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.