Statistical analysis
Species & phylogenetic diversity
We analyzed the effect of grazing intensity on SR (overall and for the
shrubs, herbs, and graminoids), H’, Evar, phylogenetic
dispersion and abundance-weighted phylogenetic dispersion using linear
mixed effects models with site as a random effect (following
Begley-Miller et al. 2014) and grazing, year, a grazing:year
interaction, and wet/dry as fixed effects. First, we tested the
grazing:year interaction using a likelihood ratio test. If the
interaction was not significant (p > 0.05), then we removed
it from the model and tested the remaining fixed effects. If a
significant effect of grazing or year was found (p < 0.05),
then a post-hoc analysis was performed with Tukey pair-wise comparisons.
To control for the possibility that changes in phylogenetic dispersion
may result from the transition of communities from dwarf shrubs to
graminoids, we also tested the effect of grazing on phylogenetic
dispersion and abundance-weighted phylogenetic dispersion with the same
procedure described above, while controlling for the proportion of
species that are graminoids (for phylogenetic dispersion) and the
proportion of the relative abundance that are graminoids (for
abundance-weighted phylogenetic dispersion). All analyses were performed
in R version 3.6.0 (R Core Team 2019).
Community structure
To compare the community structure of plots we used the Bray-Curtis
dissimilarity index, calculated using vegdist from the R package
“vegan” (Oksanen et al. 2016), as a measurement of the distance
between plant communities based on our relative species abundance data.
To partition variance within the distance matrix, we used a
non-parametric permutational multivariate analysis of variance
(PERMANOVA), as implemented in the vegan function adonis .
Significance values and pseudo F-statistics were obtained from
permutations (n = 1000) restricted within each site due to our nested
experimental design. Given that this technique allowed us to perform a
multivariate analysis, we include grazing, year, a grazing:year
interaction, and wet/dry as covariates. When significant values (p
< 0.05) were obtained, we performed a post-hoc analysis with
Bonferroni corrections to correct for multiple comparisons in the
PERMANOVA.
To visualize and corroborate the results of the PERMANOVA, we used a
non-metric multi-dimensional scaling (NMDS) from the functionmetaMDS in vegan. NMDS is an ordination technique that represents
highly dimensional data by maximizing the correlation of
ranked-distances between the original highly dimensional data and a two
dimensional representation (Faith et al. 1987, Minchin 1987). A stress
score is calculated as a measure of how accurately the two dimensional
ordination represents the distances in the original data; stress scores
< 0.2 are generally considered acceptable (Clarke 1993).
Communities grouped closely together in the ordination space are
interpreted as being more similar than those placed farther away.