Results
Nutrient addition and herbivore exclusion had no significant interactive effects on any variables measured except for spatial asynchrony (Fig. 1). That is, herbivore exclusion decreased spatial asynchrony under ambient conditions but not under fertilized conditions. Although nutrient addition and herbivore exclusion had no significant interactive effects on gamma stability, herbivore exclusion reduced gamma stability by 11 % on average compared with that of the control under the ambient conditions. Additionally, under the ambient conditions, the effects of herbivores on spatial asynchrony and gamma stability tended to be more apparent at sites where herbivore index was higher (Fig. S5). Nutrient addition alone decreased alpha diversity and evenness, but it did not affect beta diversity. Nutrient addition increased temporal community dissimilarity by increasing temporal balanced variation and decreasing temporal abundance gradients, whereas it decreased spatial abundance gradients. Moreover, nutrient addition decreased alpha stability and marginally decreased gamma stability. Similarly, herbivore exclusion decreased alpha diversity and evenness, but it did not affect beta diversity. Herbivore exclusion increased spatial community dissimilarity by increasing spatial balanced variation, and it also marginally increased temporal balanced variation. Herbivore exclusion had no significant effects on alpha and gamma stability, but marginally reduced spatial asynchrony (Fig. 1; see Table S3 for test statistics).
The SEM clarified the direct and indirect effects of nutrient addition, herbivore exclusion, and their interaction on stability at the local and larger spatial scales (Fig. 2). Nutrient addition and herbivore exclusion alone influenced gamma stability through different pathways. Nutrient addition decreased gamma stability by decreasing alpha stability, but not spatial asynchrony. The negative effect of nutrient addition on alpha stability was mediated by decreased alpha diversity, evenness, and increased temporal community dissimilarity. Moreover, temporal community dissimilarity was the primary factor by which nutrient addition decreased alpha and gamma stability, contributing ca. 50 % of the decline in stability. In contrast, herbivore exclusion weakly decreased gamma stability by decreasing spatial asynchrony, although it also had a weak negative effect on alpha stability by decreasing alpha diversity (Fig. 2). A decrease in spatial asynchrony with herbivore exclusion was counteracted by its positive interaction with nutrient addition. Spatial asynchrony was positively correlated with beta diversity but not with spatial community dissimilarity. The effects of herbivore exclusion and the interactive effects of nutrient addition and herbivore exclusion on spatial asynchrony were not mediated by beta diversity or spatial community dissimilarity. Results were generally robust to the inclusion of environmental factors (see supplementary text and Fig. S6).
The variation in temporal community dissimilarity was mainly driven by temporal balanced variation, which was negatively correlated with alpha stability (slope and 95 % confidence intervals (CI): -0.68, CI = [-1.12, -0.24]; Fig. 3A). In contrast, temporal abundance gradients only accounted for a small portion of temporal community dissimilarity and were unrelated to alpha stability (-0.50, CI = [-1.78, 0.77]). The variation in spatial community dissimilarity was mainly driven by spatial balanced variation, which was unrelated with spatial asynchrony (-0.02, CI = [-0.24, 0.21]). In contrast, spatial abundance gradients only accounted for a small portion of spatial community dissimilarity but were negatively correlated with spatial asynchrony (-0.86, CI = [-1.71, -0.01]).