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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
Somalia 0 2 4 km Mcfayden Nature 1950
Somalia 0 2 4 km Mcfayden Nature 1950
Somalia 0 200 400 m Mcfayden Nature 1950
Australia 0 500 1000 m Dunkerley & Brown Arid Environments 1995
Mali 0 2 4 km Couteron & Kokou Plant Ecology 1997
Mexico Cornet & Delhoume 0 500 1000 m Diversity and Pattern In Plant Communities 1988
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
background study sites measurement statistical conclusions Conceptual model Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
background study sites measurement statistical conclusions Conceptual model established plant Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
background study sites measurement statistical conclusions Conceptual model established plant Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
background study sites measurement statistical conclusions Conceptual model established plant vegetated patch Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
background study sites measurement statistical conclusions Conceptual model established plant area of facilitation Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
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
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
background study sites measurement statistical conclusions Conceptual model What determines consistency? Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
background study sites measurement statistical conclusions Consistency Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
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
background study sites measurement statistical conclusions Shape/Orientation Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
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
background study sites measurement statistical conclusions Formal models formulation • cellular automata • equation-based Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
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
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
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
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
0 100 200 m Central New Mexico 34°11’34”N 106°32’08”W
0 150 300 m North Western New Mexico 34°47’44”N 106°15’56”W
0 250 500 m Central Arizona 35°23’26”N 111°36’20”W
0 100 200 m Central Arizona 35°24’32”N 111°35’29”W
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
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
background study sites measurement statistical conclusions Study sites • piñon juniper woodland piñon-juniper • 5 sites Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
Piñon-juniper Piñon juniper woodland
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
background study sites measurement statistical conclusions Sites Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
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
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
background study sites measurement statistical conclusions Mapping vegetation Input: 1m color aerial orthoimagery Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
background study sites measurement statistical conclusions Mapping vegetation Input: 1m color aerial orthoimagery Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
background study sites measurement statistical conclusions Quantifying vegetation shape landscape metrics Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
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
background study sites measurement statistical conclusions Quantifying vegetation shape Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
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
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
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
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
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
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
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
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
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
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
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
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
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
background study sites measurement statistical conclusions Statistical correlation water WI, RSP shape MSI ? density CA Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
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
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
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
background study sites measurement statistical conclusions Expected relationships water WI, RSP shape density MSI CA Hugh Stimson – SNRE University of Michigan – 15 Dec 2008
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
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
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
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
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
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

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