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Predictive modeling of spatial patterns of soil nutrients associated with fertility islands in the Mojave and Sonoran deserts. Erika L. Mudrak, Jennifer.

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Presentation on theme: "Predictive modeling of spatial patterns of soil nutrients associated with fertility islands in the Mojave and Sonoran deserts. Erika L. Mudrak, Jennifer."— Presentation transcript:

1 Predictive modeling of spatial patterns of soil nutrients associated with fertility islands in the Mojave and Sonoran deserts. Erika L. Mudrak, Jennifer L. Schafer, Andres Fuentes Ramirez, Claus Holzapfel, and Kirk A. Moloney

2 Fertility Islands Shrub canopies −provide windbreak −provide shade −funnel and retain moisture native annuals grow −increased accumulation of organic matter −Increased soil nutrients under the shrub Creates resource heterogeneity Structurally defines the landscape Larrea tridentata creosote bush

3 Project Goals: Ultimate: Develop landscape-scale, spatially-explicit agent-based models - patterns of invasion by non-native annuals -effect of fire cycle and climate change on these dynamics -test possible management plans Current: Characterization of landscape: perennial plant community soil nutrient availability water availability annual plant community soil nutrient availability

4 Measuring fertility islands Jackson and Caldwell 1993 Journal of Ecology Thompson et al. 2005 Journal of Arid Environments Li et al 2011 Ecological Research Schlesinger et al. 1996 Ecology Lag distance (cm) Semi-variance ( γ )

5 Goal: Develop a model of soil nutrient concentration as a function of distance from nearby shrubs direction (N or S) the size of those nearby shrubs landscape heterogeneity underlying autocorrelation structure. Soil nutrient distribution

6 Sonoran Barry M Goldwater AFAF Mojave Ft. Irwin NTC

7 PRS (Plant Root Simulator)™-probes NH 4 + + NO 3 - N H 2 PO 4 - P K + K Ca 2+ Ca Mg 2+ Mg Plant available forms of macronutrients Buried during growing season: Late January – Late March 2011

8 distance from nearby shrubs the size of those nearby shrubs landscape heterogeneity direction (N or S) underlying autocorrelation structure PRS (Plant Root Simulator)™-probes NH 4 + + NO 3 - N H 2 PO 4 - P K + K Ca 2+ Ca Mg 2+ Mg Plant available forms of macronutrients ?

9 Nutrient Level distance from nearby shrubs the size of those nearby shrubs landscape position (trend) direction (N or S) underlying autocorrelation structure 0 20 40 60 80 100 120 140 160 180 200 220 240 x x x x x x x x x x x x x Distance from shrub (cm) x = sample location ? ? ?

10 distance from nearby shrubs the size of those nearby shrubs ‒ small, medium, large landscape heterogeneity direction (N or S) underlying autocorrelation structure

11 distance from nearby shrubs the size of those nearby shrubs ‒ small, medium, large landscape heterogeneity ‒ 3 regions direction (N or S) underlying autocorrelation structure. 25 x 25m

12 distance from nearby shrubs the size of those nearby shrubs ‒ small, medium, large landscape heterogeneity ‒ 3 regions direction (N or S) underlying autocorrelation structure. 25 x 25m

13 distance from nearby shrubs the size of those nearby shrubs ‒ small, medium, large landscape heterogeneity ‒ 3 regions direction (N or S) underlying autocorrelation structure. 25 x 25m

14 18 shrubs 3 sizes × 3 regions × 2 directions distance from nearby shrubs the size of those nearby shrubs ‒ small, medium, large landscape heterogeneity ‒ 3 regions direction (N or S) ‒ north, south underlying autocorrelation structure

15 N P K Ca Mg Mojave mg/m 2 /63 days Sonoran mg/m 2 /46 days

16 Regional Trend No shrub influence nutrient xy = x 2 + x + x 2 y + xy + y 2 x + y + y 2 + ε xy, Model Types Linear Shrub as random effect nutrient = m ∙ dist + c + ε Negative Exponential Shrub as random effect nutrient = a ∙ exp(-b ∙ dist) + d + ε c m a d b

17 a i = a 0 + a 0s +a 1 ∙Area +a 1s ∙Area+ ε ai, ε ai ~ N(0, σ a ) b i = b 0 + b 0s +b 1 ∙Area +b 1s ∙Area+ ε bi, ε bi ~ N(0, σ b ) d i = d 0 + d 0s +d 1 ∙Area +d 1s ∙Area+ ε di, ε di ~ N(0, σ d ) a i = a 0 + a 0s +a 1 ∙Area +a 1s ∙Area+ ε ai b i = b 0 + b 0s +b 1 ∙Area +b 1s ∙Area+ ε bi d i = d 0 + d 0s +d 1 ∙Area +d 1s ∙Area+ ε di abdabd Allow parameters a, b, and d to depend on shrub size transect direction Model Selection Removed non significant parameters one a time Compared candidate models with AIC Checked model residuals for spatial trends and autocorrelation None! Negative exponential: Shrubs must be considered a random effect! Nutrient ~ a ∙ exp(- b ∙ Distance) + d + ε Non-linear hierarchical modeling

18 N P K Ca Mg Mojave mg/m 2 /63 days Sonoran mg/m 2 /46 days Neg. Exp. Regional Linear Regional

19 Northing Easting Northing Translating model equations to raster hotspot map Nutrient Concentration Regional Model Stochastic!

20 00 Shrub MapN: Neg. Exp. P: RegionalMg: LinearCa: Neg.Exp. K: Neg. Exp. Sonoran Study Site mg/m 2 /46 days