Plant diversity metrics

Species richness per quadrat (alpha diversity) was assessed as one of the most simplest metrics of biodiversity. 
An index of community unicity was calculated based on species' occupancy within Denmark, i.e. Atlas Flora Danica, AFD \citep{RN15064}. These data consist of presence and absence records of all vascular plants in 1300 grid cells, each 5 × 5 km, dispersed across the country. Each species i recorded in a quadrat was given a value equivalent to the inverse of its range size and the resulting values summed per quadrat, thus
  \(\sum_{i=1}^S\frac{1}{n\ AFD\ grid\ cells\ with\ species\ i\ present}\), in which S is the number of species in a given quadrat.
The ratio of forbs to graminoids was included as an indicator of floral resources available to anthophilous insects, thus \(\ \frac{n\ intercepts\left(\text{forbs}\right)}{n\ intercepts\left(\text{graminoids}\right)}\), or the equivalent for biomass estimates.
Finally, the amount of leaf litter was used as an indication of grazing naturalness.

Statistical analysis

First, an overall model of intercepts per vascular plant species  as a function of above-ground biomass was built as a generalized linear model. Next, the residual variation of this model was investigated using analysis of variance with dry mass per point-intercept as the dependent variable and species identity, block and treatment as factors, using data from 24 quadrats recorded i 2020. This was done to investigate the assumption that species identity would explain variation in this ratio. Subsequently, one linear regression model per plant species was built. This was done for plant species with three or more data points, and additionally for genera with more than one species present and for functional groups meeting the same criterion. The functional groups were:  Broad-leaved graminoids (leaf blades > 2 mm), narrow-leaved graminoids (leaf blades < 2 mm),  Juncus effusus-type rushes (for which intercepts with stems were recorded, as they bear no leaf blades), forbs, woody plants (trees and shrubs, incl Calluna vulgaris and Cytisus scoparius). Initially, separate models were built for forbs with basal leaves, e.g. rosettes, vs. post-and-flag type forbs, but model estimates were very similar, so the two groups were combined to produced a single model with comparable R2 and lower standard error. A separate model was built for standing dead litter. No data transformations were used. All regressions models were forced through the origin, because otherwise - when predicted biomass was accrued per plot over species - total biomass per plot would gain a spurious strong positive relationship with plot species richness.
Second, for the 45 quadrats sampled in 2021, calibrated biomass values per species per plot were calculated from point-intercept data and summed over species present in plots (total biomass, plus forb and graminoid biomass separately). For each species present in a plot, the best available model was used, i.e. first choice was a species-specific model, second choice a genus-specific model, third choice a model for functional group and, in case none of these were available, a general model based on all point-intercepts was used.
Generalized linear models (GLM) were used to assess the effect of grazing treatment on the two biodiversity metrics, richness and unicity, and on forb:graminoid ratio and litter amount, while considering block, topographic position and treatment. Block was nested in topographic position, which was either hill or marine foreland. GLM with Poisson errors and log link function was used for species richness and for litter (standing dead intercepts), whereas ordinary Gaussian regression was used for the forb:graminoid ratio.
For litter and for forb:graminoid ratio, the procedure was run for raw intercept counts and for calibrated biomass in parallel.

Results

[1) first year data: overall models of above-ground plant biomass]
The initial generalized linear model of harvested dry mass per point-intercept across species and plots showed the expected positive linear relationship, but with much un-explained variation (R= 0.517). The subsequent ANOVA showed species identity to be the by far most important factor accounting for the residual variation, explaining 56.4% of the deviance. In contrast, treatment explained less than 2% of the total deviance. Thus, there was a significant degree of variation in mass per intercept across species, justifying the attempt of making single-species calibration models.
[2) first year data: calibration models per species, genus etc]
In the 24 quadrats recorded i 2020, a total of 60 plant species were found, of which 35 occurred in more than three quadrats. For 22 species, linear regression models of biomass on intercepts yielded a p-value < 0.05 as were accepted as single-species prediction models. Five genera with more than one species present yielded acceptable models, i.e. Agrostis, Carex, Galium,  Festuca and Juncus (effusus-type) and, similarly, the four functional types as well as for total biomass and for standing litter. The regression models are presented in Supplementary materials (Appendix 2: Table S1).
[3) second year data: Number of species found, gamma (descriptive stats)]
The total number of species per treatment found across plots differed quite markedly, with full exclosure having the fewest species in total (Table 1). Similarly, the average species density, i.e. number of species per plot (mean alpha diversity), varied being treatments, with winter-only and year-round grazing showing the highest levels (Table 1).