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 dispersed

Competition

Allelopathy

Poisson

No interaction

Attractive

clonal growth form

short dispersal

environmental 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 3276003

6191

10

361

9140

361

9170

361

9200

361

9230

361

9260

0 10 20 30 405Meters

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 3276003

6191

10

361

9140

361

9170

361

9200

361

9230

361

9260

0 10 20 30 405Meters

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)

Fre

qu

en

cy

0

25

50

75

100

125

0 0.01 0.1 1 10

Distribution of Mojave Larrea Volumes(stem measurement)

Volume (m3)

Fre

qu

en

cy

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)

Fre

qu

en

cy

0

25

50

75

100

125

0 0.01 0.1 1 100 0.01 0.1 1 10

303 shrubs1060 shrubs

88.30 m3

713 shrubs

797.25 m3

591.25 m3

Mojave Larrea

Sonoran Larrea

Mojave Ambrosia

0 5 10 15 20

0.5

1.0

1.5

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

-03

5e

-02

5e

-01

5e

+0

05

e+

01

Larrea in Sonoran

Voronoi tile area (m2)

La

rre

a S

hru

b v

olu

me

(m

3)

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)

gin

homLar

Am

br

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 mmr

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 20.01

e-0

31

e-0

21

e-0

11

e+

00

1e

+0

1

Voronoi tile area (m2)

Sh

rub

vo

lum

e (

m3

)

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 inh

omr

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)