spatial distribution and growth patterns of creosote bush ( larrea tridentata )
DESCRIPTION
Spatial distribution and growth patterns of creosote bush ( Larrea tridentata ) and burrobush ( Ambrosa dumosa ) in the Mojave and Sonoran Deserts Erika Mudrak , Kirk Moloney, Andres Fuentes-Ramirez, Jennifer Schafer, Carolyn Haines, Claus Holzapfel. ESA August, 2011. N. S. - PowerPoint PPT PresentationTRANSCRIPT
Spatial distribution and growth patterns of creosote bush (Larrea tridentata)
and burrobush (Ambrosa dumosa) in the Mojave and Sonoran Deserts
Erika Mudrak, Kirk Moloney, Andres Fuentes-Ramirez, Jennifer Schafer, Carolyn Haines, Claus Holzapfel
ESA August, 2011
N S
Holzapfel and Mahall 1999, Brooks 2002, Schenk et al. 2003, Esque et al. 2010
Invasion by Non-native Annuals
N S
Brooks 1999, Brooks 2000
Invasion by Non-native Annuals
Fire
N S
Brooks and Matchett 2006
Invasion by Non-native Annuals
Fire
N S
Ravi et al. 2009
Project Goals: Ultimate: Develop landscape-scale, spatially-explicit agent-based models
- patterns of invasion by non-native plants- effect of fire cycle and climate change on these dynamics- test possible management plans Current: Characterization of landscape: annual plant communitysoil nutrient availabilitywater availabilitymicrotopography
Step 1- Describe and model shrub patterns
uniform random clustered clustered
Inhibitory/over dispersedCompetitionAllelopathy
PoissonNo interaction
Attractiveclonal growth formshort dispersalenvironmental heterogeneity
uniform random clustered clustered
Inhibitory/over dispersed No
interaction
Attractive
Scale of inhibition?
Size of a cluster?
Multi-type point pattern
Marked point pattern
Aims• Data acquisition
– represent shrub distribution as point patterns
• Exploratory and descriptive analyses– Quantify spatial distribution of shrubs
• Modeling pattern generating processes– Specify a pattern’s probability density – Gibbs Models
• Applications and future work
Study area inBarry M. Goldwater Range, AZ
Sonoran Desert
Aerial Imagery taken May 2007, 50 cm resolution
327520 327540 327560 327580 32760036
1911
036
1914
036
1917
036
1920
036
1923
036
1926
00 10 20 30 405
Meters
GPS locations of shrub-island centers
WGS84 UTM zone 12N
map by Erika Mudrak for Desert Flame Research group, 12/16/2010
H
D1
D2
creosote bush Larrea tridentata
burrobush Ambrosia dumosa
Study area inBarry M. Goldwater Range, AZ
Sonoran Desert
Aerial Imagery taken May 2007, 50 cm resolution
327520 327540 327560 327580 32760036
1911
036
1914
036
1917
036
1920
036
1923
036
1926
00 10 20 30 405
Meters
GPS locations of shrub-island centers
WGS84 UTM zone 12N
map by Erika Mudrak for Desert Flame Research group, 12/16/2010
Projection of bottom area of shrub islands, modeled as ellipse from hand measurements
(to scale, 20cm resolution)
¯
Aims• Data acquisition
– Record distribution as point patterns
• Exploratory and descriptive analyses– Quantify spatial distribution of shrubs
• Modeling pattern generating processes– Specify a pattern’ probability density
• Applications and future work
Distribution of Sonoran Larrea Volumes(stem measurement)
Volume (m3)
Freq
uenc
y
0
25
50
75
100
125
0 0.01 0.1 1 10
Distribution of Mojave Larrea Volumes(stem measurement)
Volume (m3)
Freq
uenc
y
0
25
50
75
100
125
0 0.01 0.1 1 100 0.01 0.1 1 10
Distribution of Mojave Ambrosia Volumes
Volume (m3)
Freq
uenc
y
0
25
50
75
100
125
0 0.01 0.1 1 100 0.01 0.1 1 10
303 shrubs1060 shrubs88.30 m3
713 shrubs
797.25 m3
591.25 m3
Mojave Larrea
Sonoran Larrea
Mojave Ambrosia
0 5 10 15 200.
51.
01.
5
Pair correlation function, Larrea in Sonora Study Area
radius (m)
gr
observed value of g(r) for data patterntheoretical value of g(r) for CSR95% confidence envelope
713 points 0.0661 shrubs/ m2
Sonoran Larrea
Regularly spaced to about 2.3 m
Pair correlation function (PCF)
radius (m)
95% critical envelope
A. Baddeley and R. TurnerSpatstat: an R package for analyzing spatial point patterns.Journal of Statistical Software 12 (2005) 1-42.
0 5 10 15 20
0.4
0.6
0.8
1.0
Conditional MeanLarrea Volume in Sonoran Study Area
radius (m)
Er
Shrubs with close neighbors tend to be smaller than average.
Sonoran Larrea Mark Correlation Function f=vol1*vol2
Conditional Mean
Schlather et al 2004Stoyan and Stoyan 1994
radius (m)
2 5 10 20
5e-0
35e
-02
5e-0
15e
+00
5e+0
1
Larrea in Sonoran
Voronoi tile area (m2)
Larre
a S
hrub
vol
ume
(m3)
Crowded shrubs tend to be smaller
Competition is important
Voronoi TesselationLarrea in Sonoran
Voronoi TesselationLarrea in Sonoran
log (shrub volume) = -3.24 + 1.24*log (tile area) R2=0.21 ***
Voronoi TesselationLarrea in Sonoran
Polygon area (m2)
Shr
ub v
olum
e (m
3)
0 5 10 15 20
0.0
0.5
1.0
1.5
2.0
Pair correlation function, Larrea in Mojave Study Area
radius (m)
gr
Regularly spaced to about 3.15 m
0 5 10 15 20
0.6
0.8
1.0
1.2
1.4
PCF inhomogenous cross function, Larrea1 Ambrosia2
radius (m)
g inho
mL
arA
mbr
Ambrosia: 1060 shrubs0.098 shrubs / m2
Larrea: 303 shrubs 0.028 shrubs / m2
Larrea and Ambrosia inhibit each other
PCF for Larrea alone Inhomogenous cross PCF
Mojave Larrea and Ambrosia
radius (m) radius (m)
0 5 10 15 20
0.0
0.5
1.0
1.5
2.0
Mark Correlation Function f=[m1*m2]Larrea Volume in Mojave Study Area
radius (m)
k mm
r
0 5 10 15 20
1.0
2.0
3.0
Conditional MeanLarrea Volume in Mojave Study Area
radius (m)
Er
Mark Correlation Function f=vol1*vol2 Conditional Mean
Ambrosia
Larrea
Mojave Larrea and Ambrosia
radius (m)radius (m)Shrubs with close neighbors tend to be smaller than average.
Dirichlet TesselationLarrea and Ambrosia in Mojave
Dirichlet TesselationLarrea and Ambrosia in Mojave
0.5 1.0 2.0 5.0 10.0 20.01e
-03
1e-0
21e
-01
1e+0
01e
+01
Voronoi tile area (m2)
Shr
ub v
olum
e (m
3)
log (shrub vol) = -0.98 + 0.65*log (tile area)R2=0.13 ***
log (shrub vol) = -3.5 + 0.37*log (tile area)R2=0.05 ***
Crowded shrubs tend to be smaller
Relationships not as strong as in Sonoran
Voronoi TesselationLarrea and Ambrosia in Mojave
Polygon area (m2)
Shr
ub v
olum
e (m
3)
Spatial Patterning: - Competition is important: Crowded shrubs are smaller
- Sonoran Larrea are regularly spaced to about 2.3 m
- Mojave Larrea are spaced to about 3.15 m- multispecies pattern and inhomogeneity of
Ambrosia complicate things
Aims• Data acquisition
– Record distribution as point patterns
• Exploratory and descriptive analyses– Quantify spatial distribution of shrubs
• Modeling pattern generating processes– Specify a pattern’s probability density
• Applications and future work
Strauss process
r : interaction radiusg : strength of
interactiong = 0: Poissong = 1: Hard Core
Fitted Strauss processSonoran Larrea
r =2.6 mg = 0.71
r
Sonoran Larrea
Observed Pattern Generated Process
Observed Pattern Generated Process
Summary Fitting Gibbs models to observed point patterns can
• Generalize landscape model results
• Generalize model applications to different specific areas.
Future Directions - Incorporate environmental factors (topography,
nutrients) into Gibbs models
- Simultaneously model spatial location and shrub volume
- Model soil nutrient pattern and annual patterns as functions of shrub size and distance to shrub
Questions? Acknowledgements
Hadas Parag
Mojave Desert: Dave Housman Alex Misiura, Ruth Sparks,
Rodeway Inn
Sonoran Desert: Richard Whittle, Teresa Walker, Yucca Motel
Smoothed Pearson residuals
rpoispp(200)Strauss process
r : interaction radiusg : strength of
interactiong = 0: Poissong = 1: Hard Core
Fitted Strauss processSonoran Larrea
r =2.6 mg = 0.71
0 5 10 15 20
0.6
0.8
1.0
1.2
1.4
Inhomogenous Pair correlation functionAmbrosia and Larrea - Indistinct
radius (m)
g inho
mr
0 5 10 15 20
0.0
1.0
2.0
3.0
Mark Correlation Function f=[m1*m2]Larrea and Ambrosia Volume in Mojave Study Area
radius (m)
k mmr
0 5 10 15 20
0.3
0.5
0.7
Conditional MeanLarrea and Ambrosia Volume in Mojave Study Area
radius (m)
Er
Ambrosia Larrea Volume
Inhomogenous Pair Correlation Function
Mark Correlation Function f=vol1*vol2
Conditional Mean
(Larrea and Ambrosia indistinct)