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).