Transcript Likelihood and Information Theoretic Methods in Forest Ecology

Case Study 2
Neighborhood Models of the Allelopathic
Effects of an Invasive Tree Species
Gómez-Aparicio, L. and C. D. Canham. 2008. Neighborhood analyses of the
allelopathic effects of the invasive tree Ailanthus altissima in North
American forests. Journal of Ecology 96:447-458.
The cast of characters…
Lorena Gómez-Aparicio
(Instituto de Recursos Naturales y
Agrobiología, Sevilla, Spain)
Tree of heaven
(Ailanthus altissima)
Introduced from China in 1784
Neighborhood Effects of Canopy Trees on
Ecosystem Properties
Estimated footprint of a 30 cm
DBH Tree of Heaven…
Gómez-Aparicio, L. and C. D. Canham. 2008.
Neighborhood models of the effects of invasive
tree species on ecosystem processes. Ecol.
Monogr. 78:69-86
0.35
pH
0.08
Ca
0.30
0.25
Relative effect of a 30-cm DBH Ailanthus altissima
Bottom line: Ailanthus increases soil
fertility relative to background effects of
the native tree species…
0.10
0.06
0.20
0.04
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0.10
0.02
0.05
0.00
0.00
0
5
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25
0
5
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20
25
0.35
0.10
K
0.08
Mass N
0.30
0.25
0.06
0.20
0.04
0.15
0.10
0.02
0.05
0.00
0.00
0
5
10
15
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25
0.10
NO3-
0.30
0
Net nitrification
0.08
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0.06
0.15
0.04
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Distance (m)
5
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25
Allelopathic effects of Ailanthus




Direct effects of the invasive species on nutrient availability are
not the whole story….
Lab studies have isolated an allelopathic exudate from Ailanthus
(ailanthone)
Could allelopathy by Ailanthus negate any positive effects of the
species on soil N and Ca?
Will the magnitude of the allelopathic effect vary for different
species of tree seedlings?
Gómez-Aparicio, L. and C. D. Canham. 2008. Neighborhood analyses of the allelopathic effects
of the invasive tree Ailanthus altissima in North American forests. Journal of Ecology 96:447458.
Basic field methods

Select 20 locations in each of 3 sites with a range of abundance of
A. altissima within the immediate neighborhood (and map the
exact locations of those trees relative to the sample locations)

Two quadrats at each location, one with activated carbon mixed
into the soil

Plant a seedling of each of three native tree species into each
quadrat
Statistical model
Response = sitej* sizel * Ailanthus effect (A)
A  exp
ANI
 t  ANI

i
max



where t = treatment (activated carbon or control),
and  can be positive (facilitation) or negative (inhibition).
ANI   DBHi exp   distancei 
n

i 1
where DBH and distance are the size and distance
to neighboring Ailanthus…
NOTE: separate models were fit using either  = 0 or  = 2
Alternate Models

Our “null” model: Set Ailanthus effect to 1, and just fit a model for
site and plant size effects…
Response = sitej* sizel

An alternate model: test whether the magnitude of allelopathic
effects was site specific:
Response = sitej* sizel * Ailanthus effect (A)
A  exp
ANI
 tj  ANI

i
max



But now,  varies as a function
of both treatment and site…
The error term and PDF

Error terms varied depending on the response variable
-
Survival: logistic regression (more later…)
-
Seed emergence: binomial
-
Growth: normally distributed, but with variance a power
function of the mean
yij  N ( ˆyij , 2 ),  2  ˆyij
Note: estimates of  for the 3 seedling species were ~ 1.5
Model Comparison (as Hypothesis Tests)
Parameter Estimates
1.2
ANI   DBHi exp   distancei 
Acer rubrum
1.0

i 1
Shapes of the effective
allelopathic footprint of Ailanthus
for the 3 native seedling species
The implications of alpha ():
models with  = 0 had the highest
likelihood (and lowest AIC).
Thus, the density of Ailanthus
(stems > 2 cm DBH) was more
important than their cumulative
biomass…
index (ANI)
Ailanthus Ailanthus
neighborhood
neighborhood index (ANI)
n
Extension growth
Extension biomass
Leaf biomass
Leaf area
Root biomass
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10
1.2
Acer saccharum
1.0
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0.6
0.4
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0.0
0
2
1.2
Quercus rubra
1.0
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0.6
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0.0
0
2
Distance (m)
1.0
0.4
0.4
Responses
of native tree seedlings
to
0.8
0.8
Ailanthus allelopathy…
0.6
0.6
0.2
0.2
Red oak (Quercus rubra)
Allelopathy shifts the
to downright nasty…
0.0
0.0 neighborhood effect from negative
0.6
0.4
Proportionate Change
0.2
1.0
1.2
0.8
1.0
0.0
0.2
0.6
0.4
1.2
(j) QURU - Extension growth
1.0
without allelopathy1.0
0.8
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0.2
0.0
0.0
allelopathy
0.2
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1.0
0.0
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0.4
(k) QURU - Extension biomass
0.8
1.0
0.0
0.0
0.2
0.4
0.6
0.8
0.8
AC
Control
0.2
0.6
0.6
1.0
Ailanthus neighborhood index (ANI)
Solid circles: activated carbon (no allelopathy); Open circles: control
1.0
Sugar maple (Acer saccharum)
2.0
2.0
2.0
Allelopathy shifts the neighborhood effect from neutral
to negative…
1.5
1.0
0.5
0.0
Proportionate Change
Neighborhood effects multiplier (X)
3.5
0.2
0.6
0.4
0.8
1.0
(d) ACRU - Leaf area
1.5
1.5
1.0
1.0
0.5
0.0
1.2
0.2
0.8
0.6
0.4
1.0
(e) ACSA - Extension growth
0.5
0.0
1.2
3.0
1.0
1.0
2.5
0.8
0.8
2.0
0.6
0.6
1.5
0.4
0.4
0.2
0.2
without allelopathy
1.0
0.5
0.0
2.0
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0.6
0.4
0.8
1.0
0.0
0.0
1.2
(g) ACSA - Root biomass
0.2
0.8
0.6
0.4
1.0
0.0
0.0
1.2
(h) ACSA - Leaf biomass
1.0
1.0
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0.8
0.6
0.6
0.4
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0.2
0.2
0.2
0.4
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0.8
1.0
(f) ACSA - Extension biomass
0.2
0.4
0.6
0.8
1.0
0.6
0.8
1.0
(i) ACSA - Leaf area
1.5
1.0
0.5
0.0
0.0
allelopathy
0.2
0.6
0.4
1.2
0.8
1.0
0.0
0.0
0.2
(j) QURU - Extension growth
0.6
0.4
1.2
0.8
1.0
0.0
0.0
0.2
(k) QURU - Extension biomass
Ailanthus Neighborhood Index (ANI)
1.0
1.0
0.8
0.8
0.4
AC
Control
Solid0.6circles: activated carbon (no
allelopathy); Open circles: control
0.6
Red maple (Acer rubrum)
Proportionate Change
Allelopathy shifts the neighborhood effect from
strongly positive to neutral…
3.5
Without
allelopathy
3.5
(b) ACRU - Extension biomass
3.0
3.0
2.5
2.5
2.0
2.0
2.0
1.5
1.5
1.5
1.0
1.0
1.0
3.0
2.5
0.5
0.0
3.5
3.0
ultiplier (X)
3.5
(a) ACRU - Extension growth
allelopathy
0.2
0.4
0.6
(d) ACRU - Leaf area
0.8
1.0
0.5
0.0
1.2
0.2
0.4
0.6
0.8
(e) ACSA - Extension growth
1.0
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0.0
1.2
(c) ACRU - Leaf biomass
0.2
0.4
1.0
2.5
0.8
0.8
2.0
0.6
0.6
1.5
0.4
0.4
0.8
(f) ACSA - Extension biomass
Ailanthus Neighborhood Index (ANI)
1.0
0.6
1.0