*2.6. Statistical Methods*

All statistical analyses were done in Program R v3.3.2 (R Core Development Team 2016, Vienna, Austria). A likelihood-based generalised linear modelling framework was used to assess experimental predictors and dependencies. For each data set, an *a priori* model set was created, and strength of support was evaluated by using Akaike's information criterion, adjusted for small sample sizes (AIC*c*). Model weights were calculated using the MuMIn package [30]. Akaike weights ( *wi*) were used to assess model support; these represent the relative likelihood of a given model compared to others in the evaluation set (which can be of varying complexity and non-nested), by adjusting the likelihood for bias associated with fitting the parameters [31,32]. The relative support from the data for competing models was evaluated using the evidence ratio (ER), the ratio of the respective model's *wi*. The percentage deviance (%DE) explained by each model relative to the null (intercept only) was used to assess structural goodness of fit.

In cases where multiple measurements of the dependent variable were taken at each level of a predictor (see Section 3.4), resampling was used (with one outcome selected randomly for any given predictor level and repeated 10,000 times) to avoid pseudoreplication, with the models fitted repeatedly to each subsample. The median prediction from the set of models fitted to the resampled data was used to determine the slope of the predictor and 95% confidence intervals. As a check, these were also compared to models fitted to the medians of the raw data (i.e., ignoring within-sample heterogeneity).

The 24 plots were analysed to assess the influence of *Acacia* sp. on *Eucalyptus* sp., and total site productivity. In this case, the *a priori* models represented additive combinations of the following predictors (of varying complexity): Proportion of *A. dealbata* biomass, the average size of *A. dealbata*, the number of species, or the variance of the pairwise distances between trees. Dependent variables were total basal area of a site or, alternatively, the average size of the eucalypts (DBH cm).

To test whether the availability of soil nutrients (C and N) had an influence on the average size of eucalypts or the total basal area (see Section 3.3), fitted linear models were restricted to either one or two terms due to sample-size limitations (nine total sites). Average size of *A. dealbata* was determined to be the most important factor influencing site productivity during the 24-plot analysis (Section 3.1 and see Results), and therefore was included as a control term in all *a priori* models. The other predictor variable assessed was either: C, N, or pre-total mineralisation of N. Phosphorus was also considered but there were negligible di fferences across sites.
