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

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

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

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

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

Sonoran Barry M Goldwater AFAF Mojave Ft. Irwin NTC

PRS (Plant Root Simulator)™-probes NH 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

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 NO 3 - N H 2 PO 4 - P K + K Ca 2+ Ca Mg 2+ Mg Plant available forms of macronutrients ?

Nutrient Level distance from nearby shrubs the size of those nearby shrubs landscape position (trend) direction (N or S) underlying autocorrelation structure x x x x x x x x x x x x x Distance from shrub (cm) x = sample location ? ? ?

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

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

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

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

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

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

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

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

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

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

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

Mojave Study Site Shrub MapN: Negative Exponential P: RegionalMg: Regional Ca: Negative ExponentialK: Negative Exponential mg/m 2 /63 days

Model Validation sampled transects on new shrubs 8 shrubs 4 sizes × 2 directions Buried late January - late March 2012

Model Validation Field samples Modeled values

Model Validation 100 simulations mean R 2 value % of times P < 0.05 Field samples Modeled values

Sonoran Study Site K: Neg. Exp. mg/m 2 /46 days mean R 2 = 34% significant: 100% N: Neg. Exp. mg/m 2 /46 days mean R 2 = 63% significant: 100% Mg: Linear mg/m 2 /46 days mean R 2 = 4% significant: 13% P: Regional mg/m 2 /46 days mean R 2 = 3% significant: 9% Ca: Neg.Exp. mg/m 2 /46 days mean R 2 = 15% significant: 74% Results from 100 model simulations Model Validation

Mojave Study Site Ca: Negative Exponential mg/m 2 /63 days mean R 2 = 4% significant: 17% N: Negative Exponential mg/m 2 /63 days mean R 2 = 9% significant: 72% K: Negative Exponential mg/m 2 /63 days mean R 2 = 45% significant: 100% Mg: Regional mg/m 2 /63 days mean R 2 = 2% significant: 4% P: Regional mg/m 2 /63 days mean R 2 = 3% significant: 9% Results from 100 model simulations Model Validation

Conclusions Models were successful for nutrients with strong relationships with distance to shrub. – Modeled by negative exponential function –N and K in the Sonoran and K in the Mojave were very successful. –N in the Mojave: Significant, but weak explanatory power Due to co-dominance of Ambrosia? More rain in 2012, N particularly sensitive to water pulsing

Future Directions Apply models to shrub distributions estimated from aerial photos Burned Unburned N S Create models for nutrients after experimental fire

Thank you! Carolyn Haines, Marjolein Schat- Field work! Ft. Irwin support: David Housman, Ruth Sparks, Alex Misiura Barry Goldwater AFAF support: Teresa Walker, Richard Whittle Dennis Lock of the Iowa State University Statistics Consulting Services Project RC-1721 Holzapfel & Moloney

Nutrient Level distance from nearby shrubs the size of those nearby shrubs landscape position (trend) direction (N or S) underlying autocorrelation structure x x x x x x x x x x x x x x x x x x x x x near middle far Mojave Sonoran near middle far Distance from shrub (cm) x = sample location

Northing Easting Northing Translating model equations to raster hotspot map

SonoranMojave nutrientModel FormMean R 2 % signifModel FormMean R 2 % signif NNeg Exp63%100%Neg Exp9%72% PRegional Trend 1.8%4%Regional Trend 2.5%9% KNeg Exp34%100%Neg Exp45%100% CaNeg Exp15%74%Neg Exp4%17% MgLinear3.7%13%Regional Trend 1.8%4% Results from 100 model simulations Model Validation

N P K Ca Mg Mojave mg/m 2 /63 days Sonoran mg/m 2 /46 days Neg. Exp. Regional Linear Regional Mean R 2 % signif 9% 72% 2.5% 9% 4% 17% 1.8% 4% 63% 100% 1.8% 4% 34% 100% 15% 74% 3.7% 13% Mean R 2 % signif 45% 100%