Statistical analysis
We used ANOVAs to assess the responses of biomass, production, and energy transfer efficiencies to experimental manipulations. Specifically, we used three-way ANOVAs to test the responses of biomass and production of phytoplankton and zooplankton, as well as the energy transfer efficiency between these two trophic levels (i.e.,\(E_{\text{her}}\)), to manipulations in nutrient supply, zooplankton community composition, and the presence of predators. Similarly, two-way ANOVAs were applied to test the responses of predator biomass and production, and energy transfer efficiency between zooplankton and predator (i.e.,\(E_{\text{pre}}\)) and food chain efficiency (i.e., FCE), to manipulations in nutrient supply and zooplankton community composition. We also applied two-way ANOVAs to explore how nutrient supply and zooplankton community composition influence strengths of top-down control and trophic cascades. In addition, we also explored responses of TP and TN, as well as elemental composition at each trophic level to experimental manipulations using a three-way ANOVA. For all these analyses, Tukey post hoc tests were performed for pairwise comparisons.
To further test the productivity hypothesis (hypothesis I in Fig. 1a) and energy transfer hypothesis (hypothesis II in Fig. 1b), we applied stepwise regression models with trophic cascade strength as response variable and energy transfer efficiencies (\(E_{\text{her}}\),\(E_{\text{pre}}\), and FCE), primary productivity, and their interactions as explanatory variables. We performed bidirectional model selection by iteratively adding variables to an intercept model and reducing variables from a full model, and selected models with the lowest Akaike Information Criterion (AIC) values. Similarly, we also performed stepwise regression models to test the effects of primary productivity and energy transfer efficiencies on the strength of top-down control on zooplankton biomass. Multivariate regression was performed to assess the contributions of selected variables. All the statistics were performed in R (R Core Team, 2019).