Step 1: Best performing models for invader cover and resident diversity
We used linear mixed-effects models to determine relationships between the four experimental treatments and invader cover, and between treatments, invasion and resident diversity. Our mixed-effect models were multilevel linear models with both ‘fixed’ and ‘random’ effects, implemented through R package ‘nlme’ (Pinheiro et al. 2022).
Response variables : We examined cover of the fast and slow invader groups separately and in combination (total cover). Group-level cover was not overly dominated by particular species (Fig. S4). Our invader cover analysis only included plots where invaders were sown and had colonised (Appendix S2). All invader covers were log-transformed.
We examined effects of invasion on resident effective species richness (following Tilman et al. 2001) (hereon resident diversity). Resident diversity was strongly correlated with resident richness (r = 0.78) but not with total resident cover (r = 0.28, Table S7). We focus on resident diversity and not resident cover as it corresponds more closely with our interests (Catford et al. 2012b). We define the resident community as all species that were not experimentally sown even if they colonised the plots during the experiment. Invaders rarely colonised plots where they were not sown (Table S2). The resident diversity model included all plots where invaders were sown, regardless of whether invaders were present. Resident diversity was square-root transformed.
Regression model structure : We considered invader cover as a function of disturbance, successional stage, seed dose, invader type and growth season. For resident diversity, we considered invader richness and total invader cover instead of invader seed dose. Plot was included as a random intercept and growth season as an interacting random slope to account for repeat measurements and variation in individual plots over time. From these fixed effects, we constructed two separate global models for each response variable. First, a base model where each treatment was considered as a non-interacting effect. Second, an interaction model where two-way interactions between the experimental treatments were considered (Appendix S2, Tables S3-S6 & S9-11).
Model selection : For each base and interaction model, we ranked the performance of the full model and all potential subsets using Bayesian Information Criterion (BIC). From this, we considered all models within 6 BIC points of the best performing model. For each best performing model (lowest BIC), we calculated marginal and conditional R2 values, representing total variance explained by the entire model (fixed & random effects) and fixed effects only (Nakagawa & Schielzeth 2013). Based on BIC and marginal R2 values, the interaction models performed better than base models, especially for invader cover (Tables S8-11). For each response variable, the competing models (<6 BIC points) were either subsets of the best model or had a better performing model nested within them. For simplicity and because the ecological interpretation of the competing models is effectively the same, we focus on the best interaction model for each response variable.