Supplemental Materials: Community Control on Growth and Survival of an Exotic Shrub

Supplemental Materials: Community control on growth and survival of an exotic shrub

Biological Invasions

Brym, Allen, & Ibañez

Corresponding Author: Zack Brym, Utah State University,

Transplant Experiment

Survival Model Selection and Results

We tried model variations that included fixed effects and eventually an error term (Table S1). First, an intercept and a fixed effect for light (L) were used, in coordination with our hypothesis that light would limit seedling recruitment. Additional models added point average moisture (W) and a prediction of moisture based on average measurements per plot, though only point level moisture was used in the best-fit sub-model F and the analytical extension (binning light parameter) sub-model G. The intercept value was split to represent each of four transects in the experimental design and three habitats (closed canopy, edge, open canopy). Sub-models largely show a decrease (i.e., better fit) in Deviance Information Criterion (DIC) as complexity increase (Burnham & Anderson, 2002).

Growth Model Selection and Results

We tried model variations that included only fixed effects, and other models with added random effects [] with respect to plot and row (Table S2). After preliminary exploration of the data, an initial model was constructed to incorporate the biological aspects that seemed most relevant (initial size, soil moisture, light, and number of neighborhood conspecific saplings). We compared the sub-models and selected the one with the lowest DIC. Sub-model D was chosen and is comprised of all fixed-effect coefficients and incorporates variation by row using observed moisture data (Table S2). Similar results were found for total harvest biomass as aboveground and root biomass (Table S3).

Forest Census

Light Estimation

Based on measurement of light using canopy photos and the neighborhood survey we evaluated the relationship between total basal area of all individuals within a 10 m radius and light availability using a simple linear model:

ψLi = a*ln(B10i)+b

ψLi is the value of light estimated from the canopy photos (Global Site Factor, it ranges from 0 to 1, being 1 full sun light), the biotic variable B10 represents the total basal area in a 10 m radius around the point the canopy photo was taken for individual i. The linear regression estimates of the parameters were a:-0.1631 and b:1.7032, R2=0.7383 (Fig. S1). For the forest census data we then estimated the light reaching each plant as a function of its neighbors. Because there is uncertainty in our prediction of the light environment we did not use that estimate directly but sampled it from a distribution:

Zi ~ Normal(ψLi , 0.1)

ψLi = -0.1631*ln(B10i) + 1.7032

where Z represents the light available to individual i as a function of its neighborhood in a 10m radius.These calculations were made using the program R (R v2.11.1, R Foundation for Statistical Computing).

Model Selection and Results for adult growth

We tried variations of the model using only environmental variables and then added levels of complexity from the neighborhood surveys (Table S4). Variables included in the sub-models are: intercept values for each of the soil types t found in the studied area (γt), the total basal area of all species within a 20 m radius (B20i), the total basal area of conspecific individuals within a 10 m radius (B10Ci),the total basal area of E. umbellata in a 5 m radius (B5Ei). We compared the submodels and selected the one with the set of covariates that best fit the data using deviance information criterion (DIC).

As expected the progression of models lowered the DIC as variables were added to the model. However, we opted for a more parsimonious model with a lightly higher DIC. Conspecific basal area in a 10 m radius (B10Ci) was removed because it was biologically redundant to the spatial scale at which we evaluated light and had little effect in improving model predictions. Basal area for E. umbellata in a 5 m radius (B5Ei) was also removed as the majority of data demonstrated an absence of E. umbellata (Table S4). The results of the model (Table S5) reflected this bias of data and had little effect in improving the model predictions.Sub-model E was chosen for the final analysis.

Works Cited

Burnham, K.P., & Anderson, D.R. (2002). Model Selection and Mutimodel Inference: a practical information-theoretic approach [2nd Edition]. Springer Science and Business Media, Inc.

Table S1. Progression of submodels leading to predictions of seedling survival. DIC values are reported for model fit.

Submodel / Description / DIC
Model A / i = 0 + ILi
intercept and light (L) / 5650
Model B / i = 0 + 1Wi + 2Li
intercept, moisture (W), and light (L) / 4640
Model C / i = 0+ 1WP(i) + 2Li
intercept per transect (T), predicted moisture (W) per plot (P), and light (L) / 4639
Model D / i = T(i) + 5Wi + 6Li
intercept per transect (T), moisture (W), and light (L) / 3821
Model E / i = H(i) + 4Wi + 5Li
intercept per habitat(H), moisture (W), and light (L) / 3079
Model F / i = 0 + 1Wi + 2Li+ 
intercept, moisture (W), and light (L). This model is the best-fit. / 3079
Model G / i = 0 + 1Wi + 2Li,j + 
intercept, predicted moisture (W) per row (R), and light (L) with j bins. This model is an analytical extension of the best-fit. / 4400

Table S2. Progression of submodels leading to predictions of harvested dry mass. R2 values are reported for predicted vs. observed values of harvested mass.

Submodel / Description / DIC
Model A / i = 1Hi + 2Wi + 3Li+ 4Ji
Initial size (H), moisture (W), light (L), number of neighborhood conspecific saplings (J) / 427
Model B / i = 1Hi + 2Wi + 3Li+ 4B10Ti + plot + row
random effects () for plot and row are added to this model along with the total neighborhood basal area in a 10 m radius (B10Ti). / 389
Model C / i = 1Hi + 2Wi + 3Li+ 4Ji + plot + row
Similar to submodel B, but JireplacesB10Ti / 390
Model D / i = 0 + 1Hi + 2Wi + 3Li
Linear model similar to submodel A, but Ji is removed. This model is described as the best-fit model. / 366

Table S3.Posterior mean parameter values for the transplant experiment best-fit model of all above-ground and below-ground partitions. Credible intervals that do not include zero are considered statistically significant.

Above-Ground Dry Biomass
Parameter / Mean / St. Dev. / 95% Credible Interval
intercept0 / 0.3566 / 0.4191 / -0.4625 / 1.1940
initial size1 / 0.0149 / 0.0041 / 0.0066 / 0.0226
soil moisture2 / 0.0422 / 0.0091 / 0.0262 / 0.0620
light3 / 0.2816 / 0.5228 / -0.7408 / 1.2880
variance2 / 2.759 / 0.2708 / 2.253 / 3.316
Root Dry Biomass
Parameter / Mean / St. Dev. / 95% Credible Interval
intercept0 / 0.9289 / 0.4099 / 0.0952 / 1.7050
initial size1 / 0.0104 / 0.0040 / 0.0028 / 0.0185
soil moisture2 / 0.0418 / 0.0094 / 0.0260 / 0.0634
light3 / -0.0435 / 0.5225 / -1.0800 / 0.9705
variance 2 / 2.593 / 0.2538 / 2.123 / 3.111

Table S4. Progression of submodels leading to the final model used for growth predictions as evaluated by deviance information criterion (DIC).

Submodel / Model Description / DIC
Submodel A / χi =γt+γ5Mi+γ6sAi
Establish best predictive environmental variables / 29920
Submodel B / χi =γts+γ5sMi+γ6sAi+λ1sB20i +λ2sB10Ci+λ3sB5Ei
Add best combination of neighborhood survey data / 29530
Submodel C / χi = γts+γ5sMi+γ6sAi+λ1sB20i +λ2sB10Ci+λ3sB5Ei + sI
Add initial size of individuals / 28860
Submodel D / χi =γts+γ5sMi+γ6sAi+ γ7sZi + λ 1sB10Ci+ λ 2sB5Ei+ sI
Incorporate light function of basal area for large-scale interactions / 23310
Submodel E / χi =γ1s+γ2sMi+γ3sAi+ γ4sZi + λ sB1i+ sI
Remove Conspecific at 10 m Elaeagnus at 5 m and replaced with the single variable total basal area at 1 m. Simplified soil intercept to a single species specific intercept. This model is described as the best-fit. / 23710

Table S5. Mean values for fixed effect coefficient of all understory species. Standard deviation is included in parenthesis with significant values bolded (95%CI not include 0).

Species / intercept
γ1 / slope
γ2 / aspect
γ3 / estimatedlight
γ4 / neighbor density
 / initial size
 / variance
E. umbellata / -3.538 / -0.120 / 0.068 / 0.270 / -0.831 / -5.428 / 2.159
(1.033) / (0.290) / (0.204) / (0.126) / (0.274) / (03.53) / (0.889)
S. albidum / -2.214 / 0.066 / -0.047 / 0.098 / -0.014 / -0.896 / 2.749
(0.053) / (0.064) / (0.094) / (0.056) / (0.069) / (0.106) / (0.243)
H. virginiana / -3.404 / 0.006 / -0.057 / -0.470 / -0.032 / -3.500 / 5.070
(0.162) / (0.041) / (0.045) / (0.018) / (0.039) / (0.554) / (0.777)
A. arborea / -2.786 / 0.090 / -0.184 / -0.460 / -0.016 / -3.082 / 6.870
(0.110) / (0.059) / (0.065) / (0.026) / (0.044) / (0.41) / (1.532)
C. florida / -3.464 / 0.255 / 0.048 / -0.513 / -0.042 / -3.838 / 10.210
(0.184) / (0.101) / (0.091) / (0.079) / (0.075) / (0.741) / (5.079)
O. virginiana / -1.883 / 0.008 / 0.386 / -0.379 / 0.005 / 0.156 / 9.480
(0.106) / (0.111) / (0.101) / (0.05) / (0.095) / (0.445) / (4.425)
A. rubrum / -1.723 / 0.117 / -0.106 / -0.399 / -0.025 / -0.524 / 4.950
(0.014) / (0.027) / (0.026) / (0.014) / (0.023) / (0.049) / (0.452)
C. glabra / -2.708 / 0.012 / 0.045 / 0.128 / 0.053 / -0.498 / 1.888
(0.081) / (0.075) / (0.071) / (0.079) / (0.073) / (0.067) / (0.218)
C. ovata / -2.281 / -0.026 / -0.243 / -0.189 / -0.037 / -0.833 / 7.496
(0.207) / (0.169) / (0.145) / (0.279) / (0.228) / (0.237) / (13.38)
F. grandifolia / -1.905 / -0.184 / 0.097 / 0.114 / 0.634 / -0.885 / 7.083
(0.168) / (0.236) / (0.242) / (0.163) / (0.926) / (0.204) / (4.382)
Q. alba / -3.212 / 0.003 / 0.073 / -0.228 / 0.114 / -0.024 / 2.476
(0.158) / (0.069) / (0.08) / (0.193) / (0.080) / (0.063) / (0.838)
Q. velutina / -2.995 / 0.058 / -0.194 / 0.217 / -0.136 / -0.356 / 1.979
(0.069) / (0.052) / (0.050) / (0.036) / (0.125) / (0.051) / (0.155)
P. serotina / -2.061 / -0.080 / -0.219 / -0.466 / -0.044 / -0.769 / 4.565
(0.014) / (0.027) / (0.026) / (0.015) / (0.026) / (0.044) / (0.473)
T. americana / -1.693 / 0.208 / -0.331 / -0.599 / 0.210 / -0.421 / 36.300
(0.165) / (0.410) / (0.343) / (0.114) / (0.269) / (0.305) / (51.73)
U. americana / -1.726 / -0.217 / -0.334 / -0.510 / 0.012 / -0.986 / 13.360
(0.144) / (0.147) / (0.170) / (0.048) / (0.163) / (0.587) / (9.370)

Figure S1. Relationship of total basal area for all individuals in a 10m radius and light [global solar fraction] (R2=0.7383).

Figure S2. Correlation coefficients for predicted and observed values of adult growth.

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