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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 L. Schafer, Andres Fuentes Ramirez, Claus Holzapfel, and Kirk A. Moloney. Fertility Islands. Shrub canopies provide windbreak - PowerPoint PPT Presentation
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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 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%