SUPPLEMENTARY INFORMATION
Appendix S1: Differences in productivity between valleys and slopes
Differences in productivity between the two habitats were tested by sampling above-ground
biomass of grasses and forbs in 21 quadrates of 20X20cm in the control plots of each habitat
(a stratified random sampling of 7 quadrates per plot). The results indicated that valleys were
much more productive than slopes (mean+1SE above-ground biomass = 10.70+0.70 vs.
5.17+0.58 g), that differences among plots within each habitat were not significant (P > 0.05),
and that the differences between the two habitats were caused by higher biomass of grass
species in the valleys (see figure below). Repeated measures analysis of the data with group
type (grasses vs. forbs) as a within-subject effect and habitat type as a between-subject effect
indicated that the effects of habitat type, group type, and their interactions were all highly
significant (P < 0.0001 for all effects,).
Appendix S2: Statistical analysis of the grass removal experiment
The effect of habitat type (valley vs. slope), treatment (control vs. grass removal), and their
interaction on species richness at the quadrate scale was analyzed using the SAR model:
yijk   0  1 Habitat i   2Treatment j  3 ( Habitat  Treatment) ij   ijk ,   W   
where y is the average richness per quadrate within a given cluster, i is an index for a pair of
matched plots in a given habitat (valley = 0, slope = 1), j is an index for a particular plot in a
given habitat and under a given treatment (control = 0, grass removal = 1), k is an index for
the particular cluster of quadrates (N = 60 clusters),  is the vector of error terms, spatially
weighted using the weights matrix W (we used standardized weights where each neighbor in
the plot-pair has the same weight),  is the spatial error coefficient, and  is a vector of
uncorrelated error terms. The effect of habitat type, treatment, and their interaction on species
richness at the cluster scale was analyzed using the same model with yijk representing the
number of species per cluster (N = 60 clusters). The effect at the plot scale was tested using
linear regression similar to the spatial model, but with no correlation between the error terms
(N = 12 plots):
yij   0  1 Habitat i   2Treatment j  3 ( Habitat  Treatment) ij   ij ,  ij ~ N (0,  2 ) .
The corresponding effects on beta diversity (βRC) were tested using linear regression. The
model constructed for the quadrate scale was:
yijk   0  1 Habitat i   2Treatment j  3 ( Habitat  Treatment) ij   ijk ,  ijk ~ N (0,  2 )
Where yijk is the average value of βRC per cluster, and i, j, and k are indices for pairs of
matched plots, individual plots, and clusters, respectively (N = 60 clusters). A similar model
was used for analyzing beta diversity at the cluster scale but here k indicates a pair of clusters
between which the value of βRC is calculated (N = 120 pairs). In the latter analysis correlation
exists between beta diversity indices that are based on the same cluster. We controlled for the
correlation by fitting the regression model using methods for general linear models.
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Appendix S3: Analysis of species richness and beta diversity in the sowing experiment
Here we present a similar analysis for that presented in figure 5 of the main text, but calculate
richness, beta diversity, and the null values of beta diversity based on the quadrates for which
data on species abundance were available for the first year (four quadrates in the valleys and
six quadrates on the slopes). The upper two panels show the average number of species per
quadrate in the valleys (left) and on the slopes (right) during the three years of the study. For
each year we determined richness at the seedling stage and at the adult (flowering) stage. The
lower four panels present the results obtained from the null model analysis of beta diversity. In
contrast to the analysis presented in figure 5, here species were sampled based on their relative
abundance in the first year (seedling stage of 2011). For each type of habitat, beta diversity was
determined using two indices, a presence-absence index (Jaccard index of dissimilarity) and an
abundance-based index (Bray & Curtis measure of dissimilarity). Histograms represent the
distribution of the relevant index under the null hypothesis and vertical dashed lines indicate
the observed values. ES=effect size (see main text for definition)
Valley
Slope
Seedlings
Adults
Year
Jaccard
Jaccard
P<0.0031
ES=0.149
P<0.5055
ES=-0.002
Bray &
Curtis
Bray &
Curtis
P<0.0001
ES=1.851
P<0.0190
ES=0.076
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Beta diversity