1. 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

2. NS Holzapfel and Mahall 1999, Brooks 2002, Schenk et al. 2003, Esque et al. 2010

4. Invasion by Non-native Annuals NS Brooks 1999, Brooks 2000

5. Invasion by Non-native Annuals Fire NS Brooks and Matchett 2006

6. Invasion by Non-native Annuals Fire NS Ravi et al. 2009

7. 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 community soil nutrient availability water availability microtopography Step 1- Describe and model shrub patterns

9. uniformrandomclustered Inhibitory/over dispersed Competition Allelopathy Poisson No interaction Attractive clonal growth form short dispersal environmental heterogeneity

10. uniformrandomclustered Inhibitory/over dispersed No interaction Attractive Scale of inhibition? Size of a cluster? Multi-type point pattern Marked point pattern

11. 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

12. Study area in Barry M. Goldwater Range, AZ Sonoran Desert Aerial Imagery taken May 2007, 50 cm resolution 327520327540327560327580327600 3619110 3619140 3619170 3619200 3619230 3619260 WGS84 UTM zone 12N map by Erika Mudrak for Desert Flame Research group, 12/16/2010

13. H D1D1 D2D2 creosote bush Larrea tridentata burrobush Ambrosia dumosa

14. Study area in Barry M. Goldwater Range, AZ Sonoran Desert Aerial Imagery taken May 2007, 50 cm resolution 327520327540327560327580327600 3619110 3619140 3619170 3619200 3619230 3619260 WGS84 UTM zone 12N map by Erika Mudrak for Desert Flame Research group, 12/16/2010

15. 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

16. 303 shrubs 1060 shrubs 88.30 m3 713 shrubs 797.25 m3 591.25 m3 Mojave Larrea Sonoran Larrea Mojave Ambrosia

17. 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. Turner Spatstat: an R package for analyzing spatial point patterns. Journal of Statistical Software 12 (2005) 1-42.

18. Shrubs with close neighbors tend to be smaller than average. Sonoran Larrea Mark Correlation Function f=vol 1 *vol 2 Conditional Mean Schlather et al 2004Stoyan and Stoyan 1994 radius (m)

19. Crowded shrubs tend to be smaller Competition is important log (shrub volume) = -3.24 + 1.24*log (tile area) R 2 =0.21 *** Voronoi Tesselation Larrea in Sonoran Polygon area (m2) Shrub volume (m3)

20. Regularly spaced to about 3.15 m Ambrosia: 1060 shrubs 0.098 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)

21. Mark Correlation Function f=vol 1 *vol 2 Conditional Mean Ambrosia Larrea Mojave Larrea and Ambrosia radius (m) Shrubs with close neighbors tend to be smaller than average.

22. log (shrub vol) = -0.98 + 0.65*log (tile area) R 2 =0.13 *** log (shrub vol) = -3.5 + 0.37*log (tile area) R 2 =0.05 *** Crowded shrubs tend to be smaller Relationships not as strong as in Sonoran Voronoi Tesselation Larrea and Ambrosia in Mojave Polygon area (m2) Shrub volume (m3)

23. 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

24. 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

25. Strauss process r : interaction radius  : strength of interaction  = 0: Poisson  = 1: Hard Core Fitted Strauss process Sonoran Larrea r =2.6 m  = 0.71 r Sonoran Larrea

26. Observed Pattern Generated Process

28. Observed Pattern Generated Process

29. Summary Fitting Gibbs models to observed point patterns can Generalize landscape model results Generalize model applications to different specific areas.

30. 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

31. Questions? Acknowledgements Hadas Parag Mojave Desert: Dave Housman Alex Misiura, Ruth Sparks, Rodeway Inn Sonoran Desert: Richard Whittle, Teresa Walker, Yucca Motel

32. Strauss process r : interaction radius  : strength of interaction  = 0: Poisson  = 1: Hard Core Fitted Strauss process Sonoran Larrea r =2.6 m  = 0.71

33. Inhomogenous Pair Correlation Function Mark Correlation Function f=vol1*vol2 Conditional Mean (Larrea and Ambrosia indistinct)