Supplement2Mixed-effects model results for growth, percent survival, and percent root tip colonization. R function is the type of function used to estimate parameters for each model. ΔAIC values are the difference between the best model (first model listed) and the alternative models

Growth / Model / R function / ΔAIC
Additive (with random) / lme / 0
Additive (no random) / gls / 1.98
Community treatment / lme / 4
Global / lme / 6.4
Initial soil treatment / lme / 9.7
Survival / Model / R function / ΔAIC
Community treatment / lmer / 0
Global / lmer / 1.4
Initial Soil treatment / lmer / 1.7
Additive / lmer / 3.2
Colonization / Model / R function / ΔAIC
Global / lmer / 0
Community treatment / lmer / 8.6
Additive / lmer / 9.9
Initial soil treatment / lmer / 10.5

The growth data were analyzed using a normal error distribution. The survival data were treated as binary data and tested using a binomial error distribution and a logit link function. The colonization data were treated as binomial counts with colonized and uncolonized root tips representing successes and failures, respectively and with a binomial error distribution and logit link function. Four models were tested for each response variable: the fixed-effects were set as soil bioassay treatment, community treatment, an additive model with both, and a global model with an additive effect of soil bioassay treatment, community treatment, and their interaction. The random effects tested were outplanting blocks, initial soil collection plot, and initial soil collection plot crossed in outplant block. Model comparison for each response variable was done with Akaike Information Criterion (AIC), and models with AIC < 2 units difference were assumed to have equal empirical support (Burnham and Anderson 2002); therefore, simpler models were selected when differences were < 2 units. Lower AIC values were considered to have greater empirical support when differences were ≥ 2 units.

Maximum likelihood methods were used to compare models, and restricted-maximum likelihood was used for parameter estimation of the optimal model (Pinheiro and Bates 2000). AIC was used to select both the optimal model and test the incorporation of random effects in the optimal mixed model. For growth, generalized least squares using the gls function in the nlme library was used to compare the optimal model with random effects to the optimal model with no random effects, and variance was weighted by soil bioassay treatment within outplant block in using the VarIdent() command in the nlme library which allowed unequal variance across initial soil treatments due to the lower variability in sterilized control soils compared with forest derived soils (Pinheiro and Bates 2000). In order to ensure that the removal of block from the random effects in the growth model was not altering the results by strengthening the degrees of freedom, we compared means of the six outplant plots and eleven initial soil treatments with a simple ANOVA. The test had similar results to our linear mixed-model (F2,8=2.63, p=0.13 andF1,4=21.16, p=0.0, for the effect of initial soil type and outplant forest type, respectively and a mean (CI) difference in increment growth between hemlock and hardwood forest equal to 0.41 (0.23 – 0.58)).

References

Burnham KP, Anderson DR (2002) Model selection and multimodal inference, a practical information theoretic approach, 2ndedn. Springer, New York

Pinheiro JC, Bates DM (2000) Mixed-effects Models in S and S-PLUS, Springer-Verlag, New York