defense (edited, pdf)

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

0 200 400 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


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.



Conceptual modelConceptual model




established plant




established plant

vegetated patch




established plant

area of facilitation




established plant

area of facilitation• water retention

il i• soil organic content• temperate microclimate• soil structure• soil structure




What determines consistency?What determines consistency?

Wh t d t i h &What determines shape & orientation?


MexicoMexicoCornet & Delhoume

Diversity and Pattern InDiversity and Pattern In Plant Communities 1988

0 500 1000 m


ConsistencyConsistency





Wh t d t i h &What determines shape & orientation?



Shape/OrientationShape/Orientation



Formal modelsFormal models

motivationmotivation

• testing plausibility of conceptual model• testing plausibility of conceptual model• exploring dynamic outcomes




formulationformulation

• cellular automata• cellular automata• equation-based




outcomesoutcomes

from Reitkerk et al Science 2004 p. 1928modified from Thiery Ecology 1994


modified from Thiery Ecology 1994



outcomesoutcomes

from Reitkerk et al Science 2004 p. 1929




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



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


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


Question:Question:

Is the subtle patterning observable at p gsome semi-arid locations attributable to resource-limited self patterning?p g



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.



Study sitesStudy sites

• piñon juniper woodland• piñon-juniper woodland

• 5 sites• 5 sites


Piñon juniper woodlandPiñon-juniper woodland


SitesSites

3 in northern Arizona3 in northern Arizona

2 in northern New Mexico2 in northern New Mexico



SitesSites



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



MeasurementMeasurement

• Mapping vegetation• Mapping vegetation

• Quantifying vegetation shape• Quantifying vegetation shape

EstimationEstimation

• Modeling surface water hydrology• Modeling surface water hydrology



Mapping vegetationMapping vegetation

Input:Input: 1m color aerial orthoimageryorthoimagery



Quantifying vegetation shapeQuantifying vegetation shape

landscape metricslandscape metrics





• Shape Index

p = perimeter of a patch a = area of a patch





• Mean Shape Index (MSI)

pij = perimeter of patch ij aij = area of a patch ij





also tried:

• Area Weighted Mean Shape Index• Mean Patch Fractal Dimesion• Area Weighted Mean Patch Fractal Dimension





• Class Area (CA)

aij = area of a patch ij





• Mean Shape Index (MSI) pattern

• Class Area (CA) density



Modeling surface water hydrologyModeling surface water hydrology

Input:Input:

• digital elevation model• digital elevation model• 1/3rd arc-second National Elevation Dataset




• Relative Stream Power (RSP)• Relative Stream Power (RSP)

• Wetness Index (WI)• Wetness Index (WI)





As = accumulation surface S = slope





RSP accumulation lRSP accumulationsurface

slope





highest when accumulation is high andhighest when accumulation is high and slope is high

estimates the erosive force of flowing waterwater





A = accumulation surface S = slopeAs = accumulation surface S = slope



Modeling surface waterModeling surface water hydrology

• Wetness Index (WI)accumulation

surface

WI

slope

WI





highest when accumulation is high andhighest when accumulation is high and slope is low

estimates amount of ground water



Statistical correlationStatistical correlation

waterWI, RSP

?shape density

?MSI CA



Spatial lag model regressionSpatial lag model regression

• accounts for spatial autocorrelation• accounts for spatial autocorrelation• accounts for interactivity



Expected under self patterningExpected under self-patterning

waterWI, RSP

shape densityMSI CA



Expected in any caseExpected in any case

waterWI, RSP

shape densityMSI CA



Expected relationshipsExpected relationships

waterWI, RSP

shape densityMSI CA



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



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



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



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



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?



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.


defense (edited, pdf)

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