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 tridentatacreosote 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 communitysoil nutrient availability

water availability

annual plant community

soil nutrient availability

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)

Sem

i-var

ianc

e (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

SonoranBarry M Goldwater AFAF

MojaveFt. Irwin NTC

PRS (Plant Root Simulator)™-probes

NH4+ + NO3

- NH2PO4

- P K+ KCa2+ CaMg2+ Mg

Plant available forms of macronutrients

Buried during growing season:

Late January – Late March2011

• distance from nearby shrubs• the size of those nearby shrubs• landscape heterogeneity• direction (N or S)• underlying autocorrelation

structure

PRS (Plant Root Simulator)™-probes

NH4+ + NO3

- NH2PO4

- P K+ KCa2+ CaMg2+ Mg

Plant available forms of macronutrients

?

Nut

rient

Lev

el

• 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

?

?

?

• 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

Mojavem

g/m

2 /63

days

mg/

m2 /6

3 da

ysm

g/m

2 /63

days

mg/

m2 /6

3 da

ysm

g/m

2 /63

days

Sonoran

mg/

m2 /4

6 da

ysm

g/m

2 /46

days

mg/

m2 /4

6 da

ysm

g/m

2 /46

days

mg/

m2 /4

6 da

ys

Regional TrendNo shrub influence

nutrientxy = x2 + x + x2y + xy + y2x + y + y2 + εxy,

Model Types

LinearShrub as random effect

nutrient = m ∙ dist + c + ε

Negative ExponentialShrub as random effect

nutrient = a ∙ exp(-b ∙ dist) + d + ε

cm

ad

b

ai = a0 + a0s +a1∙Area +a1s∙Area+ εai, εai ~ N(0, σa)

bi = b0 + b0s +b1∙Area +b1s∙Area+ εbi, εbi ~ N(0, σb)

di = d0 + d0s +d1∙Area +d1s∙Area+ εdi, εdi ~ N(0, σd)

ai = a0 + a0s +a1∙Area +a1s∙Area+ εai

bi = b0 + b0s +b1∙Area +b1s∙Area+ εbi

di = d0 + d0s +d1∙Area +d1s∙Area+ εdi

a

b

d

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

Mojavem

g/m

2 /63

days

mg/

m2 /6

3 da

ysm

g/m

2 /63

days

mg/

m2 /6

3 da

ysm

g/m

2 /63

days

Sonoran

mg/

m2 /4

6 da

ysm

g/m

2 /46

days

mg/

m2 /4

6 da

ysm

g/m

2 /46

days

mg/

m2 /4

6 da

ys

Neg. Exp.

Neg. Exp.

Neg. Exp.

Neg. Exp.

Neg. Exp. Neg. Exp.

Regional Linear

RegionalRegional

Northing

Eas

ting

NorthingTranslating model equationsto raster hotspot map

Nut

rient

Con

cent

ratio

n

Regional Model

Stochastic!

Shrub Map N: Neg. Exp.

P: Regional Mg: LinearCa: Neg.Exp.

K: Neg. Exp.

Sonoran Study Site

mg/

m2 /4

6 da

ys

mg/

m2 /4

6 da

ys

mg/

m2 /4

6 da

ys

mg/

m2 /4

6 da

ys

mg/

m2 /4

6 da

ys

Mojave Study Site

Shrub Map N: Negative Exponential

P: Regional Mg: Regional

Ca: Negative Exponential K: Negative Exponential

mg/

m2 /6

3 da

ysm

g/m

2 /63

days

mg/

m2 /6

3 da

ysm

g/m

2 /63

days

mg/

m2 /6

3 da

ys

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 R2 value• % of times P < 0.05

Field samples Modeled values

Sonoran Study Site

K: Neg. Exp.

mg/

m2 /4

6 da

ys

mean R2 = 34%significant: 100%

N: Neg. Exp.

mg/

m2 /4

6 da

ys

mean R2 = 63%significant: 100%

Mg: Linear

mg/

m2 /4

6 da

ys

mean R2 = 4%significant: 13%

P: Regional

mg/

m2 /4

6 da

ys

mean R2 = 3%significant: 9%

Ca: Neg.Exp.

mg/

m2 /4

6 da

ys

mean R2 = 15%significant: 74%

Results from 100 model simulations

Model Validation

Mojave Study Site

Ca: Negative Exponential

mg/

m2 /6

3 da

ys

mean R2 = 4%significant: 17%

N: Negative Exponential

mg/

m2 /6

3 da

ys

mean R2 = 9%significant: 72%

K: Negative Exponential

mg/

m2 /6

3 da

ys

mean R2 = 45%significant: 100%

Mg: Regional

mg/

m2 /6

3 da

ys

mean R2 = 2%significant: 4%

P: Regional

mg/

m2 /6

3 da

ys

mean R2 = 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

0 50 100 150

5015

025

035

0

Sonoran K

Distance (cm)

g/1

0cm

2/pe

riod

BurnedUnburned

NS

• 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-1721Holzapfel & Moloney

Nut

rient

Lev

el

• distance from nearby shrubs• the size of those nearby shrubs• landscape position (trend)• direction (N or S)• underlying autocorrelation

structure

0 20 40 60 80 100 120 140 160 180 200 220 240 260 280

x x x x x x x x x x x

x x x x x x x x x x

x x x x x x x x x x

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 x x x x x x x

x x x x x x x x x x

near

middle

far

Moj

ave

Son

oran

near

middle

far

Distance from shrub (cm)

x = sample location

Northing

Eas

ting

NorthingTranslating model equationsto raster hotspot map

Sonoran Mojave

nutrient Model Form Mean R2 % signif Model Form Mean R2 % signif

N Neg Exp 63% 100% Neg Exp 9% 72%

P Regional Trend

1.8% 4% Regional Trend

2.5% 9%

K Neg Exp 34% 100% Neg Exp 45% 100%

Ca Neg Exp 15% 74% Neg Exp 4% 17%

Mg Linear 3.7% 13% Regional Trend

1.8% 4%

Results from 100 model simulations

Model Validation

N

P

K

Ca

Mg

Mojavem

g/m

2 /63

days

mg/

m2 /6

3 da

ysm

g/m

2 /63

days

mg/

m2 /6

3 da

ysm

g/m

2 /63

days

Sonoran

mg/

m2 /4

6 da

ysm

g/m

2 /46

days

mg/

m2 /4

6 da

ysm

g/m

2 /46

days

mg/

m2 /4

6 da

ys

Neg. Exp.

Neg. Exp.

Neg. Exp.

Neg. Exp.

Neg. Exp. Neg. Exp.

Regional Linear

RegionalRegional

MeanR2

% signif

9% 72%

2.5% 9%

4% 17%

1.8% 4%

63% 100%

1.8% 4%

34% 100%

15% 74%

3.7% 13%

MeanR2

% signif

45% 100%