Data Analysis
To test how grassland types, prairie dog grazing and seasons relate to
taxonomic, functional and CWM trait measures, generalized and linear
mixed models were fitted. Prairie dog disturbance (WP and WOP), season
(wet or dry) and grassland type (Agri, Arid, Mount and Calc) were
treated as fixed factors and grassland location as a random factor. We
tested for interactions as well, to see if the effects were modified
between variables, pointing to relevant ecological processes. Residual
graphics were used to examine homoscedasticity. Since FEve, FDiv, Fspe,
and evenness range between zero and one, they were analyzed using beta
regressions with the glmmTMB package (Brooks et al. 2017). A generalized
linear mixed model following a Poisson distribution was fitted for
richness using the lme4 package (Bates et al. 2015). All other models
were fitted using linear mixed models using the lme4 package. To remove
skews, RaoQ, CWMheight, CWMleaf area, C3 cover were log transformed and
annual cover, prostrate cover, forb cover, sub-shrub cover were log
transformed + 1. F-tests, Chi2, respectively, and
degrees of freedom were obtained using parametric bootstrap with 10,000
iterations for glmms and the Kenward–Roger’s approximation for lmms,
respectively, both obtained in the pbkrtest package (Halekoh and
Højsgaard, 2014). Beta regression inferences were obtained using Anova
tables from the car package (Fox and Weisberg, 2019). We considered all
the variables and their interactions to be biologically important and
hence included them all in the full model. Best fit models were selected
by comparing AICc (Bartoń et al. 2018; Appendix S2, Table S1) and
selecting the model with the lowest one. Marginal pseudo-R² (R²m) values
were obtained with the Nakagawa et al. (2017) method available in the
performance package (Lüdecke et al. 2020). Once the best fit model was
selected, Tukey’s HSD post-hoc test was used to compare levels within
variables using the emmeans package (Lenth, 2021). All analyses were
conducted using R Version 4.0.3 (R Core Team, 2020). Error probabilities
are interpreted as recommended by Muff et al. (2021) with respect to
their strength of evidence rather than significance.
Table 2. Results of linear and generalized linear mixed models to test
how grassland types, prairie dog grazing and seasons relate to
taxonomic, functional and CWM trait measures. Prairie dog disturbance
(WP and WOP), season (wet or dry) and grassland type (Agri, Arid, Mount
and Calc) were treated as fixed factors and grassland location as a
random factor. The table is shown only for final models selected based
on Akaike’s Information Criterion (AIC).