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study sitesbackground measurement statistical conclusions
Self patterning of piñon-juniper woodlands inSelf patterning of piñon-juniper woodlands in the American southwest.
Hugh Stimson
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
Somalia Mcfayden
0 2 4 kmMcfayden
Nature 1950
Somalia Mcfayden
0 2 4 kmMcfayden
Nature 1950
Somalia Mcfayden
0 200 400 mMcfayden
Nature 1950
Australia Dunkerley & BrownDunkerley & Brown
Arid Environments 19950 500 1000 m
MaliCouteron & KokouCouteron & Kokou Plant Ecology 1997
0 2 4 km
MexicoMexicoCornet & Delhoume
Diversity and Pattern InDiversity and Pattern In Plant Communities 1988
0 500 1000 m
MexicoMexicoCornet & Delhoume
Diversity and Pattern InDiversity and Pattern In Plant Communities 1988
0 500 1000 m
study sitesbackground measurement statistical conclusions
Self patterning vegetation world wideSelf patterning vegetation world-wide
Description and conceptual models:Description and conceptual models:• Somalia 1950• Niger 1970Niger 1970• Mexico 1988• Australia 1995• West African savanna 1997• others
Dynamic modeling: 1995 on.
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
study sitesbackground measurement statistical conclusions
Conceptual modelConceptual model
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
study sitesbackground measurement statistical conclusions
Conceptual modelConceptual model
established plant
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
study sitesbackground measurement statistical conclusions
Conceptual modelConceptual model
established plant
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
study sitesbackground measurement statistical conclusions
Conceptual modelConceptual model
established plant
vegetated patch
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
study sitesbackground measurement statistical conclusions
Conceptual modelConceptual model
established plant
area of facilitation
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
study sitesbackground measurement statistical conclusions
Conceptual modelConceptual model
established plant
area of facilitation• water retention
il i• soil organic content• temperate microclimate• soil structure• soil structure
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
study sitesbackground measurement statistical conclusions
Conceptual modelConceptual model
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
study sitesbackground measurement statistical conclusions
Conceptual modelConceptual model
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
study sitesbackground measurement statistical conclusions
Conceptual modelConceptual model
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
study sitesbackground measurement statistical conclusions
Conceptual modelConceptual model
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
study sitesbackground measurement statistical conclusions
Conceptual modelConceptual model
What determines consistency?What determines consistency?
Wh t d t i h &What determines shape & orientation?
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
MexicoMexicoCornet & Delhoume
Diversity and Pattern InDiversity and Pattern In Plant Communities 1988
0 500 1000 m
MexicoMexicoCornet & Delhoume
Diversity and Pattern InDiversity and Pattern In Plant Communities 1988
0 500 1000 m
study sitesbackground measurement statistical conclusions
Conceptual modelConceptual model
What determines consistency?What determines consistency?
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
study sitesbackground measurement statistical conclusions
ConsistencyConsistency
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
study sitesbackground measurement statistical conclusions
ConsistencyConsistency
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
study sitesbackground measurement statistical conclusions
ConsistencyConsistency
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
study sitesbackground measurement statistical conclusions
ConsistencyConsistency
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
study sitesbackground measurement statistical conclusions
ConsistencyConsistency
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
study sitesbackground measurement statistical conclusions
Conceptual modelConceptual model
What determines consistency?What determines consistency?
Wh t d t i h &What determines shape & orientation?
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
study sitesbackground measurement statistical conclusions
Shape/OrientationShape/Orientation
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
study sitesbackground measurement statistical conclusions
Shape/OrientationShape/Orientation
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
study sitesbackground measurement statistical conclusions
Shape/OrientationShape/Orientation
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
study sitesbackground measurement statistical conclusions
Shape/OrientationShape/Orientation
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
study sitesbackground measurement statistical conclusions
Shape/OrientationShape/Orientation
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
study sitesbackground measurement statistical conclusions
Formal modelsFormal models
motivationmotivation
• testing plausibility of conceptual model• testing plausibility of conceptual model• exploring dynamic outcomes
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
study sitesbackground measurement statistical conclusions
Formal modelsFormal models
formulationformulation
• cellular automata• cellular automata• equation-based
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
study sitesbackground measurement statistical conclusions
Formal modelsFormal models
outcomesoutcomes
from Reitkerk et al Science 2004 p. 1928modified from Thiery Ecology 1994
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
modified from Thiery Ecology 1994
study sitesbackground measurement statistical conclusions
Formal modelsFormal models
outcomesoutcomes
from Reitkerk et al Science 2004 p. 1929
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
study sitesbackground measurement statistical conclusions
Formal modelsFormal models
self-patterned semi-arid systems are theorized toself-patterned semi-arid systems are theorized to
• be more efficient at retaining precipitationg p p
• undergo “catastrophic shifts” under a threshold
• not re-establish unless returned to above that thresholdabove that threshold
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
study sitesbackground measurement statistical conclusions
In AmericaIn America
"The patterns proved very difficult to recognize in the field so that air photographs arein the field, so that air photographs are essential for their study.“
McfaydenNature 1950 p 121Nature 1950 p. 121
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
Central New Mexico34°11’34”N 106°32’08”W
0 100 200 m
North Western New Mexico34°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
Question:Question:
Is the subtle patterning observable at p gsome semi-arid locations attributable to resource-limited self patterning?p g
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
study sitesbackground measurement statistical conclusions
Question:Question:
Is the subtle patterning observable at p gsome semi-arid locations attributable to water-limited self organization?g
Approach:
Test the spatial correlation of pattern with surface water conditionssurface water conditions.
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
study sitesbackground measurement statistical conclusions
Study sitesStudy sites
• piñon juniper woodland• piñon-juniper woodland
• 5 sites• 5 sites
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
Piñon juniper woodlandPiñon-juniper woodland
study sitesbackground measurement statistical conclusions
SitesSites
3 in northern Arizona3 in northern Arizona
2 in northern New Mexico2 in northern New Mexico
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
study sitesbackground measurement statistical conclusions
SitesSites
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
study sitesbackground measurement statistical conclusions
SitesSites
site size (ha) canopy cover elevation (m)
Arizona:1 1150 25% 1960 to 2230
2 2030 16% 1680 to 1880Arizona: 2 2030 16% 1680 to 1880
3 2500 27% 1940 to 2260
N M i4 250 52% 1900 to 2000
New Mexico:5 450 27% 1890 to 1990
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
study sitesbackground measurement statistical conclusions
MeasurementMeasurement
• Mapping vegetation• Mapping vegetation
• Quantifying vegetation shape• Quantifying vegetation shape
EstimationEstimation
• Modeling surface water hydrology• Modeling surface water hydrology
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
study sitesbackground measurement statistical conclusions
Mapping vegetationMapping vegetation
Input:Input: 1m color aerial orthoimageryorthoimagery
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
study sitesbackground measurement statistical conclusions
Mapping vegetationMapping vegetation
Input:Input: 1m color aerial orthoimageryorthoimagery
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
study sitesbackground measurement statistical conclusions
Quantifying vegetation shapeQuantifying vegetation shape
landscape metricslandscape metrics
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
study sitesbackground measurement statistical conclusions
Quantifying vegetation shapeQuantifying vegetation shape
landscape metricslandscape metrics
• Shape Index
p = perimeter of a patch a = area of a patch
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
study sitesbackground measurement statistical conclusions
Quantifying vegetation shapeQuantifying vegetation shape
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
study sitesbackground measurement statistical conclusions
Quantifying vegetation shapeQuantifying vegetation shape
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
study sitesbackground measurement statistical conclusions
Quantifying vegetation shapeQuantifying vegetation shape
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
study sitesbackground measurement statistical conclusions
Quantifying vegetation shapeQuantifying vegetation shape
landscape metricslandscape metrics
• Shape Index
p = perimeter of a patch a = area of a patch
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
study sitesbackground measurement statistical conclusions
Quantifying vegetation shapeQuantifying vegetation shape
landscape metricslandscape 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
study sitesbackground measurement statistical conclusions
Quantifying vegetation shapeQuantifying vegetation shape
landscape metricslandscape 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
study sitesbackground measurement statistical conclusions
Quantifying vegetation shapeQuantifying vegetation shape
landscape metricslandscape metrics
• Class Area (CA)
aij = area of a patch ij
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
study sitesbackground measurement statistical conclusions
Quantifying vegetation shapeQuantifying vegetation shape
landscape metricslandscape metrics
• Mean Shape Index (MSI) pattern
• Class Area (CA) density
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
study sitesbackground measurement statistical conclusions
Modeling surface water hydrologyModeling surface water hydrology
Input:Input:
• digital elevation model• digital elevation model• 1/3rd arc-second National Elevation Dataset
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
study sitesbackground measurement statistical conclusions
Modeling surface water hydrologyModeling surface water hydrology
• Relative Stream Power (RSP)• Relative Stream Power (RSP)
• Wetness Index (WI)• Wetness Index (WI)
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
study sitesbackground measurement statistical conclusions
Modeling surface water hydrologyModeling surface water hydrology
• Relative Stream Power (RSP)• Relative Stream Power (RSP)
As = accumulation surface S = slope
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
study sitesbackground measurement statistical conclusions
Modeling surface water hydrologyModeling surface water hydrology
• Relative Stream Power (RSP)• Relative Stream Power (RSP)
RSP accumulation lRSP accumulationsurface
slope
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
study sitesbackground measurement statistical conclusions
Modeling surface water hydrologyModeling surface water hydrology
• Relative Stream Power (RSP)• Relative Stream Power (RSP)
highest when accumulation is high andhighest when accumulation is high and slope is high
estimates the erosive force of flowing waterwater
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
study sitesbackground measurement statistical conclusions
Modeling surface water hydrologyModeling surface water hydrology
• Wetness Index (WI)• Wetness Index (WI)
A = accumulation surface S = slopeAs = accumulation surface S = slope
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
study sitesbackground measurement statistical conclusions
Modeling surface waterModeling surface water hydrology
• Wetness Index (WI)accumulation
surface
WI
slope
WI
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
study sitesbackground measurement statistical conclusions
Modeling surface water hydrologyModeling surface water hydrology
• Wetness Index (WI)• Wetness Index (WI)
highest when accumulation is high andhighest when accumulation is high and slope is low
estimates amount of ground water
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
study sitesbackground measurement statistical conclusions
Statistical correlationStatistical correlation
waterWI, RSP
?shape density
?MSI CA
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
study sitesbackground measurement statistical conclusions
Spatial lag model regressionSpatial lag model regression
• accounts for spatial autocorrelation• accounts for spatial autocorrelation• accounts for interactivity
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
study sitesbackground measurement statistical conclusions
Expected under self patterningExpected under self-patterning
waterWI, RSP
shape densityMSI CA
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
study sitesbackground measurement statistical conclusions
Expected under self patterningExpected under self-patterning
waterWI, RSP
shape densityMSI CA
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
study sitesbackground measurement statistical conclusions
Expected under self patterningExpected under self-patterning
waterWI, RSP
shape densityMSI CA
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
study sitesbackground measurement statistical conclusions
Expected under self patterningExpected under self-patterning
waterWI, RSP
shape densityMSI CA
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
study sitesbackground measurement statistical conclusions
Expected under self patterningExpected under self-patterning
waterWI, RSP
shape densityMSI CA
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
study sitesbackground measurement statistical conclusions
Expected in any caseExpected in any case
waterWI, RSP
shape densityMSI CA
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
study sitesbackground measurement statistical conclusions
Expected in any caseExpected in any case
waterWI, RSP
shape densityMSI CA
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
study sitesbackground measurement statistical conclusions
Expected in any caseExpected in any case
waterWI, RSP
shape densityMSI CA
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
study sitesbackground measurement statistical conclusions
Expected relationshipsExpected relationships
waterWI, RSP
shape densityMSI CA
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
study sitesbackground measurement statistical conclusions
Measured relationships Arizona sitesMeasured relationships – Arizona sites
waterWI, RSP
WI 0 67 ( ) WIWI: 0.67 (-)RSP: 0.67
WI: noneRSP: 0.67
shape density0.89
MSI CA0.80
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
study sitesbackground measurement statistical conclusions
Measured relationships Arizona sitesMeasured relationships – Arizona sites
waterWI RSPWI, RSP
WI: 0.67 (-)RSP: 0.67
WI: noneRSP: 0.67
??
shapeMSI
densityCA
0.89
0.80
Interpretation• some relationships consistent with hypothesisp 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
study sitesbackground measurement statistical conclusions
Measured relationships New Mexico sitesMeasured relationships – New Mexico sites
waterWI, RSP
WI 0 60 (+) WI 8 ( )WI: 0.60 (+)RSP: 0.60
WI: 0.78 (+)RSP: 0.78
shape density0.84
MSI CA0.71
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
study sitesbackground measurement statistical conclusions
Measured relationships New Mexico sitesMeasured relationships – New Mexico sites
waterWI RSPWI, RSP
WI: 0.60 (+)RSP: 0.60
WI: 0.78 (+)RSP: 0.78 ?
shapeMSI
densityCA
0.84
MSI CA0.71
Interpretation• one relationship consistent with hypothesisp yp• one relationship inconsistent with hypothesis• expected ecological relationship present
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
study sitesbackground measurement statistical conclusions
QuestionsQuestions
• If self patterning happens in Arizona, why not in New Mexico?
• How could there be no relationship between ground waterHow could there be no relationship between ground water and vegetation density in Arizona?
Wh i th l ti hi b t t d• 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?
Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
study sitesbackground measurement statistical conclusions
ConclusionsConclusions
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
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