ANOVA Results for Model Comparisons

Online Resource 3. GLMM and ANOVA results for effect of predictor variables on the main model.

3a. Main model: Pedicel length ~ gall occupant + Syconium volume + (1|tree identity).

Random variable: Tree identity; Fixed variables: Gall occupant, Syconium volume

ANOVA results for model comparisons:
Model / df / AIC / BIC / logLik / Test / L.Ratio / p-value
Effect of tree identity
Without tree identity / 1 / 9 / 3380.75 / 3441.21 / -1681.38
With tree identity / 2 / 10 / 3285.62 / 3352.79 / -1632.81 / 1 vs 2 / 97.14 / 0.0001
Since the AIC value for model 2 (model with tree identity included as random variable) is lower than the model without tree identity (model 1), tree identity has an effect on the pedicel length. Therefore, tree identity was retained in the main model.
Effect of gall occupant
With gall occupant / 1 / 10 / 3285.62 / 3352.79 / -1632.81
Without gall occupant / 2 / 4 / 5974.70 / 6001.57 / -2983.35 / 1 vs 2 / 2701.08 / 0.0001
Since the AIC value for model 1 is lower than model 2, the model with gall occupant is better and therefore this predictor variable was retained in the main model.
Effect of syconium volume
With syconium volume / 1 / 10 / 3285.62 / 3352.79 / -1632.81
Without syconium volume / 2 / 9 / 3491.61 / 3552.07 / -1736.80 / 1 vs 2 / 207.99 / 0.0001
Since the AIC value for model 1 is lower than model 2, the model with syconium volume is better and therefore we retained this predictor variable in the main model.

3b. Main model: Flower length ~ gall occupant + Syconium volume + (1|tree identity)

Random variable: Tree identity; Fixed variables: Gall occupant, Syconium volume

ANOVA results for model comparisons:
Model / df / AIC / BIC / logLik / Test / L.Ratio / p-value
Effect of tree identity
Without tree identity / 1 / 9 / 821.82 / 882.28 / -401.91
With tree identity / 2 / 10 / 706.19 / 773.36 / -343.09 / 1 vs 2 / 117.63 / 0.0001
Since the AIC value for model 2 (model with tree identity included as random variable) is lower than the model without tree identity (model 1), tree identity has an effect on the pedicel length. Therefore, tree identity was retained in the main model.
Effect of gall occupant
With gall occupant / 1 / 10 / 706.19 / 773.36 / -343.09
Without gall occupant / 2 / 4 / 5801.46 / 5828.33 / -2896.73 / 1 vs 2 / 5107.28 / 0.0001
Since the AIC value for model 1 is lower than model 2, model with gall occupant is better and therefore this predictor variable was retained in the main model.
Effect of syconium volume
With syconium volume / 1 / 10 / 706.19 / 773.36 / -343.09
Without syconium volume / 2 / 9 / 1027.35 / 1087.81 / -504.68 / 1 vs 2 / 323.16 / 0.0001
Since the AIC value for model 1 is lower than model 2, model with syconium volume is better and therefore we retained this predictor variable in the main model.

3c. Details of the model output: Pedicel length ~ gall occupant + Syconium volume + (1|tree identity)

Model 1: Without tree identity as random effect
Model 1 <- gls(sqrt(pedicel length) ~ gall occupant + syconium volume, method = "ML", data = data)
summary(pedicel length.lm)
Generalized least squares fit by maximum likelihood
Model: sqrt(pedicel length) ~ gall occupant + syconium volume
Data: data / AIC / BIC / logLik
3380.75 / 3441.2 / -1681.38
Coefficients: / Value / Std.Error / t-value / p-value
(Intercept): Apocrypta sp. 2 / 1.05 / 0.03 / 34.36 / 0.00
Gall occupant: Apo. westwoodi / 0.13 / 0.06 / 2.33 / 0.02
Gall occupant: A. testacea / -0.03 / 0.05 / -0.68 / 0.49
Gall occupant: A. fusca / -0.10 / 0.06 / -1.72 / 0.09
Gall occupant: A. agraensis / -0.01 / 0.05 / -0.20 / 0.84
Gall occupant: C.fusciceps / 0.03 / 0.03 / 1.08 / 0.28
Gall occupant: Seed / -0.44 / 0.03 / -14.27 / 0.00
Syconium volume / 0.00 / 0.00 / 16.83 / 0.00
Correlation: / Intercept:
Apocrypta sp. 2 / Gall occupant: Apo. westwoodi / Gall occupant:
A. testacea / Gall occupant:
A. fusca / Gall occupant:
A. agraensis / Gall occupant:
C. fusciceps / Gall occupant:
Seed
Gall occupant: Apo. westwoodi / -0.50
Gall occupant: A. testacea / -0.55 / 0.30
Gall occupant: A. fusca / -0.49 / 0.27 / 0.30
Gall occupant: A. agraensis / -0.58 / 0.32 / 0.36 / 0.33
Gall occupant: C. fusciceps / -0.85 / 0.49 / 0.55 / 0.50 / 0.62
Gall occupant: Seed / -0.85 / 0.49 / 0.55 / 0.50 / 0.62 / 0.96
Syconium volume / -0.28 / 0.02 / -0.01 / -0.03 / -0.08 / -0.23 / -0.23
Standardized residuals: / Min / Q1 / Med / Q3 / Max
-3.37 / -0.69 / 0.04 / 0.73 / 3.39
Residual standard error: / 0.32
Degrees of freedom: total / 6108
Degrees of freedom: residual / 6100
Model 2: With tree identity as random effect
Model2 <- lme(sqrt(pedicel length) ~ gall occupant + syconium volume, random=~1|tree identity, method= "ML", data = data)
Summary(pedicel length.lme)
Linear mixed-effects model fit by maximum likelihood
Data: data
AIC / BIC / logLik
3285.616 / 3352.79 / -1632.81
Random effects:
Formula: ~1 | tree identity
Intercept / Residual
StdDev: / 0.08 / 0.32
Fixed effects: sqrt(pedicel length) ~ gall occupant + syconium volume
Value / Std.Error / df / t-value / p-value
(Intercept): Apocrypta sp. 2 / 0.91 / 0.05 / 6096 / 17.68 / 0.00
Gall occupant: Apo. westwoodi / 0.14 / 0.06 / 6096 / 2.42 / 0.02
Gall occupant: A. testacea / -0.01 / 0.05 / 6096 / -0.28 / 0.78
Gall occupant: A. fusca / -0.05 / 0.06 / 6096 / -0.87 / 0.38
Gall occupant: A. agraensis / 0.03 / 0.05 / 6096 / 0.60 / 0.55
Gall occupant: C. fusciceps / 0.08 / 0.03 / 6096 / 2.64 / 0.01
Gall occupant: Seed / -0.41 / 0.03 / 6096 / -13.41 / 0.00
Syconium volume / 0.00 / 0.00 / 6096 / 14.54 / 0.00
Correlation: / Intercept:
Apocrypta sp. 2 / Gall occupant: Apo. westwoodi / Gall occupant:
A. testacea / Gall occupant:
A. fusca / Gall occupant:
A. agraensis / Gall occupant:
C. fusciceps / Gall occupant:
Seed
Gall occupant: Apo. westwoodi / -0.30
Gall occupant: A. testacea / -0.34 / 0.30
Gall occupant: A. fusca / -0.33 / 0.26 / 0.30
Gall occupant: A. agraensis / -0.39 / 0.31 / 0.36 / 0.33
Gall occupant: C.fusciceps / -0.54 / 0.48 / 0.55 / 0.50 / 0.63
Gall occupant: Seed / -0.53 / 0.48 / 0.55 / 0.50 / 0.63 / 0.96
Syconium volume / -0.34 / 0.03 / 0.03 / 0.07 / 0.01 / -0.08 / -0.11
Standardized Within-Group Residuals:
Min / Q1 / Med / Q3 / Max
-3.392 / -0.72 / -0.01 / 0.70 / 3.40
Number of Observations: / 6108
Number of Groups: / 5

3d. Details of the model output: Flower length ~ gall occupant + Syconium volume + (1|tree identity)

Model 1: Without tree identity as random effect
Flower length.lm <- gls(sqrt(flower length) ~ gall occupant + syconium volume, method = "ML", data = data) # no random effect
summary(flower length.lm)
Generalized least squares fit by maximum likelihood
Model: sqrt(flower length) ~ gall occupant + syconium volume
Data: data
AIC / BIC / logLik
821.8189 / 882.2751 / -401.9095
Coefficients: / Value / Std.Error / t-value / p-value
(Intercept): Apocrypta sp. 2 / 1.92 / 0.025 / 77.61 / 0.00
Gall occupant: Apo .westwoodi / 0.62 / 0.046 / 13.45 / 0.00
Gall occupant: A. testacea / 0.23 / 0.041 / 5.51 / 0.00
Gall occupant: A. fusca / -0.15 / 0.046 / -3.25 / 0.00
Gall occupant: A. agraensis / -0.10 / 0.038 / -2.72 / 0.01
Gall occupant: C. fusciceps / -0.11 / 0.025 / -4.53 / 0.00
Gall occupant: Seed / -0.66 / 0.025 / -26.77 / 0.00
Syconium volume / 0.00 / 0.000 / 21.72 / 0.00
Correlation: / Intercept:
Apocrypta sp. 2 / Gall occupant:
A. westwoodi / Gall occupant: A. testacea / Gall occupant: A. fusca / Gall occupant: A. agraensis / Gall occupant: C.fusciceps / Gall occupant:
Seed
Gall occupant: A. westwoodi / -0.50
Gall occupant: A. testacea / -0.55 / 0.30
Gall occupant: A. fusca / -0.49 / 0.27 / 0.30
Gall occupant: A. agraensis / -0.58 / 0.32 / 0.36 / 0.33
Gall occupant: C. fusciceps / -0.85 / 0.49 / 0.55 / 0.50 / 0.62
Gall occupant: Seed / -0.85 / 0.49 / 0.55 / 0.50 / 0.62 / 0.96
Syconium volume / -0.28 / 0.02 / -0.01 / -0.03 / -0.08 / -0.23 / -0.23
Standardized residuals:
Min / Q1 / Med / Q3 / Max
-3.86 / -0.73 / 0.01 / 0.73 / 3.47
Residual standard error: / 0.26
Degrees of freedom: total / 6108
Degrees of freedom: residual / 6100
Model 2: With tree identity as random effect
Flower length.lme <- lme(sqrt(flower length.mm) ~ gall occupant + syconium volume, random=~1|tree identity, method= "ML", data = data)
summary(flower length.lme)
Linear mixed-effects model fit by maximum likelihood
Data: data
AIC / BIC / logLik
706.19 / 773.36 / -343.09
Random effects:
Formula: ~1 | tree identity
Intercept / Residual
StdDev: / 0.08 / 0.26
Fixed effects: sqrt(flower length) ~ gall occupant + syconium volume
Value / Std.Error / df / t-value / p-value
(Intercept): Apocrypta sp. 2 / 1.84 / 0.05 / 6096.00 / 39.07 / 0.00
Gall occupant: A. westwoodi / 0.62 / 0.05 / 6096.00 / 13.70 / 0.00
Gall occupant: A. testacea / 0.24 / 0.04 / 6096.00 / 5.90 / 0.00
Gall occupant: A. fusca / -0.12 / 0.05 / 6096.00 / -2.70 / 0.01
Gall occupant: A. agraensis / -0.11 / 0.04 / 6096.00 / -2.96 / 0.00
Gall occupant: C. fusciceps / -0.10 / 0.03 / 6096.00 / -3.82 / 0.00
Gall occupant: Seed / -0.67 / 0.02 / 6096.00 / -26.84 / 0.00
Syconium volume / 0.00 / 0.00 / 6096.00 / 18.26 / 0.00
Correlation: / (Intercept):
Apocrypta sp. 2 / gall occupant:
A. westwoodi / gall occupant: A. testacea / gall occupant: A. fusca / gall occupant: A. agraensis / gall occupant: C.fusciceps / gall occupant:
Seed
Gall occupant: A. westwoodi / -0.26
Gall occupant: A. testacea / -0.30 / 0.30
Gall occupant: A. fusca / -0.29 / 0.26 / 0.30
Gall occupant: A. agraensis / -0.34 / 0.31 / 0.36 / 0.33
Gall occupant: C. fusciceps / -0.48 / 0.48 / 0.55 / 0.50 / 0.63
Gall occupant: Seed / -0.47 / 0.48 / 0.55 / 0.50 / 0.63 / 0.96
Syconium volume / -0.30 / 0.03 / 0.03 / 0.07 / 0.01 / -0.08 / -0.11
Standardized Within-Group Residuals:
Min / Q1 / Med / Q3 / Max
-3.89 / -0.74 / -0.01 / 0.71 / 3.59
Number of Observations: / 6108
Number of Groups: / 5