## 2 Materials and Methods
### Statistical Analysis  
The effects of the environmental conditions (dune type, slope type and patch type) on total vegetation cover, species richness (i.e., number of observed species), beta diversity (i.e., distance to group centroid in ordination) and species assemblages were evaluated as follows:  
1. Environmental effects on vegetation cover (first row in Figure 2) were evaluated by fitting mixed effects linear models with random effects of the dune identity (e.g., M1 = mobile dune #1, etc.) and sampling year (e.g., 2007) to take into account unmeasured sources of variation affecting plant cover across spatial locations and sampling time periods. Significance levels of differences between estimated marginal means of the groups were corrected using the Bonferroni method. 2. Environmental effects on species richness (i.e., count of unique species) (second row in Figure 2) were evaluated with the same approach as in case (1), only using mixed effects generalized linear models, with a Poisson distribution, instead of mixed effects linear models, since the dependent variable was the species count. Significance levels of differences between estimated marginal means of the groups were corrected using the Bonferroni method. 3. Environmental effects on beta diversity (third row in Figure 2) were evaluated using [PERSON]'s PERMDISP2 procedure for the analysis of multivariate homogeneity of group dispersions [52], where the distances of group members to the group centroid are subject to ANOVA. Samples were placed in multivariate space using the \(\beta_{t}\)[53; 54] measure of dissimilarity. Significance levels of differences between group means were corrected using [PERSON]'s \"Honest Significant Difference\" method. 4. Environmental effects on species composition were evaluated using redundancy Analysis (RDA) ordination (Figure 3), separately for each pair of groups being compared, followed by a permutation test to assess the significance of the constraints, corrected using the Bonferroni method. Figure 3: Redundancy analysis (RDA) of species composition, constrained by dune type (top), dune type and slope type combinations (middle), or dune type and patch type combinations (bottom). Species scores are shown in red, site scores are shown in black. Sites belonging to each of the two groups being compared are marked with a convex hull polygon (M = mobile dune; F = fixed dune; W = windward; C = crest; S = slipface; O = open; B = bush, *** \(p<0.001\), *** \(p<0.01\), * \(p<0.05\), NS = not significant). Figure 2: Distribution of vegetation cover, species richness and beta diversity among samples, separately for each dune type (“Type”), dune type and slope combination (“Type + Slope”), and dune type and patch combination (“Type + Patch”) (M = mobile dune; F = fixed dune; W = windward; C = crest; S = slipface; O = open; B = bush). The latter four types of models, where the dependent variables were either (1) cover, (2) richness, (3) beta diversity, or (4) plant assemblage, were fitted separately for three \"levels\" of observation:  
1. Comparing dune types,
2. Comparing dune type/slope combinations, and
3. Comparing dune type/patch combinations. The results regarding the environmental effects on cover, richness, beta diversity and plant assemblages are summarized in Table 1 and visualized in Figure 2 (cover, richness and beta diversity) and Figure 3 (plant assemblages). Species turnover, when moving from mobile to fixed dunes, was calculated at three levels: considering the species assemblage in all samples combined, separately for samples from each slope type and separately for samples from each patch type (Figure 4). Species turnover was defined using the \(\beta_{t}\) index, contrasting the complete list of species in mobile vs. fixed dunes [53].