central Arizona35°23’26”N 111°36’20”W 0 250 500 m
Central Arizona35°24’32”N 111°35’29”W 0 100 200 m
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?
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.
study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
Study sites
• piñon-juniper woodland
• 5 sites
Piñon-juniper woodland
study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
Sites
3 in northern Arizona
2 in northern New Mexico
study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
Sites
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
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
study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
Mapping vegetation
Input: 1m color aerial orthoimagery
study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
Mapping vegetation
Input: 1m color aerial orthoimagery
study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
Quantifying vegetation shape
landscape metrics
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
study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
Quantifying vegetation shape
study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
Quantifying vegetation shape
study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
Quantifying vegetation shape
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
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
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
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
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
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
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)
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
study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
Modeling surface water hydrology
• Relative Stream Power (RSP)
RSP accumulation
surfaceslop
e
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
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
study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
Modeling surface water hydrology
• Wetness Index (WI)
accumulationsurface
slope
WI
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
study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
Statistical correlation
waterWI, RSP
shapeMSI
densityCA?
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
study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
waterWI, RSP
shapeMSI
densityCA
Expected under self-patterning
study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
waterWI, RSP
shapeMSI
densityCA
Expected under self-patterning
study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
waterWI, RSP
shapeMSI
densityCA
Expected under self-patterning
study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
waterWI, RSP
shapeMSI
densityCA
Expected under self-patterning
study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
waterWI, RSP
shapeMSI
densityCA
Expected under self-patterning
study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
waterWI, RSP
shapeMSI
densityCA
Expected in any case
study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
waterWI, RSP
shapeMSI
densityCA
Expected in any case
study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
waterWI, RSP
shapeMSI
densityCA
Expected in any case
study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
waterWI, RSP
shapeMSI
densityCA
Expected relationships
study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
waterWI, RSP
shapeMSI
densityCA
Measured relationships – Arizona sites
WI: 0.67 (-)RSP: 0.67
WI: noneRSP: 0.67
0.89
0.80
study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
Measured relationships – Arizona siteswater
WI, RSP
shapeMSI
densityCA
WI: 0.67 (-)RSP: 0.67
WI: noneRSP: 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
study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
waterWI, RSP
shapeMSI
densityCA
Measured relationships – New Mexico sites
WI: 0.60 (+)RSP: 0.60
WI: 0.78 (+)RSP: 0.78
0.84
0.71
study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
Measured relationships – New Mexico sites water
WI, RSP
shapeMSI
densityCA
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
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?
study sitesbackground measurement statistical conclusions
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
ConclusionsEven 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.
