Statistical analysis
To test the effects of soil biota, harvest time and their interactions
on performance of invasive and co-occurring native plant species, we
fitted Bayesian multilevel models using the function brm of the R
package brms (Bürkner 2017) in R 4.0.3 (R Core Team 2020). To meet the
assumption of normality, total biomass was sqrt-root-transformed, while
the root mass fraction was natural-log transformed. We included plant
species invasion status (invasive vs native), presence of soil biota
(live vs sterilized), harvest time (i.e., first vs second) and
their interactions as fixed effects in all models.
To account for non-independence of individuals of the plant species and
for phylogenetic non-independence of the same species, we included
species nested within genus as random factors in all models. In
addition, to control for the potential effects of reproductive strategy
of the different plant species (i.e., sexual vs vegetative), we included
reproductive strategy as a random factor in the models.
We used the default priors set by the brms package, ran four independent
chains. The total number of iterations per chain was 4000, and the
number of warm-up samples was 2000. To effectively ‘centers’ the effects
to the grand mean (i.e., the mean value across all data observations),
we used the sum coding to directly test hypotheses about the main
effects and interactive effects based on each coefficient’s posterior
distribution (Schad et al. 2020). And we used the functions contrasts
and contr.sum of the stats package to implement this in brms. We
considered the fixed effects of soil biota, harvest time and invasive
status, and their interactions as significant when their 95% credible
interval of the posterior distribution did not overlap zero, and when
the 90% credible interval did not overlap zero as marginally
significant. In addition, we analyzed the effects of soil biota, harvest
time and their interactions on performance each congeneric pairs of
invasive and native plant species using the same statistical analysis.